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WAVES OF SAND AND SNOW

WAVES OF SAND
AND SNOW

AND THE EDDIES WHICH MAKE THEM

BY
Doctor of Science (Manchester University), Fellow of the Royal rs i ” ae
Geographical, Geological, and Chemical Societies, v\ tt.
and of the Royal Colonial Institute ~S *

WITH 88 PHOTOGRAPHS TAKEN BY THE AUTHOR
30 DIAGRAMS AND 2 MAPS

THE OPEN COURT PUBLISHING COMPANY
378-388 WABASH AVENUE
CHICAGO

(All rights reserved)

TO
THE MEMORY OF MY MOTHER,
ANNE CHARLOTTE CORNISH,
WHO TAUGHT ME AS A BOY
TO OBSERVE AND REVERENCE
THE CREATION,

I DEDICATE THIS BOOK

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PREFACE

IN 1895 I went to live on the South Coast, and
every day the waves of the sea—beautiful,
mysterious, and insistent—drew me more and more
to the path on the cliff whence I could watch them
curl and break, and listen to their splash upon the
sandy shore. I stood there on the afternoon of
a calm day in early autumn at the time of low
water of a spring tide. The little waves, gliding
slowly in over the flat sands, bent round the ends
of a shoal, as waves of light are refracted, and,
meeting, passed through each other, each to con-
tinue its own course. Elsewhere a long, low wave,
impinging obliquely on a small bank of sand, was
thrown backwards at an angle of reflection equal
to that at which it had struck the obstacle. And
as I watched I thought what a fine thing it would
be if the study of all kinds of waves could be co-
ordinated. I had just finished another piece of
work, so I embarked at once on a course of reading
on waves of all kinds, which was, moreover, not
altogether new ground to me. I found that the

ideas which Newton and his successors have so
9

10 PREFACE

marvellously developed in the theory of waves
originated in the common knowledge of the “ un-

’

dulating inequalities,’ as Dr. Johnson calls them,
which wind makes upon the sea. Periodicity, and
the transmission of an impulse by the material, are
the aspects of sea waves which are repeated in
the transit of light and sound, and owing to these
analogies we speak of “ waves” of light and sound,
although a corrugated surface of progressive in-
equalities is no part of their character.

I found, however, that while the physicists had
applied with great success the ideas got from the
aspect of the heaving sea to the study of sound,
light, electricity, and other matters, geographers and
geologists had not sufficiently availed themselves
of these ideas in the study of certain natural in-
equalities which, from their form and movement,
are as nearly related to sea waves in one way as
the pulsations of sound are in another. I also
found that the mathematical study of the waves of
the sea had been pushed nearly as far as the avail-
able data allowed, so that further progress in their
study could best be secured by observations accom-
panied by measurement, which I was capable of
undertaking.

Thus having surveyed the whole subject of
waves, I decided to confine myself for the pur-

ge

PREFACE 11

pose of original research to the study of the surface
waves of the atmosphere, hydrosphere, and litho-
sphere, or air, water, and earth, calling the subject
‘“kumatology,’ and classing it as a department
of physical geography. This is the practical form
of the idea which has led me by an untrodden path
to the Land of the Unknown. In this country
there are no sign-posts to direct the traveller, no
roads for him to follow, no maps to show him how
to shape his course. ‘Here watchfulness, patience,
and docility to experience are the only passports.
But it is a delightful land, and its call is like “ the
call of the wild.”

At first my home on the South Coast was a
favourable position for observations both of waves
of water and of sand, but presently travel became
necessary in order to develop the subject. The
home was given up, and I wandered abroad among
sandhills and snowdrifts, explored amphibiously the
sandbanks of estuaries, measured waves in storms
at sea, timed the throbbing surge of torrents, the
heaving of whirlpools, and the drumming thunder
of waterfalls. I was by good fortune in Kingston,
Jamaica, when the earthquake of January, 1907,
wrecked the city, and I mapped the seismic waves
which traversed the island. Later, I studied on
the spot those curious gravitation waves in vol-

12 PREFACE

canic rock which so greatly hamper work on the
Panama Canal by bulging up the bottom of the
Culebra Cut, and I am now pursuing the study
of this kind of wave.

My observations have been communicated from
time to time to the Royal Geographical Society, the
British Association, and the Royal Society of Arts,
and will be found in their Journals and Proceed-
ings from 1896 to 1913.1. My observations of
water waves, up to 1909, have also been published
in book form,? and the present volume contains
those on waves of sand and snow.

That waves, progressive transverse inequalities,
should be produced by wind in sand and snow is
a strange thing, which ought to excite our sur-
prise, for the familiar action of wind upon loose
bodies is of the opposite kind. First, it blows them
from salient to sheltered positions, thus tending to
obliterate transverse inequalities ; secondly, it finds
out weak places in materials which it is capable
of eroding, gouging out grooves, which it lengthens
until it has driven through a longitudinal furrow.
Thus the more familiar action of wind is to

* See Appendix, catalogue of original papers by the author.
2 “(Waves of the Sea and other Water Waves.” By Vaughan
Cornish. Published by Fisher Unwin, Igto.

PREFACE 13

obliterate the transverse, and create longitudinal,
inequalities.

Yet the smooth surface of the dry sand of the
desert and of the dry snow of the prairie is ruffled
transversely by the wind, and the transverse in-
equalities grow in size and become more nearly
regular in length and height, travelling, moreover,
in orderly procession before the wind, as passive
waves. Currents of water produce similar pro-
gressive waves on the surface of sandbanks. The
means by which these waves of sand and snow
originate, grow, and move are peculiar and interest-
ing. What I have been able to add to previous
knowledge of waves in sand and snow and the
eddies which make them is told in the following
chapters, where I have also recorded certain inci-
dental investigations on rippled clouds, on
mushrooms,” on the undulations produced by

‘6

‘ snow-

sledges, on quicksands, miniature deltas, and other
matters.

I have to thank Dr. J. Scott Keltie, Secretary
of the Royal Geographical Society, for permission
to reproduce some of the plates and figures from
my papers in the Geographical Journal.

hee Oe
WOODVILLE, CAMBERLEY.

September, 1913.

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CONTENTS

PART I

AEOLIAN SAND-WAVES

CHAPTER I

PAGE
DESERT SAND-DUNES . : : 5 : - 31

Sand-waves near Helwan, their height and length—
Formation of peaks on the ridges—Course of the wind
as it blows over a series of the ridges, direct current
and eddy—Note on the wind-screen of motor vehicles
and the return current—Height of wave limited by
velocity of wind—Significance of constant ratio of
length to height—The eddy-curve ichthyomorphic, with
blunt head and fine tail—Longitudinal bank to leeward
of a peak—On the formation of the pits called fuljes—
Travelling mounds of sand of crescentic shape, called
barchans—Rate of advance of the sand-waves—Mode
by which the undulations originate in a level deposit
of sand—On a limit to the size of level ridges due to
fineness of the sand—Large dunes east of the Suez
Canal—Illusion of mountainous size—Formation of
dew upon the sands—Dunes west of Suez Canal; in-
fluence of moist ground on their formation—Effect of
electrification upon the mobility of sand—On the sizes

of the sand-grains.
15

16 CONTENTS

CHAPTER II
PAGE
AEOLIAN SAND-RIPPLES

All aeolian sand-waves have a rippled surface— 75
Description of the formation of aeolian sand-ripples
in level deposits of loose sand blown from the beach—
Measurements of height and length—The ripples grow
without change of shape—Ratio of length to height
the same as in the larger sand-waves—Rate of advance
—Winnowing of fine from coarse sand-grains observed
during growth of aeolian ripples—‘ Erosion ripples”
formed where the level of the sand is being lowered—
The formation of a protecting cover of “lag gravel”
on the crests—Experiments by means of an artificial
blast—No rippling of assorted sand-grains of uniform
large size, although travelling freely — Immediate
rippling when small sand-grains mixed with them—
Explanation offered, that eddy in lee of larger grains
tosses away the smaller, hence the existence of ripples
upon the larger waves—Ripples in shell-sand showing
lines of notches in the wave-fronts where the troughs
are deeper.

PART II
SNOW-WAVES AND SNOWDRIFTS

CHAPTER III
SNOW-WAVES AND SNOW-RIPPLES : : -) igs
Ripples in Moist Snow.

Damp snow and dry snow—Ripples in moist snow
during snowfall observed in Hyde Park—They face up-

CONTENTS

wind—Recede by erosion of wind-facing cliff—During
lulls travel up-wind—Mode of erosion of partially con-
solidated snow : first, transverse ; finally, longitudinal
ridges, with a transition stage between—Stratification
shown by erosion.

Waves in Dry Drifting Snow.

Formed near Montreal at minus 8° Fahrenheit—Length
and height— Flatter than sand-waves— Movement
visible and more rapid than that of sand—Surface un-
rippled—Measurements of snow-waves in Manitoba,
formed during removal of snow—Waves formed during
snowfall—Their formation upon a plane surface free
from obstructions.

Crescentic Snow-Waves or Snow-Barchans.
Formed in patches of loose snow travelling on a hard
surface—Finer lines than sand-barchans both in profile
and plan—Formation of crust on surface of snow and
its effect in arresting growth and movement of snow-
waves—Explained as due to sublimation—Increase in
density of snow which has been drifted by wind—
Compared with increase of density due to pressure.

Ripples in Snow-Sand.
Mode of formation of granular snow or “ snow-sand”
—Rate of movement—Growth and movement more
rapid than those of sand-ripples—Measurements of
length and height—Obliteration in lee of larger ridge.

Forms produced by Wind-erosion in Compact Snow (Studies
in Canada.)
Measurements of transverse ridges, facing up-wind—
Shape of pits—Longitudinal structures—Note on the
longitudinal sand-dunes of the great Indian Desert,

18

CONTENTS

The Eddy-form of Snow-Waves and Snowdrifts.

Complex forms of drifts produced by fixed obstacles—
All contained by a boundary curve having blunt head
and fine tail—This is the boundary of the eddy caused
by the obstruction—Complex forms are stages of
filling in of eddy-space, and due to insufficient supply
of snow—The eddy-curve and its relation to the forms
of fish and cetaceans—of the wings of birds—of the
submerged part of ships—of torpedoes and non-rigid
airships—Forms of holes scoured out in snow round
the trunks of trees—Relation of snow-barchans to
the eddy-curve—The relation of form and movement
between the travelling crescentic snowdrifts and the
swirl made in water by an oar—Shape of the eddy in
snow-waves—Inference as to the distance to which
hedges and belts of trees extend shelter from wind.

On the Three Modes of Deposition of Drifted Material

depending upon Rate of Subsidence.

Behaviour of gravel, sand, and dust before the wind—
Of shingle, sand, and mud under the action of waves
and currents—Single tail of sand behind a narrow
obstacle—Double tail of snow-powder—Single train
of black smoke, but double track of steam, from
chimneys—How fallen leaves drift before the wind—
On “banner clouds” and on sandbanks to leeward of
promontories—On the action of an obliquely crossing
wind upon the swell of the sea.

CONTENTS 19

CHAPTER IV
PAGE
SNOW-MUSHROOMS AND CAHOTS ° . C . 211

Snow-Mushrooms.

Weather and snowfall in the Selkirk mountains, B.C.
—Snowcaps on high stumps of felled tree sat Glacier
House resemble large mushrooms—Diameter, 9 feet
—Weight about 1 ton—Shape due to bending under
its own weight—Mode of growth—Reason of their per-
manence.

On the Sparseness of the Falling Snowflakes.

Cahots, French name for undulations made by sledges
in snow—Formed on the ice of the St. Lawrence—In
the streets of Montreal—None in Manitoba during
midwinter—Similar undulations on an ordinary rough
road at Coniston, Lancashire, produced by a sledge.
Experiments with a small model sledge—The undula-
tions are produced without an initial inequality—And
during slow and steady motion—They are due to a
loose but adhesive condition of the road—Other
examples of transverse inequalities of roads.

PART III
SUB-AQUEOUS SAND-WAVES

CHAPTER V
RIPPLE-MARK AND CURRENT-MARK . : . W257
Ripple-mark.

Sir G. H. Darwin’s experimental reproduction of ripple-
marks—My measurements of natural ripple-mark—
Osborne Reynolds’ experiments.

2

20 CONTENTS

Current-mark.
PAGE

In very slow streams with a smooth surface—Effect of
making the course of the stream straight—Action of
current upon a body projecting above the bed of the
stream—Current-mark in shallow streams with a waved
surface and a velocity of 1°5 feet per second—Moving
down-stream—The same in a stream with a velocity of
2:2 feet per second move up-stream—Dr. Owens’
experiments on the diminished rate of settlement of
sand in sandy water—Explanation of the up-stream
movement of the current-mark or sand-ripples in a
shallow stream with a rapid motion—Effect of pro-
gressive water-waves upon the current-mark of streams
—Ratio of length to height of current-mark compared
with that of ripple-mark.

CHAPTER VI

SAND-WAVES IN TIDAL CURRENTS . a . - 291

The Mawdach Estuary, Barmouth, N. Wales, its drying
sandbanks and their waved surface—Measurements of
length and height—D shape of estuaries—Influence on
course of tidal currents and effect in producing un-
symmetrical sand-waves upon the drying sandbanks—
Measurements showing how far these sand-waves de-
part from uniformity—Ratio of length to height—Sand-
waves in the estuaries of the Findhorn and South Esk
—The estuary of the Severn: smooth sandbanks at
Severn Bridge, waved sandbank near Severn Tunnel,
explanation of the difference—Sand-waves in estuary
of the Dovey, North Wales—Stakes fixed in sandbank
and measurements of size and movement of sand-waves
during seventeen days—Effect of velocity of current

CONTENTS 91

PAGE
and depth of water upon the sand-waves—Sand-waves

upon the North Goodwin Sand—Pools left after partial
obliteration of sand-waves, similarity of their form to

that of the pits called fuljes which occur in sandy
deserts.

Sand-reefs in the Mississippi.

Their size and movement—Not true transverse waves
—Their formation in freshly deposited sediment—How
the size of the sand-grains limits the size of the sand-
wave—Suggested effect of greater heterogeneity of
material to increase the limiting size of the sand-wave
—On the relation of velocity of current to size of sand-
wave in water of sufficient depth.

CHAPTER VII

ON THE SMALLEST DELTA, ON THE COMPOSITION OF QUICK-
SAND, AND ON ‘MACKEREL SKY” : 3 40

On the Transverse and Longitudinal Ridges formed in the
Flow of Watery Sand, and on the Smallest Delta.

Settlement of sand through water and subsidence of
water through sand—Transverse and longitudinal ridges
formed during the latter process—Rapid deposition of
the small longitudinal ridges in radiating branches—

Their diameter equal to that of a fully-grown drop of
water.

On the Composition of Quicksand.

Observations of Mr. C. Carus-Wilson on presence of
marsh gas—Experiments of Mr. C. E. S. Phillips on
effect of included gas—Author’s observations on effect

22, CONTENTS

of imprisoned air—On the effect of some finer earthy
particles to prevent the escape of air from sand—The
three kinds of fluid, gaseous, liquid, and granular, and
suggestion that an emulsion of all three produces a
quicksand.

On the Rippled Clouds called ‘‘ Mackerel Sky.”

Ruskin’s remark— Mathematical investigations by
Helmholtz and others—Sir G. H. Darwin’s description
—The author’s observations—Shape of the clouds—
Their wave-length—Description of author’s photo-
graphs—The positive and negative compared—The
former shows the white clouds, the latter the blue sky
—It is the latter which has the form of ripple-mark in
sand—The clouds correspond, not to ripple-mark but
to the eddies of water which make the ripple-mark.

APPENDIX : : : : : . 1372

INDEX . ; : : : ; : 370

Plate

Io.

rT.

12.

ILLUSTRATIONS

PLATES.
Tidal sand-waves in the estuary of the River Dovey . Frontispiece
Page
Aeolian sand-waves near Helwan ‘ : : ay eS3
Aeolian sand-waves with undulating crests (¢op) é)' Ag
Transverse ridges with longitudinal projections (bottom) as
The pits termed fuljes (top) : : Bay by,
The hillocks termed barchans (bottom) . : 2 ae |
Accumulation of blown sand caused by a fence of reeds
near Helwan (top) . il
Accumulation of blown sand caused by marram grass at
Aberdovey (bottom) - : : : He ests
Sand-dune with crest reversed by wind (top) . 59

On the slope of a sand-dune having water at its foot (bottom) 59

Pyramidal summit of sand-dune at Ismailia (sand on lee side
in act of slipping) . é ‘ : : aero

Sand-dune encroaching on a plantation at Ismailia (top) an! G7,
On the top of an encroaching sand-dune at Ismailia (bottom) 67

Sand grains from the cliff of a sand-dune at Ismailia

(magnified) . : : : : : Ae ay
Aeolian sand-ripples at Southbourne (¢op) 77
Aeolian sand-ripples at Southbourne, in which the sorting of

grains is indicated (bottom) , ‘ : ari,
Aeolian sand-ripples at Southbourne, in which the sand

grains have been much sorted (top) F 85
Aeolian sand-ripples at Ismailia, to ieeeatd of a sand- dune

where there is an upward current of air (bottom) . 85

Drifting waves of dry snow near Montreal ae aaa
minus 8° Fahrenheit) ‘ : ; 09
23

24

Plate
No.

tee
14.
15.
16.

r7.
18,

19.
20.

21.

22.
23.
24.

25.
26.

27.

28.

29.

30.

Rie

32.
33-

34-

ILLUSTRATIONS

Drifting waves of dry snow near Winnipeg

Drifting waves of dry snow at Winnipeg

Ripples in granular snow

Ripples in coarse granular snow

Granular snow rippled, and a drift of fresh snow unrippled .

Ripple-like ledges formed by oe snow- pane aries
on the lee face of a drift

Erosion-ripples in the surface layers of snow .
Erosion-ripples in compact snow, showing its stratification .

Erosion structures intermediate between the transverse and
longitudinal, showing the stratification of the snow

Longitudinal structures formed by erosion of snow
Longitudinal ridges of snow to leeward of obstructions

Beginnings of a snowdrift on the lee side of aie near
Montreal ‘ :

Snowdrift near Grantown-on-Spey, showing curve of the
upward current of the wind-eddy on the lee side

Snowdrift near AnaIPES epoMte overhanging cornice on
lee side ; : :

Snowdrift near Winnipeg, with small longitudinal ridge on
lee side formed between the currents which converge
from right and left, taken looking up-wind

The snowdrift with small Rea eh ridge on lee side,
transverse view ‘ . :

Snowdrift near Winnipeg, with large se eat tai structure
on the lee side , : é

Bank of snow collected between currents converging on
lee side of house (whilst the snow was drifting it
ascended like smoke from the pointed summit)

Snowdrift round a house on the Be sais a space
swept bare by the wind . : :

Hollow kept clear of snow by the wind round an outhouse .

Bank of drifted snow against the lee side of a house at
Winnipeg s

Space near a tree kept free from snow by the wind

Plate

49.

50.

SI.

52.

53:

54:

55:

ILLUSTRATIONS

Bosses of snow, Glacier House, B.C.
Bosses of snow in a valley of the Selkirk Range, B.C.
Bosses of snow formed on stumps of trees, Glacier House, B.C.

“ Snow-mushrooms,” or caps of snow formed on tree stumps,
Glacier House, B.C. M4 :

A “button-mushroom ” in snow

The “prize-mushroom” of Glacier House, a symmetrical
snow-cap nine feet in diameter . ; : :

A nine-foot snow-mushroom seen from below
Twelve-foot snow-cap on a broken tree at Glacier House
Twelve-foot snow-cap seen from below

Snow-cap formed upon the cross-piece of a errs ais
and upon the wires : :

Snow-cap upon a telegraph pole and wires

“Cahots”’ (i.e, “ jolts”), the undulations made by sledges in
snow, Montreal é : ; :

“Cahots,” the undulations made in a road by the sledges
which descend from the Saddlestone Quarry, Coniston,
Lancs : F : ; ;

The sledge, used as a drag, which makes the “cahots” at
Coniston :

Cart and sledge descending steep track, and wheeled truck
used to transport the sledge over flatter portions of the

road .

Undulations made by a model sledge drawn slowly and
steadily through slightly moist sand : :

Transverse furrows produced by the tread of cattle on their
way to and from a pond .

Transverse furrows produced by the tread of cattle .

Symmetrical ripple-mark produced by waves of the sea at
Montrose (top) ,
Unsymmetrical ripple-mark produced ‘by waves of the sea
(bottom)
Ripple-mark at Grange, Lancs, in sand of a somewhat
tenacious kind

Ripple-mark in quaking sand at lea Lancs

207

Plate

73:

ILLUSTRATIONS

Sand rippled by two sets of waves, which were proba)
simultaneous ; at Grange, Lancs .

Sub-aqueous sand-waves moving up-stream and carrying
with them their superposed water waves; at Cannes .

Current-mark made during rain by a temporary stream ona
sandy road, photographed after the road had dried

Current-mark on the sands of the Dovey estuary, with larger
sand-waves which have been flattened as the tidal water
ran off

Tidal sand-waves, winding channels of ebbing tide, and
shining mud patches in places, where horizontal eddy-
ing probably occurs. Mawdach estuary -

Tidal sand-waves in the estuary of the South Esk, Montrose

The river Severn between Beachley Point and Severn Tunnel,
showing the Dun Sands 3

Two sets of tidal sand-waves caused by successive currents
in different directions, on the Dun Sands, river Severn.

Tidal sand-waves and current-mark ; Dun Sands, river Severn
Map of the estuary of the river Dovey

Tidal sand-waves of which the daily movement was measured ;
Dovey estuary (top) :
Tidal sand-waves with current-mark in troughs ; Dovey
estuary (bottom) : :

Tidal sand-waves and low-water channels ; Dovey zee
Winding channels of the ebbing tide ; Dovey estuary

Tidal sand-waves, at right angles to the sea shore, in a “low,”
or depression ; at “Mundesley (top) :

Tidal sand-waves iu obliterated on the sea shore ; at
Mundesley (bottom) :

Tidal sand-waves on the North Goodwin

Pools formed in the trough of a tidal sand-wave by the
washing-off of crests during ebb-tide ; at Montrose

A fan-shaped deposit of sand, showing a stream of water
which soaks into the porous material ; at the foot of the
East cliff, Bournemouth : :

Tongues of sand, each of which is instantaneously formed
by the sudden subsidence of the water by which the
sand grains were carried ; at Bournemouth

Page

271

275

283

287

293

297
301
304
307
311
314

314
317
320

327

327
ed

333

341

344

Plate
No.

74:

75:

76.
77:
78.

79:

80.

Fig.

a Sa pany a

10.

ILLUSTRATIONS

Deposit of cliff-sand, containing an admixture of fine par-
ticles, left after subsidence of water, showing transverse
ridges ; at Bournemouth : :

Deposit of cliff-sand, containing an admixture of fine par-
ticles, showing transverse ridges formed by subsidence
of water ; at Bournemouth :

Deposit of muddy sand carried down the cliff by sisi
showing no transverse ridges ; at Bournemouth

Rippled cirrus cloud, seen from Branksome Chine, near
Bournemouth

A “mackerel sky,” seen from Branksome Chine, near Bourne-
mouth, August 5, 1900, looking west

Wave-clouds, or “mackerel sky,” seen from Branksome
Chine, near Bournemouth, August 5, 1900, looking
south : : : :

Negative of the eae of wave-clouds, in which the
blue sky appears light and the clouds dark, showing
that it is the blue sky and not the cloud which more
closely resembles the ripple-mark of sand

FIGURES IN THE TEXT.
Sir G. H. Darwin’s diagram of currents ne over ripple-
mark : é ‘ : : A
Profile of sand-dune with crest reversed by contrary wind .

Sand-dune with undulating crest, Shewine development of
peaks and saddles . : *

Profile of twenty-nine snow-waves near Winnipeg

Profile of twenty-four aeolian sand-waves, near Helwan,
Egypt : Z :

Barchans of snow and sand, from photographs
A patch of rippled snow, plan .

Conversion of above to a barchan, early stage
The same at a later stage

Erosion waves in compact snow, with grooves showing
stratification, wind from the right hand ‘

27

Page

347

35°
353

357

361

365

368

39
62

65
107

109
114
129

129
130

134

28
Fig.
No.
iii ts
12.
13.
14.
15.
16.

7.
18.
19.

20.

21.

22.
23.
24.
25.

26.

ay
28.

29.
30.

ILLUSTRATIONS

Erosion form analogous to a barchan, wind from the left,
from a photograph :

Fence and completed snowdrift
Stages of growth of snowdrift formed by a fence

Snowdrift on both sides of a fence, on the right completed,
on the left incomplete, from a photograph .

The fundamental curve of snowdrifts .

Plan of snowdrift caused by clump of bushes, wind from the
left ; : : : : :

Profile (dotted) and central longitudinal section of the same
drift . , ° ; : 5

Section across the dotted line of Fig. 16

Plan of the principal snowdrift around a house on the prairie,
near Winnipeg, wind from the left : ‘

Profile and central longitudinal section of same snowdrift

Transverse section of snowdrift on lee side of an outhouse
on the prairie

Plan of hollow round a tree, wind from the left
Longitudinal section of the same
Cross section of the same, lee side

Hollow, etc., cut by wind, from left, around a stone, from a
photograph taken in Scotland, February, 1goo

Hollow cut by wind, from left, around a heap of manure on
a field, from a photograph . : :

Longitudinal growth on lee side of a travelling snowdrift
Snow mushroom with hollow beneath, from a photograph
Current-mark on road after a thunderstorm

Plan of five ridges showing positions on four succeeding
days, Dovey estuary, scale 1”=16’. 3 3

321

PART I

AEOLIAN SAND-WAVES

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CHAPTER? ,\1
DESERT SAND-DUNES

Sand-waves near Helwan, their height and length—Formation
of peaks on the ridges—Course of the wind as it blows
over a series of the ridges, direct current and eddy—
Note on the wind-screen of motor vehicles and the return
current—Height of wave limited by velocity of wind—
Significance of constant ratio of length to height—The
eddy-curve ichthyomorphic, with blunt head and fine tail—
Longitudinal bank to leeward of a peak—On the forma-
tion of the pits called fuljes—Travelling mounds of sand
of crescentic shape, called barchans—Rate of advance of
the sand-waves—Mode by which the undulations originate
in a level deposit of sand—On a limit to the size of level
ridges due to fineness of the sand—Large dunes east of
the Suez Canal—lIllusion of mountainous size—Formation
of dew upon the sands—Dunes west of Suez Canal ;
influence of moist ground on their formation—Effect of
electrification upon the mobility of sand—On the sizes of
the sand-grains.

ON May 7, 1899, when staying at Helwan, near
Cairo, I crossed the Nile one morning in order

to see the desert on the west bank near the
31

32 WAVES OF SAND AND SNOW

pyramids of Sakhara. I had to land upon an
extensive stretch of loose sand uncovered by the
subsidence of the river, which was then at a
low stage. The river-borne sand is very different
from the somewhat coarse, rounded, quartz sand
of the desert, being composed of minute
particles of many different minerals, including
flakes of light-coloured mica and _ splinters of
dark-coloured minerals derived from eruptive
rocks. Many of the splinters stuck in a wire
sieve with a mesh of ;},-inch diameter, but many
slipped through a mesh of sq of an inch. The
sand that lay even a little above the present level

of the river was thoroughly dried by the action
of the sun and of the desiccating desert wind.
A brisk wind was blowing of about the force ,which
sailors describe as a “‘ moderate breeze,” which has
a velocity of 15 miles an hour. The light sand
drifted freely before it, not only close to the
surface but also in considerable quantity for a
height of several feet above. The appearance of
the sand-bank was very remarkable, for the
surface was in regular ridges and furrows, or
waves, transverse to the wind. They were on an
average 1 foot 8 inches in height with a wave-
length ‘from: crest to crest of 30 feet oy mehes
They were desk-shaped, having a long slope on

‘UeMIDH JeoU

SOAVM-pUvS ULIJOOWY—'Z ALVIG

33

DESERT SAND-DUNES 35

the weather side, whilst the lee side consisted of a
‘straight cliff standing at the maximum angle
allowed by the looseness of the material—that is
to say, about 332° The rise is 1 vertically in
14 horizontally. The angle of the weather slope
is 33°, the rise being 1 vertically in 163 horizon-
tally, the length of the mound being thus eighteen
times as great as the height. The weather side
was covered with minute waves or ripples of a
few inches from crest to crest, with which I shall
deal in the next chapter. The slipping lee face
was unrippled. A _ photograph taken looking
towards the Nile (Plate I1) shows a remarkably
regular series of aeolian sand-waves. When look-
ing up wind the series of waves stands out boldly
owing to the marked difference in the light reflected
from the steep lee slopes and from the adjacent
upper part of the weather slopes, which is nearly
horizontal. Looking down wind the steep lee slope
is out of sight, and there is so little contrast between
the weather slopes of succeeding waves that it is
not easy to realize how much the surface undu-
lates. I paid a second visit to the sandbank in
the afternoon, when the wind had increased in force
to about the strength of a “fresh breeze,” which
has a velocity of 21 miles an hour. The ridges
or waves were higher than in the morning—that

36 WAVES OF SAND AND SNOW

is to say, their “ amplitude ” or height from trough
to crest was greater. The actual level of the
troughs had been lowered, as was evident from
the fact that a relatively hard floor of a compact
material was exposed, whereas in the morning there
was some depth of loose sand even in the troughs.
Whether the absolute level of the crests had been
raised or whether the increased amplitude was
accompanied by a lowering of. the crests less than
the lowering of the troughs I did not ascertain.
The average level of the surface was certainly
lower, for the sandbank was obviously being
depleted by the wind. The quantity of sand now
flying in permanent suspension was great, and it
formed a thick haze 20 or 30 feet high. It was
necessary to protect the eyes, nose, and ears from
the penetrating particles, and even then prolonged
observations were attended by considerable discom-
fort. Wandering over the sandbank, I found that
in some parts the crest of each ridge varied
considerably in height, presenting a series of peaks
and saddles. In order to determine the relation
of height to length in the waves I measured next
day, May 8th, a continuous series of 24. The
first ridge was 40 yards from the Nile, and
the measurements were taken proceeding down
wind and away from the Nile to the end of the

DESERT SAND-DUNES

37

tract of loose sand, the twenty-fourth wave being
succeeded by hard ground. The size of the waves

was as follows :—

33
52
36
54
30
25
22
21

35
27
40
29
19
35
30
18
30
29
30
15
16

Length of Wave.
ft.

ft.
ft.
ft.

nvG) 103
/O an.
EG ith:

Om.

ft.
34% ft.
37% ft.
314 ft.

Height of Wave.

2/5
2 ft:
Be it
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q ft:
2) £:

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Pa.
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aft:
Tr ft
Bits

11% in.
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8 in.
6% in.
2) ink
2% in.
6 in,

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_
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B 5

Thus the average length of the waves was 30 feet
6 inches and the average height 1 foot 8 inches.
The ratio of length to height obtained by

3

38 WAVES OF SAND AND SNOW

dividing the sum of all the lengths by the sum
of all the heights is 18°4.

It was a matter of great interest to ascertain
if this were a constant ratio—i.e., if the average
steepness of the waves were always the same, or
if it were, on the other hand, dependent upon
circumstances. Passing over for the present other
observations made on 7th and 8th, I therefore
record here the measurement of a series of waves
made on the roth (near the series measured on the
8th), proceeding down wind as before. The total
length of the series of twenty-three waves was
656 feet, the average wave-length being there-
fore 28 feet 6 inches. The individual wave-lengths
were not measured, but the height of each wave
was taken, the average being 1 foot 8°5 inches.
The ratio of length to height was therefore 16°7,
which only differs by about Io per cent. from the
ratio obtained two days before. The significance
of this result was much increased by the circum-
stance that I already found the profile of the little
ripples made by wind in the surface layers of
loose sand upon the Dorsetshire coasts to have
this shape, the ratio of length to height being
1855.1 In any group of these ripples the indi-

« “On the Formation of Sand Dunes,” by Vaughan Cornish,
Geographical Fournal, March, 1897.

DESERT SAND-DUNES 39

viduals are very uniform in size and the crests
are quite level. It is very remarkable that in
the Helwan waves there should be the same
average steepness, although the ratio of height to
length in individuals varied from 8-9 to 60.

The course of the wind as it blows over a series
of sand-waves in regular ridges, such as those in
one of the photographs, can be made out fairly
well by ordinary observation. It is, however,
much more difficult to observe in the case of the

eee
cant alt Ss mo cl A il Mi Ss

\ |
Hitt

aeolian sand-ripples, which had been my first study,
and I had obtained my first clear notion of the
process from the accompanying figure, by which
the late Sir G. H. Darwin illustrated the motion
in a current of water made to flow over a series
of very small sand-ridges.t These lines of current
and eddy he had actually seen by means of a
special ink introduced into the water which
rendered its flow visible (Fig. 1). I give the

* “Qn Ripple Mark,” by G. H. Darwin, Proc. Roy Soc.,
1883-4.

40 WAVES OF SAND AND SNOW

figure, but amplify the information it contains
from my own observations of the action of wind
on waves in sand and snow. On the lee side of
each cliff an eddy or vortex is active, a body of
air which whirls vertically round a horizontal axis.
At the crest the surface currents converge. Both
currents are loaded with sand, which deposits on
the lee side of the crest. At a position on thie
long, gently sloping weather side of the next wave
the surface currents are, on the contrary, divergent,
that at the tail end of the elongated vortex drawing
sand back! from the nodal position, whilst the

t Since I began the study of sand-waves and the eddies
which make them the use of motor vehicles has made familiar
to most of us the upward deflection of wind by an obstacle,
and the consequent return draught on a lower level. On
the front seat of the motor omnibuses now running in London
one can look over the top of the wind-screen without feeling
the wind in the eyes, the direct current of air being thrown
slightly upwards, as can be proved by raising the hand a few
inches above the head, where the wind is felt. If the hand be
held close to the floor a return draught can be felt, and this
brings the dust and dirt which accumulates at the foot of the
wind-screen. This effect is the same as that which occurs
when the wind blows outwards from the area of sand-dunes
over the neighbouring stony plain. Those sand-grains which
drop near the dunes are swept back by the return draught
which blows along the ground, and are deposited against the
cliff of the dune, the neighbouring part of the stony plain being
thus kept clear of sand. When a taxi-cab is opened by letting

DESERT SAND-DUNES 41

direct wind, descending just above the node, drives
the sand of all the upper part of the ridges
forwards. Thus the upper part of each ridge is
continually being scoured away and the eddy space
to leeward is continually being filled up. By this
process the position of each ridge continually
advances to leeward, the core of eddying air
being thus pushed forward, the progression of each
successive core of eddying air permitting likewise
the motion of the passive sand-waves.

A sand-grain of any given size and weight has
its own rate of subsidence through air. To raise
it needs an upward current of shghtly greater
velocity. The scouring out of the troughs and the
increase in amplitude of the waves depends upon
the eddy being sufficiently strong. When the
wind is strong and the ridges small their growth
proceeds, the eddy gaining in strength as the ridge
grows. But if, after the ridge has reached .its
maximum, the wind abates, the troughs begin to
silt up again, as I observed one day on the Helwan
sandbank.

down the back part an inconvenience is caused by the fact
that the front of the cab has not been designed as a wind-
screen and is too high for the purpose, so that the return
current of air, instead of striking the back of the vehicle,
cuts in over it, blowing on the back of the passenger’s head
and neck.

42 WAVES OF SAND AND SNOW

The constant ratio of length to height in the
sand-waves shows that the air-eddy maintains the
same shape whether the ridges be large or small
and whether the wind be light or strong. The
characteristic shape of an eddy is ichthyomorphic—
i.e., fish-shaped, with blunt head and fine tail.
Numerous examples of this will appear in the
course of this record. The sand ridges have fine
lines aft and a blunt fore part—i.e., have a desk
shape, and advance as if the desk were being
pushed forward. But they are passive waves.
They are moulded upon, and move by virtue of,
the eddies of air, and each of these has a blunt
head and a fine tail. The eddies, however, are
annulled when the wind ceases, whereas the sand-
ridges remain, passive but permanent.

So much of explanation for the present of the
growth and movement of ‘aeolian sand-waves
already formed in transverse ridges. The explana-
tion of the process by which these waves originate
from a level surface of loose sand must be
reserved until later.

On some parts of the Helwan sandbank the
waves, although in ridges of great lateral exten-
sion, had unlevel crests, each ridge consisting of
a series of peaks separated by saddles. The wind
sweeps through these depressions with increased

cS ein:

Pte a

eS

ea aaa

EEE OWE OL eee:

SE ar he poem s

PLATE 1,—Tidal sand-waves in the estuary of the river Dovey.

PLATE 3.—Acolian sand-waves with undulating crests.

PLATE 3.—Transverse ridges with longitudinal projections.
43

DESERT SAND-DUNES 45

pushing force and, swinging round from either
side in a right-handed and left-handed spiral, curls
upwards on the lee of the central peak. Thus in
addition to the eddy with horizontal axis formed
on the lee of a long ridge there is here an eddy,
or a pair of eddies, with inclined or vertical axis
on the lee of a peak. Sometimes the effect of
these eddies is to build up against the lee side
of the peak a mound or bank tapering to lee-
ward, with its axis parallel to the wind. This is
deposited where the spiral whirls, coming in from
either side and each heavily loaded with sand, meet
and ascend.

In other places on the sandbanks I found a
series of waves of no great lateral extension, each
ridge being a single broad mound tapering from
the centre until it merged at either end in the
general level of a plain of loose sand. From the
highest and central part of each ridge there pro-
jected at right angles a tongue of sand tapering
to leeward until it merged in the general level of
the plain. This tongue of sand had an absolutely
sharp ridge, and was concave on either side, being
apparently modelled by whirls of air.

There was, however, yet a third variety of the
action of secondary eddies on the lee side of peaks,
for there were places where depletion instead of

46 WAVES OF SAND AND SNOW

accumulation had occurred. This case is illus-
trated in Plate IV. On the lee side of the
peak the loose sand had been entirely removed,
the converging spirals of air having cut down to
the solid substratum, whereas the saddles of suc-
ceeding ridges were still connected by a bed of
loose sand. I did not ascertain at the time the
precise variation of condition which produced this
changed function of the eddies on the side of
peaks. I can, however, give an explanation which
is based upon subsequent observations. ‘Wind
blowing over loose sand is sometimes overcharged,
and drops more than it picks up. It then silts.
Sometimes the amount which it is picking up is
equal to that which it is dropping, and it then
neither silts nor scours. Thirdly, it is sometimes
picking up more than it drops, and then it scours.
In the first condition, and perhaps in the second,
a mound of sand would be deposited where the
two whirls of air coming from the right and left
meet under the peak. In the last case erosion
occurs. The result is, as is partly shown in the
photograph, to sweep bare a more or less oval
space between two succeeding peaks, whilst the
space on either side between the succeeding saddles
remains covered with loose sand. On one part
of the sandbank the general appearance was that

PLATE 4.—The pits termed fuljes.

PLATE 4.—The hillocks termed barchans.
47

DESERT SAND-DUNES 49

of an elevated, undulating plain pitted with hollows.
The profile of each pit in the direction of the wind
was the same as that of the regular waves, except
that some of the lower parts of the sand-wave
were wanting, all the sand being removed, leaving
a floor of hard material. The floor of the pit was
in some cases oval in shape; in others loose sand
lay within the oval on the lee side, making the
floor crescentic in form, recalling the shape of a
horse’s footprint. There remained, however, the
characteristic steep slope on one side and gentle
slope on the other. Pits of this shape and of great
depth were observed by Mr. W. S. Blunt! in the
Arabian Nefud, where they are called fuljes.
It has taxed the ingenuity of more than one writer
to imagine a mode of action by which the wind
could scour out holes of such a great depth and
of this peculiar and constant form. I have not
seen the large structures described by Mr. W. S.
Blunt, but wherever they are formed in loose sand
I believe that they are what I saw on the Helwan
sandbanks. The weather and lee sides of the pit
are not parts of one structure, but the lee and
weather slopes respectively of two succeeding sand-
waves. Ina later part of this work I shall describe
how I observed pits of similar shape left at low

* Appendix to “A Pilgrimage to Nejed.”

50 WAVES OF SAND AND SNOW

tide on sandbanks, in which the characteristic steep
and gentle slopes were also the lee and weather
side of succeeding waves of sand.

The higher part of the sandbank near to the
permanent bank of the river was of course the first
to be uncovered during the subsidence of the Nile,
and had therefore been longer exposed to the action
of wind. This part of the sandbank was dotted
over with mounds of loose sand separated from
each other by bare earth. Most of them were of
a definite and remarkable crescentic shape. The
profile—that is to say, the section taken in the
direction of the wind, which I call the longitudinal
section—is very nearly the same as that of the
sand-waves which are in regular ridges. It con-
sists of a gently sloping weather face and a cliff
on the lee standing at the steepest angle allowed
by the looseness of the material. The cliff is
highest in the centre, and from that position extends
forwards on either side, the mound having two arms
or horns similar in shape to the cusps of a four-
days-old moon. ‘This crescentic form of aeolian
sandhill, with a height of 20 or 30 feet, is well
known in many deserts. In those of Central Asia
it is called a barchan, in Peru a medato. The
height of those on the sandbank sometimes attained
3 feet. From the situation where I found them

DESERT SAND-DUNES 51

it was evident that the specimens on the sand-
bank were residual structures. Had I visited
Helwan earlier in the season whilst this part of
the sandbank was still covered with loose sand, I
should no doubt have found it in regular trans-
verse ridges and furrows similar to those now
occupying the tract to windward and nearer the
present margin of the river. The ridges with crests
consisting of peaks separated by saddles are an
intermediate condition. I have described two
cases: first, that in which there was an accumula-
tion of sand on the lee side of each peak, and
second that in which the loose sand was swept away
under the lee of the peak, leaving an oval patch
of bare ground. In this latter case the tract pre-
sented the appearance of a somewhat undulating
plain pitted with holes. The dark-coloured ground
in the hollows was the most conspicuous feature in
the miniature landscape, but the peaks and steep
cliff on the weather side were also noticeable. To
the right and left of the peak there was a low
saddle, the walls of the pit being lower at the
sides than across the central longitudinal section.
Let us suppose the action of the wind in gouging
out the saddles to have continued until the bare
ground was reached. The sandbank would then
be covered by a number of crescentic mounds of

52 WAVES OF SAND AND SNOW

the barchan or medafo form in close proximity
to each other. Structurally there is little differ-
ence between the elevated plain of loose sand
closely pitted by jfuljes and the low plain of bare
ground closely studded by barchan-shaped sand-
hills, but in the one case the eye takes note of the
shape of the depressions, in the other of the form
of the hillocks.

In both cases the profiles are essentially wave
profiles, differine but little from’ those ‘of mle
regular ridges formed in the earlier stages of wind
action on a deep deposit of loose sand. In the
regular ridges the crests of the waves extend in-
definitely in breadth, so that there are only two
dimensions to be studied, just as is the case in
waves of the sea. When, however, the loose sand
no longer completely covers the ground, we have
to study the plan as well as the profile of the
moving mounds of sand. Are we to regard the
mound of moving sand, called a barchan, as a
wave? When barchans occur in regular series one
behind the other, each dependent in form, position,
and movement upon the shelter afforded by that to
windward, I think they should certainly be regarded
as a group of sand-waves. The fact that they
have a definite lateral boundary imparts a complete-
ness to their study which is novel in the subject

DESERT SAND-DUNES 53

of surface waves. The idea of a lateral boundary,
or third dimension, is not, however, revolutionary
in wave theory. For instance, in examining crystals
by means of a convergent beam of polarized light
we have a cone-shaped wave-front.

I have pointed out that crescentic dunes or
barchans were left as scattered mounds where
there had once been continuous sand in consecu-
tive ridges. This part of the sandbank, now partly
bare, was, however, receiving a shower of sand
from the cloud which formed a haze 20 or 30
feet high over the sandbank. The _ freshly
deposited sand collected in patches, and I saw
that they were beginning to shape themselves so
as to produce barchans. The profile was at first
symmetrical, with a gentle slope fore and aft,
but after a time the lee slope began to steepen.
In plan the patches had the same convex end
to windward as the barchan, and to leeward
a nearly straight transverse front correspond-
ing to a line drawn from horn to horn of the
barchan. I thought that a cliff would soon form,
and cusps be produced, and this conclusion I subse-
quently confirmed by observations of the production
of similar forms in snow. ‘Thus, if loose sand hes
in patches the wind produces crescentic dunes.

On the day of my first visit to the sandbank I

54 WAVES OF SAND AND SNOW

drove a reed into the sand at the crest of a wave.
In the course of forty-eight hours it advanced
293 inches, which is at the rate of o'61 inches
per hour or 150 yards per annum.

I will now describe the process which I believe
originated the aeolian sand-waves upon the Helwan
sandbank. My views developed gradually in the
course of several years’ observations of phenomena
of this class, and their full justification will become
more evident to the reader later on when more
of the phenomena have been described. Mean-
while it will be convenient to have the explanation
now, even though much of the evidence on which
it is based be delayed.

In the first place it must be stated that the mere
rolling of sand-grains along the surface does not
produce waves. On the contrary, when there is
only this mode of motion the tendency is for wind
to obliterate transverse inequalities, the miniature
rolling stones accumulating in the hollows where
the forward velocity of the wind parallel to the
surface is least and where the resistance to forward
rolling is greatest.

The formation of waves in drifting sand is, on
the contrary, dependent upon another mode of
action of the wind, viz., that by which the sand-
grains are picked up, carried for some distance

PLATE 5.—Accumulation of blown sand caused by a fence of reeds
(near Helwan). :

PLATE 5.—Accumulation of blown sand caused by marram grass
(at Aberdovey).

55

DESERT SAND-DUNES 57

in suspension, and again dropped. As rolling,
however, goes on at the same time, account has
to be taken of this concurrent circumstance.

The condition for uniform drift of sand in sus-
pension is that the amount picked up should be
equal to the amount dropped. Then there occurs
neither scouring nor silting. If at any place the
air had less than its full charge of suspended sand,
it would scour the next section. If at any place it
became overcharged, it would silt-up the next
section. It is evident, therefore, that the continu-
ance of uniform sand-drift would require the main-
tenance of great steadiness in the velocity of the
air. But wind of sufficient strength to pick up
sand and carry it in suspension is not even approxi-
mately a steady current. On the contrary, its speed
always varies to the amount of about 50 per cent.
every few minutes, even in open places, and where
there are obstructions the variation is about
Toe, per cent... Thus, on December 16, ror, |
found that the self-registering anemometer of the
Meteorological Office in London showed a varia-
tion every few minutes of from 6 to 12 miles an
hour, on the 17th of 6 to 14 miles an hour, on the
2oth 5 to 8 miles an hour, on the 29th 9 to 21 miles
an hour, and on January 4, 1913, 5 to 10 miles an
hour. Let us suppose wind to be blowing over

58 WAVES OF SAND AND SNOW

the Helwan sandbank as it blew in London on
December 17, 1912. It would be described as
a wind of 10 miles an hour, but as a matter of
fact it is a jerky current of 6 to 14 miles an hour.
Further, this particular range of speeds is not itself
steadily persistent. If we consider the velocity at
successive minutes above any fixed place on the
ground, it is not constant; and if we follow in
imagination any particular particle or parcel of air
in its onward course, its velocity will likewise vary
greatly. It is evident, therefore, that in one place
the air will become suddenly surcharged with sand
owing to loss of speed, and will drop the excess,
forming a mound, and at the same moment in
another place it will scour out a hollow. Thus
vertical inequalities inevitably originate. I have
already explained how, when once formed, they are
increased, owing to a confluence of currents at
the crest and a separation of currents at an inter-
mediate position, and to the effect of this arrange-
ment upon sand carried in suspension. Transverse
ridges are thus soon formed. They increase in
wave length, and maintain level crests until,
apparently, a particular height is reached, when
peaks and saddles are developed.

When the ridges are small an incipient depres-
sion is quickly mended, but when they are large

LEP

PLATE 6.—On the slope of a sand-dune having water at its foot.
59

DESERT SAND-DUNES 61

it is increased. The latter effect appears to be
owing to the upper layers of loose sand being
unable to withstand the thrust to which they are
subjected owing to the sudden change in the
horizontal velocity of the air between the forward
current and the eddy, the strength of which in-
creases with the height of the ridge.

The sand driven through the saddles is drawn
in by the eddies towards the peaks, and the fact
that the average ratio of length to height is the
same when the crests are level as when they are
unlevel suggests that the lateral action of the
eddies catches and retains all the extra sand driven
through the saddles.

My next observations were of dunes about one
hundred times as high as those on the Helwan
sandbank, and composed of the coarser quartz sand
of the desert. They are situated east of the Suez
Canal on the route to El Arish. Leaving Kantara
on the canal one morning on camel-back, I
camped that night at Bir Nisf. Next day, starting
at six in the morning, I rode east as far as Abu
Ramle, and, turning back, camped for the second
night at El Ookha, and returned to Kantara on
the morning of the third day.

For some miles east of Kantara we traversed
4

62 WAVES OF SAND AND SNOW

a sandy plain of a dirty brown colour. West of
the canal, on the contrary, the sand was of a
bright yellow colour, like that of ripe wheat. The
prevailing drift of the sand is from the west. The
canal intercepts much of it, so that the level of
the sand near by on the east is now being lowered.
The roots of bushes have consequently been
exposed, and the general tone of the ground-
colour is darkened by admixture of decayed
vegetable matter.

FIG. 2.

Farther east we began to ascend a sand-buried
tract, the individual sandhills being at first round-
topped and of indefinite shape. Later I saw on
the north of our route large sand-dunes in con-
secutive parallel ridges. A group of four had
quite the appearance of a train of waves. The
long, gentle slope was on the west, and there
was a steeper slope on the east, but the wind
now daily prevalent was opposite to that which
must have produced this form. The present
moderate breeze was blowing up the steep east
face, eddying on the west of its summit, where

‘

‘(Surddyys jo jov Ur opis da] UO purs) eI[IVUIS] 7 OUNp-puvs Jo JIWIUINS [eprUVI4g—'Z ALVTg

63

DESERT SAND-DUNES 65

a ridge was growing with a steep lee cliff to the
west and the original east cliff for its weather side.
Thus each of the four large sand-dunes presented
the appearance of a wave with its crest curled back
(Fig. 2). It was evident that if the present wind
persisted long enough these sand-dunes would be
completely reversed, for the eastern faces were,
no doubt, being flattened.

ea =
A sy
ee” a 5 SS :
peg ae: pe ESE

FIG. 3.

I saw the ridge of one great sand-dune with
four peaks and three intermediate saddles (Fig. 3).
The sand being so much coarser than that of the
Helwan sandbank, the ridges can, however, grow
to a large size before the sand in a saddle is
ploughed off, making vertical sinuosities inevitable.
In some cases there were very prominent peaks
with a great mound of sand piled against their

66 WAVES OF SAND AND SNOW

lee side. They appeared almost as independent
hills. But everywhere the loose sand lay deep,
and the wind was unable, therefore, to isolate any
mound of sand so as to shape it into a barchan
or crescentic dune.

On the afternoon of the first day there was a
slight haze in the air due to suspended sand. I
was struck next morning by the changed appear-
ance of the scene. There was no haze in the
light of early day, but, on the contrary, an atmo-
sphere of singular clearness. The steep slopes,
the sharp arétes, and the pyramidal peaks of the
sand-dunes stood out with an intensity of light
~ and shadow which, combined with uniformity of
tint, was more like lunar scenery as viewed with
a telescope than any terrestrial landscape which I
had hitherto seen. The slopes of the dunes were
smooth and unspotted, and in the absence of detail
or of objects of known size there was nothing to
provide a scale of magnitude. With a low sun,
which threw long, dark shadows, the dunes, with
their bold, mountainous forms, loomed immense,
and an unbiased observer might easily have sup-
posed their height to be thousands of feet instead
of one or two hundred.

On the second day I camped on a plateau of
pure sand some 40 feet above a depression, where

mes

PLATE 8.—On the top of an encroaching sand-dune at Ismailia,
67

DESERT SAND-DUNES 69

date-palms grew and where water could be obtained
by digging. The day had been very hot, there
was no evidence of recent rain, neither could I
hear of rain having fallen recently in the neigh-
bourhood. The air was so dry that when I tried
to wash my hands the soap was left as a solid
film upon the skin owing to evaporation of the
water. Yet the sand 3 inches below the surface
was sufficiently damp to stick to the sides of the
glass sample-bottle. I slept that night in a tent
which had been pitched on the same spot before
sunset. The interior remained dry and very hot
all night, but on going out before sunrise I found
that the camp equipage outside was wringing wet -
with dew. The heat of the sun evidently does
not penetrate far into the sand, but the size of
the interstices between the sand-grains permits of
interior distillation. Rain falling on the porous
surface cannot collect in superficial channels, but
sinks through the sand. Thus moisture lies at the
foot of the sand-dune and provides dew.

At Bir Abu Ballah, south-west of Ismailia, I
saw a large mass of sand on the west of a culti-
vated tract, which had formerly been occupied by
a salt marsh. The sand was piled in a steep bank,
which had a very sinuous frontage, following appar-
ently the margin of the former salt marsh, and

70 WAVES OF SAND AND SNOW

not conforming at all to the direction of the wind.
The surface of the tract of sand showed, however,
two sets of undulations, one of which seemed to
be transverse waves due to westerly winds, and
one to be waves similarly produced by the northerly
winds now prevalent.

Apparently the accumulation of a mass of blown
sand in this place was due to diminution of mobility
by moisture. Between Ismailia and Abu Hammad
I saw other sand-dunes produced apparently by
the same cause. South of the Wady Toumilat is
a plain dotted with scrub and free from sand-
dunes, but a line of them fringes the south border
of the moist Wady which bounds the plain. Sand-
grains can drift freely and swiftly over the dry
plain, but are checked at the margin of the moist
valley, and grow into dunes. Moist ground is
apparently the origin of the dunes near Ismailia,
on the west of Lake Timsah, and in the other
flat districts which I visited in the neighbourhood
of the Nile delta moist ground seemed to have
determined the position of the dunes. In deserts
where there are great variations of wind-exposure
the positions of dune-tracts are no doubt often
determined by shelter, but I have not visited these
localities.

The influence of moist ground appeared to

PLATE 9.—Sand grains from the cliff of a
sand-dune at Ismailia (magnified).

gt

DESERT SAND-DUNES 73

be so great wherever I went that I wondered if
it could be altogether a mechanical effect. There
is a current opinion that when the atmosphere is
electrified, wind moves sand much more freely than
at other times, the material going into suspension
and remaining suspended to an unusual degree. I
therefore tried in the laboratory the effect of elect-
trifying sand, and was much struck with the great
mobility which it acquired. It has occurred to
me that sand-dunes where the underlying ground
is moist, being well “ earthed,” would be less sus-
ceptible to the effects of electrified wind. My
cousin the late Mr. E. A. Floyer, Inspector of
Egyptian Telegraphs, informed me that in the dry
desert, on the other hand, the insulation is so good
that it is often difficult to get an “earth” when
it is required for sending a telegraphic message.
From the slipping lee cliff of a sand-dune at
Abu Racan, near Ismailia, I collected a sample of
sand by pushing in a wide-mouthed glass bottle.
The position was about the centre, under the peak,
of a rather long transverse dune about 4o feet
high. Here the air eddies vertically round and
round, winnowing the sand. The uniformity of the
material which remains is remarkable. Plate IX.
reproduced from a micro-photograph, illustrates
this, but the fact is more strikingly shown by

74 WAVES OF SAND AND SNOW

the mechanical analysis which I made of the
sample. In order to make the analysis I had six
sieves of copper-gauze made with square meshes
irom 7, tO ss4 of an inch ‘im diameter ioe
passed the sand through one sieve after the other,
with prolonged tappings, and weighed the
separated portions. Twenty grams weight of the
material were taken and 19°981 grams were re-
covered, the difference of o'019 gram remaining
attached to the sieves or being otherwise lost. The
result was as follows :—

Weight. Percentage
Sand-grains more than 7; inch diameter s.« O0'000 O10G0

Less than ;4, inch but greater than j, inch... 0°003 O*°OI5

~
_

o'412 2°060
- 18°775 93°875

|
|
zl

bl,
|
«|
ot

1 : °
2 oe ” 7o7 --- 0°790 3°950
1 Fy *
a ee fi aha 3) --1| O'TOOLE, — Oa5
iless than... -. O'0CO \a1000
384 ))

Thus, in round numbers, 2 per cent. by weight
of the sand-grains had a diameter more than 7g of
an inch and 4 per cent. diameter less than jg. Of
the remaining 94 per cent., the largest grain was
not more than twice the diameter of the smallest.

CHAPTER wl

AEOLIAN SAND-RIPPLES

All aeolian sand-waves have a rippled surface—Description of
the formation of aeolian sand-ripples in level deposits of
loose sand blown from the beach—Measurements of height
and length—The ripples grow without change of shape—
Ratio of length to height the same as in the larger sand-
waves—Rate of advance—Winnowing of fine from coarse
sand-grains observed during growth of aeolian ripples—
‘“‘Erosion-ripples”’ formed where the level of the sand is
being lowered—The formation of a protecting cover of
“lag gravel” on the crests—Experiments by means of an
artificial blast—No rippling of assorted sand-grains of
uniform large size, although travelling freely—Immediate
rippling when small sand-grains mixed with them—Ex-
planation offered, that eddy in lee of larger grains tosses
away the smaller, hence the existence of ripples upon the
larger waves—Ripples in shell-sand showing lines of
notches in the wave-fronts where the troughs are deeper.

THE little sand-dunes at Helwan were covered with
small ripples of a form very much like that of the
dunes themselves—i.e., with a gentle slope to wind-

ward and a steep lee face. The great desert dunes
15

76 WAVES OF SAND AND SNOW

of quartz sand, which I have described, were like-
wise covered with ripples. In fact, all aeolian
sand-waves, whether they be the small dunes
élémentaires of French writers such as those at
Helwan, or the great dunes of the desert, have
their otherwise smooth surface corded with a
delicate and regular pattern of ripples. These
ripples have a length of some inches from crest
to crest, relatively great lateral extension or
breadth, and level crests. They face everywhere
the direction in which the air flows over the surface
of the dune, and show precisely how the shape of
the dune deflects the wind. They are formed on
all parts of the dune where the air flows parallel
to a surface of non-coherent sand. The slipping
cliff, which forms sometimes the whole, sometimes
only a part, of the lee side, is unrippled. There
are also on the greater dunes positions where the
wind, cutting down to lower layers of sand which
have become somewhat coherent owing to super-
incumbent pressure, makes another variety of minor
wave or ripple, of greater wave length but less
breadth. These, which I call erosion ripples, I
shall deal with presently, confining myself now to
ripples in loose sand, which are the most regular
and the prettiest of the patterns modelled in sand
by the wind.

oR

es
TRS

les at Southbourne

-Tipp

d

PLATE 10.—Aeolian san

ing of

les at Southbourne, in which the sort

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n

AS

as

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in}
Ke)
S
iss)
7)
S
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4
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17

: $3 A . 7 i .
ie re: di 40: bee ie IE 32a ahd

oa rf : ; ; ; " Hs
dy ie oo Sanh

AEOLIAN SAND-RIPPLES 79

Although an aeolian sand-wave cannot be formed
without the production of ripples, the converse does
not hold, for wind blowing over a horizontal surface
of loose sand can produce the ripples without the
formation of the larger kind of wave. During the
winter of 1895-6 I made numerous observations
of this action upon the loose, dry sand of the
sea-shore between Branksome Chine and Poole
Haven, on the Dorset coast, upon the beach
between Poole Haven and Studland, and among
the small sand-dunes on either side of the
entrance to Poole Harbour.! The conditions varied
so little that what was learnt on different days
may safely be combined in the following general
description.

A moderate off-shore breeze after rain dried the
surface of the neighbouring sand-dunes and a sheet
of freshly blown sand began to accumulate on the
firm, smooth, and slightly damp surface of the
sandy beach. At first the loose surface of accu-
mulating sand was smooth, but it soon became
mottled, and the mottled appearance very quickly
changed to that of transverse ridges. These had
at first a length from crest to crest of 1 inch,
which increased as time went on. But the ridges

* “On the Formation of Sand-dunes,” Geographical Fournal,
March, 1897, by Vaughan Cornish.

80 WAVES OF SAND AND SNOW

developed in breadth much more rapidly than in
length, for when the wave-length had attained
23 inches the breadth, or lateral extension, of the
ridges was no less than 3 feet 11 inches.

The newly deposited accumulation of loose sand
began to ripple when its depth was certainly not
more than } of an inch. The size of the sand-
grains was such that, on an average, I was able to
arrange fifty-four of them, touching each other, in
the space of 1 inch. The best method of measuring
the height of the little ridges is to stretch a thread
over a group of them and measure down to the
surface at the crest and trough respectively. In
the earlier observations which I am now describing,
however, I used to make a longitudinal section of
the ridge with the blade of a knife, and, lying
flat on the sand, measure the height of the ridge
above the trough directly. I used also to count
the number of sand-grains which were piled one
upon another between the uppermost continuous
layer of sand, which is that at the level of the
trough, and the summit of the ridge. By count-
ing the number of sand-grains which could be
placed side by side in the space of 1 inch I
obtained an indirect measure of the height in one
or two cases when I was not provided with a
measure suitable for taking the height of very

AEOLIAN SAND-RIPPLES 81

small ridges in quite loose sand. The following
measurements were made :—

lee eaad-grains| the flppis | erthe fipele Grane nite Taneth to the
in Inches. | in Inches.| in Inches. Height. Height.
1 35 Si : ah a
38 a It na ap,
3 as Ys tt 5 (calculated) 20
4 ata -- 14 5, (counted) 18
g To zo yi 8 ” 17
6 as 4 24 8 (calculated) 17
iz Sz $ 24 i 20
8 a5 $ at 5, or 6, 26
9 L — 34 8 (counted) 184
ie) ay 4 4+ 12 (calculated) 17
II as aD 6 16 (counted) | 18 (average)
12 — 4 7 20 5 14

(In the case of number 12 there were smaller ripples upon
the weather slope.)

The indication afforded by this table is that the
ratio of length to height remains constant during
the growth of the ripples, or, in other words, that
the shape of the wind-eddy which moulds them
is not affected by their growth. The average ratio
of length to height is 18°55, which, as has already
been pointed out, is the same as that of the sand-
waves with a wave-length of 30 feet—that is to
say, with linear dimensions 120 times as great.
I have appealed to travellers in desert regions to
make similar measurements of a series of great
dunes, but have not yet received any results.

82 WAVES OF SAND AND SNOW

If the ratio of length to height in the last ten
ripple measurements hold for the first two, of which
only the length and the diameter of the sand-grains
were measured, the sand is already regularly rippled
when the trough is one grain lower and the crest
one grain higher than the mean surface.

The movement of the ripples was measured on
several occasions. When the wind was blowing
as a strong breeze—i.e., about 27 miles an hour—
the following measurements were taken in different
positions not far from each other, but in which
ripples varied in size on account of the difference
in their exposure :—

RATE OF ADVANCE OF RIPPLES OF NINE INCHES WAVE-LENGTH.

1‘00 inch in 1°5 minutes = 0°67 inch per minute

150 7) 3'0 ” = 0'50 ”

2°25 ” 50 ” = 0°45 ” ”
3°25 ’” 15 ” = 0°43 ’” ”
4°25 ” 9°5 ” = 0°447 4 ”

the average of the five determinations being
0°50 inch per minute.

RATE OF ADVANCE OF RIPPLES OF Four INCHES WAVE-LENGTH.

I‘o inch in 2‘0 minutes = o’50 inch per minute

Lhe ” 35 ” = 0°43 ” ”
2°0 ” 5:0 ” = 0°40 ” ”
2°5 ” 6°25 ” = 0°40 ” ”

2°75 ” 7700 5) = 0°39 ’” ”)

AEOLIAN SAND-RIPPLES 83

the average of the five determinations being
o'424 inch per minute.

RATE OF ADVANCE OF RIPPLES OF THREE INCHES WAVE-LENGTH
(IN A SHELTERED SPOT).

0°25 inch in 8 minutes = 0'03 inch per minute
0°50 yy 16 ” = 203 ” ”

The movement of the ripples even in a strong
breeze is achieved almost entirely during the gusts.
Thus during a gust lasting only 45 seconds I have
seen a small ripple in an exposed position advance
nearly 1 inch.

When a patch of blown sand, drifted from a
distance, is deposited in a fairly exposed position
the surface is smooth and the texture of the sand
uniform at first, but almost as soon as rippling
commences the sand on the crests is seen to be
coarser than elsewhere. This difference becomes
more marked as the ripples grow in size. Even
during my first observation of the occurrence I
thought I could detect two modes of motion of
sand-grains, and the two modes of motion appeared
to be connected with this sorting of the sand. The
large grains which accumulated at the crests rolled
upon the surface, but the finer grains seemed to
be caught up in the air and whisked away. I shall
describe presently how I verified this by experi-

84 WAVES OF SAND AND SNOW

ment. As long as sand is being so plentifully
supplied that the deposit accumulates, or does not
become depleted, the growth of the ripples is slow,
they never attain a very large size, and the sand
upon their crests does not become coarse. But
when the supply of sand from the windward is
scanty or fails altogether the ripples grow to larger
dimensions and the sand-grains upon the crests are
coarser. This coarse sand, which becomes of the
dimensions of small gravel, ultimately collects in
a sheet, which covers and completely protects the
upper part of the ripples. The completeness of
this protection depends upon the circumstance that
individual particles of coarsest sand or very fine
gravel lie wholly above the general surface and,
being thus exposed to the horizontal pressure of
the wind, roll freely, whereas when they are
collected in a sheet the wind glides ineffectively
over their surface. The rate of their subsidence,
or fall, in air is, moreover, such that it would
need a very strong eddy to suspend them. Thus
when this sheet of coarse sand, or “lag gravel,”
has been formed it protects the sand below it and
the ripples grow by deepening of their intervening
troughs. These are dug out in sand which has
become somewhat compact owing to superincum-
bent pressure. This kind of erosion-ripple not

PLATE 11.—Acolian sand-ripples at Southbourne, in which the sand
grains have been much sorted.

PLATE 11.—Aeolian sand-ripples at Ismailia to leeward of a sand-dune
where there is an upward current of air.

85

AEOLIAN SAND-RIPPLES 87

only attains a greater wave-length than that of
ripples formed in quite loose sand, but a greater
steepness also. Thus on the nearly flat top of a
sandhill near Lake Timsah, in Egypt, I measured
such ripples with a wave-length of 7 feet 2 inches
and a height of 6 inches, being a ratio of length
to height of 14:3. This kind of rippling is quickly
produced in positions where the supply of drifting
sand is small and the wind is swirling upwards.
The lower photograph of Plate XI. shows this
erosion rippling in such a position to leeward of
a sand-dune at Abu Racan, near Ismailia. The
crest of the ripple is more nearly in the middle
than is the case with the ripples in quite loose
sand, and this form suggests that these erosion
ripples were almost or quite stationary.

The fact that there is a sorting of sand-grains
during rippling, the coarser grains accumulating
at the crest, affords a clue to the problem of the
simultaneous formation of two orders of undula-
tion, the ripple and the wave, upon the sandbank
at Helwan and elsewhere. The theory of the
formation of the wave has already been given.
Its rippled surface is due to the circumstance that
the sand-grains are of various sizes. I have been
at considerable pains to investigate the precise

manner in which the wind acts upon particles of
5

88 WAVES OF SAND AND SNOW

different size so as to produce this result, and the
outcome of the inquiry is one of considerable im-
portance in its application to many phenomena of
the transport and accumulation of fragmentary
materials both by wind and water.

Having hired a room and the _ necessary
appliances at a factory where designs are cut
in stone and glass by means of a blast of
hot sand, I proceeded to experiment with a
strong, steady blast issuing from a nozzle upon
materials obtained from natural sands by a process
of grading. I spread out a bed of coarse sand-
grains of nearly the largest size ordinarily found
upon sand-dunes—the “lag gravel,’ in fact—and
I turned upon it a strong blast of air under which
this small gravel moved with such freedom that
the grains rattled as they rolled. Nevertheless,
even under prolonged action of the blast there was
no sign of rippling. I then stopped the blast, and
taking some fine sand which was at hand, I mixed
a quantity of it with the lag gravel. I then turned
on the blast again, and almost instantaneously
ripples appeared and quickly became regular.
Their fronts were convex, being everywhere at
right angles to the direction of the blast issuing
from the nozzle. The large grains quickly collected
on the ridges in transverse barriers, whilst the rapid

AEOLIAN SAND-RIPPLES 89

accumulation of haze in the room attested the fact
that the finer particles were being thrown into
suspension. ‘Watching the process at work, I was
quickly convinced that the rippling action was due
to the concurrence of two modes of motion. In
the lee of the large grains eddies were formed which
caused the small grains there to be thrown into
suspension. The large grains, when apart, rolled
freely owing to their projection above the surface,
but when gathered in groups were less readily
moved owing to mutual shelter and interlocking,
so that they tended to mass themselves together.
The more they massed the stronger was the eddy
on their lee and the more rapid the erosion of the
fine sand there. Thus the barriers of gravel
became the crests of ripples, which had finer sand
in the troughs. The relative mobility of heavy
and large and of small and light particles under
the action of wind depends upon its direction, the
mobility of the larger particles being almost
entirely due to the component of the wind which
is parallel to the surface, whereas that of the fine
particles is largely due to the upward component
of the wind’s motion.

At Hayle, on the north coast of Cornwall, the
sand of the beach is mainly composed of frag-
ments of shell. When I visited the place one

90 WAVES OF SAND AND SNOW

August day in dry and breezy weather the wind
had covered the loose sand of the beach with
ripples 3 inches in length, which extended laterally
as much as 27 feet without a break. They
had, however, a feature not seen in the ripples of
the quartz sand near Bournemouth, each ridge
having notches at intervals, where the straight
front was interrupted for a space of about
3°5 inches, the apex of the recess being rather
more than 1°5 inches behind the general frontage.
The trough was deeper in the notches than else-
where and the sand coarser in grain. The crest
was not, however, any higher at these places. The
notches occurred at somewhat irregular intervals of
about 12 inches on each ridge, but were repeated
exactly from one ridge to another, being arranged
in lines parallel to the wind. Apparently, there-
fore, any pit formed in the trough tends to be
deepened, but there is no compensating formation
of peaks on the crests. The stronger eddy pumps
up more sand from the trough, but apparently the
flat particles of the shell-sand cannot withstand
the ploughing-off action of the direct current.

PART II

SNOW-WAVES AND SNOWDRIFTS

\

oh

CHAPTER III

SNOW-WAVES AND SNOW-RIPPLES

Ripples in Moist Snow.

Damp snow and dry snow—Ripples in moist snow during
snowfalls observed in Hyde Park—They face up-wind—
Recede by erosion of wind-facing cliff—During lulls travel
up-wind—Mode of erosion of partially consolidated snow :
first transverse, finally longitudinal ridges, with a transition
stage between—Stratification shown by erosion.

Waves in Dry, Drifting Snow.

Formed near Montreal at minus 8° Fahrenheit—Length
and height—Flatter than sand-waves—Movement visible
and more rapid than that of sand—Surface unrippled—
Measurements of snow-waves, in Manitoba, formed during
removal of snow—Waves formed during snowfall—Their
formation upon a plane surface free from obstructions.

Crescentic Snow-waves or Snow-barchans.

Formed in patches of loose snow travelling on a hard
surface—Finer lines than sand-barchans both in profile
and plan—Formation of crust on surface of snow and its
effect in arresting growth and movement of snow-waves—
Explained as due to sublimation—Increase in density of
snow which has been drifted by wind—Compared with

increase of density due tc pressure.
93

94 WAVES OF SAND AND SNOW

Ripples in Snow-sand.

Mode of formation of granular snow or “snow-sand’”—
Rate of movement—Growth and movement more rapid
than those of sand-ripples—Measurements of length and
height—Obliteration in lee of larger ridge.

Forms Produced by Wind-erosion in Compact Snow (Studies in
Canada).
Measurements of transverse ridges, facing up-wind—Shape
of pits—Longitudinal structures—Note on the longitudinal
sand-dunes of the great Indian Desert.

The Eddy Form of Snow-waves and Snowdrifts.

Complex forms of drifts produced by fixed obstacles—All
contained by a boundary curve having blunt head and
fine tail—This is the boundary of the eddy caused by the
obstruction—Complex forms are stages of filling in of
eddy-space and due to insufficient supply of snow—The
eddy-curve and its relation to the forms of fish and
cetaceans—Of the wings of birds—Of the submerged part
of ships—Of torpedoes and non-rigid airships—Forms of
holes scoured out in snow round the trunks of trees—
Relation of snow-barchans to the eddy-curve—The relation
of form and movement between the travelling crescentic
snowdrifts and the swirl made in water by an oar—Shape
of the eddy in snow-waves—Inference as to the distance
to which hedges and belts of trees extend shelter from
wind.

On the Three Modes of Deposition of Drifted Material depending
upon Rate of Subsidence.
Behaviour of gravel, sand, and dust before the wind—Of
shingle, sand, and mud under the action of waves and
currents—Single tail of sand behind a narrow obstacle—

SNOW-WAVES AND SNOW-RIPPLES 95

Double tail of snow-powder—Single train of black smoke,
but double track of steam, from chimneys—How fallen
leaves drift before the wind—On “ banner clouds” and on
sandbanks to leeward of promontories—On the action of
an obliquely crossing wind upon the swell of the sea.

LOOSE snow has two conditions, which depend
upon temperature. Near the melting-point, 32°
Fahrenheit, the particles are soft and adhesive.
Near zero Fahrenheit and below this temperature
they do not adhere but glide easily over one
another. In England and Scotland I studied
ripples in the first kind, or moist, snow. In order
to see the effect of wind upon the second kind,
or dry, snow, I spent a winter in Canada, crossing
from Montreal to Vancouver and back again. I
also studied there the forms of the banks or drifts
produced by the action of wind in the neighbour-
hood of fixed obstacles. I examined, too, the forms
which gravity gives to the caps of snow which
collect upon prominences in still weather. This
last piece of research being naturally incidental
to the tour, may, I think, be properly described
in this book, although the forms are not waves,
or produced by eddies.

Ripples in Moist Snow.
The following observations were made in
England and Scotland at temperatures but little

96 WAVES OF SAND AND SNOW

below the freezing-point. The first observations
were in Hyde Park, London. On January 23 and
24, 1907, there were about 2 inches of snow
upon the ground, and snow was still falling. There
was a moderate breeze blowing, which in exposed
positions was removing snow from the surface and
drifting it, although not copiously. The whole sur-
face was covered by small ripples about 1 inch in
wave-length and <}, inch in height, which had nearly
vertical faces on the up-wind side. They there-
fore faced in the opposite directicn to the ripples
formed by wind in loose, dry sand. Their motion
was more rapid than that of aeolian sand-ripples.
The movement was usually a recession, each little
cliff retreating owing to the removal of its substance
by the attack of the wind. But every now and
then every ripple would simultaneously advance
up-wind with a swift rush lasting for about one
second. The slower but longer-lasting retreat to
leeward then re-commenced. These changes
accompanied the gusts and lulls of the wind.
During the gusts there must have been an active
eddy with a horizontal axis and vertical whirling
on the weather side of each little cliff. When the
wind suddenly lulled it ceased to erode the cliff,
and the falling snowflakes, entangled in the eddy,
plastered up the face of the cliff, building it out

SNOW-WAVES AND SNOW-RIPPLES 97

to windward, and thus giving a sudden and swift
but momentary motion up-wind. A similar effect
was sometimes produced during moments of heavier
snowfall.

On Arthur’s Seat, near Edinburgh, on the Pent-
land Hills, and near Grantown-on-Spey I observed
the action of wind upon a snow surface when there
was no snowfall. The first case which I will de-
scribe was during the removal of the surface layers
of a recent snowfall where the material was light
and loose. The surface was beautifully covered
with ripples having wave-lengths of from 3 to 15
inches, with their cliffs facing up-wind. The cliffs,
though broadly extended, were sinuous, none being
straight for more than a few inches. The con-
centration of the wind in the re-entrant angles or
notches threatened to cut through the ridges and
thus destroy by erosion the transverse, or rippled,
form, but the drifted particles which were con-
centrated here were sufficiently adhesive to mend
the threatened breaches. The salient angles, too,
tended to become more prominent, and thus destroy
the transverse arrangement, but they were under-
cut by the wind, and the overhanging cornices
receded by collapse, so that the transverse arrange-
ment was preserved.

But the rippled, or transverse, arrangement of

98 WAVES OF SAND AND SNOW

inequalities did not long survive when the wind had
cut down to lower layers of snow which had become
compact owing to the pressure to which they had
been subjected by the superincumbent layers.

The density of snowfall varies from minute to
minute, and the result is to produce an incipient
stratification. Pressure develops this, so that the
deeper layers when uncovered have a strongly
marked horizontal stratification, the beds being
usually a fraction of an inch in thickness. The
result of this is that at first the wind here forms
long transverse cliffs of minute height facing up-
wind, but the hard particles eroded therefrom do
not adhere to the smooth surfaces, but, on the
contrary, erode after the manner of a sand-blast.
Thus, wherever a notch or re-entrant angle is
formed in a cliff it is rapidly increased, and soon
the transverse ridges are cut quite through. The
last structures to survive are longitudinal ridges
with a cliff, or sometimes an overhanging cornice,
facing the wind. These are, I believe, the
structures often referred to in narratives of polar
travels as sastrugi.

These observations of the change from trans-
verse to longitudinal structure during erosion of
compact snow were confirmed and extended during
the following winter, which I spent in Canada.

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SNOW-WAVES AND SNOW-RIPPLES 101

Waves in Dry Drifting Snow.

I arrived in Canada on December 15, 1900,
and found the country around Montreal snow-
covered, but until January 5th I saw no undulations
with their steeper side turned to leeward—nothing,
indeed, but groovings facing the wind. After the
New Year, however, the temperature fell, we had
what is called in Canada “ zero weather,’ and the
newly fallen snow particles being dry and not
adhering by dampness or by regelation to one
another, behaved quite differently.

On January 5th I went out at 10.30 a.m. to
the fields on the west of Montreal. The tempera-
ture was 8° below zero Eahrenheit; i.e., there
were 40° of frost, the sun was shining, and the
wind blew with a velocity of thirty miles an hour,
recorded at the McGill College Observatory.
Durmg the preceding night 3 inches of fresh
snow had fallen upon the hard re-frozen surface
of the old snow. This new, light, dry snow the
wind was rapidly removing to places of shelter.
On the lee side of a swell in the ground I found
a group of waves, some of which are shown in
Plate ‘XII. They resembled the aeolian waves
in dry sand which I observed at Helwan, having
the cliffs on the lee side, but they were flatter than

102 WAVES OF SAND AND SNOW

the sand-waves and their motion was much more
rapid. The weather faces were being rapidly
scoured away, whilst the lee cliffs were built out
by the arrival of snow from two directions, some
pouring over the edge of the cliff from the wind-
ward, some being swept back to it along the
surface from the leeward. Their advance was
sufficiently rapid to be easily visible, and the effect
of the silent, stealthy creep of the whole series of
waves across the field was extremely weird. The
snow thus travelling in waves was only a part
of what the wind was drifting, for much was per-
manently in suspension, whirling along at a great
rate in the air as a thin haze extending high above
my head. The waves were in isolated ridges with
hard snow between. They had an average wave-
length of 15 feet 104 inches, and an average
height of 4°9 inches, so that their length was 38°86
times their height, or in other words, they were
only half as steep as the aeolian sand-waves. The
profile of passive waves in granular material simply
shows the form of the wind eddy. A ridge of the
loose snow, which is less resistant than a ridge of
sand, cannot withstand as strong a pressure. If
the ridges were built artificially to greater steep-
ness, the horizontal thrust of the wind would plough
off the upper layers.

‘Sodiuury vou ‘mous Arp jo soava Sunjliq—'fI alvid

Fa

3

10

SNOW-WAVES AND SNOW-RIPPLES 105

The snow-waves advanced 6 feet 6 inches in
forty minutes, or at the rate of 2 inches per
minute, which is about two hundred times as fast
as the rate of advance which I observed in aeolian
sand-waves in a wind of rather less strength. The
speed of the sand-waves was, however, measured
by the advance made during forty-eight hours, and
the wind dropped during the nights. If the
measurements of the waves of sand and snow had
been made under precisely similar conditions, the
rate of advance of the latter would have been,
perhaps, fifty times as great as that of the former.

The snow-waves were not rippled upon the sur-
face. The reason of this is, no doubt, that the
friable snowflakes provided no obstructions to take
the place of the coarser sand-grains which,
travelling only on the surface and forming an eddy-
making barrier where they accumulate, produce the
rippled surface of the sand-waves in the manner
which I have already explained.

On the flat and more open prairie near Winni-
peg snow-waves are formed in larger groups than
in the fields round Montreal. On the 18th of
February, the temperature being zero Fahrenheit
and a strong wind blowing, I went out from the
city of Winnipeg on to the open prairie. Five
inches of fresh, dry snow had fallen in calm weather

106 WAVES OF SAND AND SNOW

during the previous day and night. By 10 a.m.
this was already drifting in low waves which occu-
pied the whole prairie. I measured a series of
twenty-nine which had an average wave-length of
30 feet 1 inch and an average height of 7:2 inches,
the wave-length being therefore fifty times as great
as the height. The average difference between
the length of each wave and of that preceding it
Was 22 per cent. of the mean wave-length. This
percentage I term the variability of the wave-
length. Its record gives a measure of the degree
to. which groups of waves depart from exact
uniformity.

Later in the morning, when drifting had con-
tinued longer, I measured a series of 110
consecutive waves which had an average wave-
length of 32 feet 10 inches. The variability of
wave-length was 36°5 per cent.; i.e., they were
less regular than those measured earlier. The
reason for this deterioration was easily detected.
As the waves rolled on, layers of snow in which
pressure had made the particles adhere came to
the surface, and this material was not sufficiently
fluid to travel in waves. During the remainder of
this day and in the course of the two days follow-
ing, during which the wind blew but snow did not
fall, the appearance of the snow-covered prairie

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108 WAVES OF SAND AND SNOW

underwent a transformation, for ridges facing to
windward were formed by erosion of the compact
snow. ‘The snow of the drifted waves (which face
to leeward) had, moreover, set hard during the
still nights, and remained immobile. Thus the
snow exhibited two kinds of ridges—one with their
faces towards the wind, the other facing to lee-
ward: the former with a surface grooved and
scarped, the latter with a surface generally
smoother and more rounded. The appearance to
the novice is a mere confusion of forms, but when
I had learnt the secret of the two kinds of waved
surface produced in loose and compact snow
respectively I could always recognize the two sets
of forms, and detect order where all at first had
seemed chaotic.

I have now described two occasions upon which
the formation of travelling waves occurred when
wind was removing a level deposit of loose snow.
On another day I saw the formation of such waves
during the covering of the ground by a fresh snow-
fall accompanied by wind. The surface was hard
and glazed, being that of old snow which had
thawed and been afterwards frozen. The snowfall
began at 10.30 a.m., at about the time I arrived
upon the ground, and continued throughout the
day, accompanied by a light to moderate breeze.

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110 WAVES OF SAND AND SNOW

The rate of snowfall was about half an inch per
hour, but footprints were filled up by fall and
drift at the rate of 1 inch in fifteen minutes, so
that the accumulation by drifting over the icy sur-
face was nearly eight times as rapid as the rate of
deposition by snowfall. After half an hour of
snowfall and snowdrift, viz., at 11 a.m., numerous
patches of fresh snow had formed. Their number
and size increased, but up to 12.30 p.m., when I
adjourned for luncheon, they remained irregular.
Returning at 2.30 p.m., i.e., after snowfall and
snowdrift had lasted four hours, I found that the
irregular patches had become ridges transverse to
the direction of the wind, with the steeper faces to
leeward. The distances between the ridges of a
series were 6, 12, 6, 8, and 7 feet. A boarded, or
“plank ” path at the side of a road near by was still
uncovered by snow at 4.12 p.m.—i.é., after nearly,
six hours of snowfall, when enough had fallen to
have covered it to a depth of nearly three inches if
there had been no wind. Under the actual cir-
cumstances of fall and drift the path could never
be covered except by submergence by a travelling
wave of snow.

The snow-waves as they roll on leave behind a
shallow deposit of partially consolidated snow on
which fresh snow drifts but slowly. Krom what I

‘SodiuutAy jv ‘mous Arp jo soaem Sunjiuq—ti aLvid

111

SNOW-WAVES AND SNOW-RIPPLES 1138

saw subsequently on frozen lakes I concluded that
the increased friction upon the surface of these rem-
nants rendered possible the complete covering of the
ice when the snowfall was accompanied by wind.

It was with peculiar interest that I found, not
only that more regular and extensive series of
travelling snow-waves were formed upon the flat
and open prairie than in undulating and enclosed
country, but that the waves formed also on per-
fectly level and smooth ice of a large frozen lake.
The latter observation afforded a remarkable con-
firmation of the view I had already advanced, that
waves in granular material do not require for their
formation the existence of an eddy-making obstruc-
tion, as was formerly held, but inevitably originate
upon an unobstructed surface from the silting and
scouring action which is exercised when the wind
(blowing as it always does with variable velocity)
has a speed, even in the lulls, sufficient to pick
up the particles, which must be themselves of such
a density and size that they do not follow the lines
of flow of the air, but subside at an appreciable
rate.

Crescentic Snow-waves or Snow-barchans.

When there is only a small amount of loose, dry
snow drifting over a hard surface it does not accu-

114 WAVES OF SAND AND SNOW

mulate in transverse ridges: but in low, narrow
mounds, having on the lee a cliff, which is highest
in the centre and projects forwards on either side
in horns or cusps.: The shape is that of the
crescentic sand-dunes known as medafios or

barchans, but with finer lines, the snow-barchan

Barchans of snowand sand.from photographs.

being both narrower and flatter (Fig. 6). I saw
many hundreds of these structures which had been
produced in ordinary fresh-fallen dry snow, but
in the absence of any steep eminence to give me
a good view-point I was unable to obtain a photo-
graph showing how the prairie was dotted over
with these structures.

‘mous Ivjnuvis ul soddiy—'Si aLvig

SNOW-WAVES AND SNOW-RIPPLES 117

They do not have a long life as travelling waves,
for in the still nights their surface sets hard. It
is the setting of the surface of the snow in exposed
positions, which occurs without any melting and
re-freezing, which prevents snow-waves growing, as
sand-dunes grow, to large dimensions. Thus in
weather when the temperature never rose to the
melting-point, and when there was no sign of melt-
ing in the sun, I found that snow-waves which were
formed on the prairie near Winnipeg on January
25th had on the 28th a surface so hard that it was
scarcely dented by the heel of my moccasined foot.
I found that this resistance was due to a hard
surface-layer 4 inch thick. Pieces of this crust
when broken off and held up to the sunlight
were seen to be a mosaic of small, translucent,
icy blocks cemented firmly by opaque ice. In
copses near by the snow had no crust upon it. I
suggest that the setting of the drifted snow upon
the prairie is due to sublimation,' the lower layers
evaporating under the action of the earth’s heat,
with direct condensation to the solid form in the
pores of the surface, which is chilled by radiation.
I may recall in this connection my observations

« That is to say, the transformation of a solid into a gas and

re-condensation to the solid state without the intermediate
formation of liquid.

118 WAVES OF SAND AND SNOW

upon the formation of dew among desert sand-
dunes (see ante, p. 69), for I suppose the cement-
ing matter of the hard-set snow to be, so to
speak, solid dew.

Below the icy crust the snow in the snow-waves,
though not hard, was dense, having a specific
gravity of 0-4, which was twice that of the snow
in a copse near by, which was o-2. At Glacier
House, in the Selkirk Mountains, where the atmo-
sphere is calm and there is no drifting, the density
of the snow at the surface was o1, at a
depth of 1 foot o-2, and at a depth of 4 feet
0354. Increased density of snow is due to
removal of air from the interstices, and the above
figures show, not only that the minute snowflakes
which fall in the dry climate of Manitoba in mid-
winter pack tighter than the large flakes which fall
in the Selkirk Mountains, but also that the wind,
in turning over the material, gives it an additional
compactness greater than that imparted by the
pressure of a superincumbent layer of about
3 feet in thickness.

Ripples in Granular Snow or “ Snow-sand.”

The loose particles of waves of fresh-fallen dry
snow remain unrippled, the surface of these waves

PLATE 16,—Ripples in coarse granular snow.

SNOW-WAVES AND SNOW-RIPPLES 121

being smooth except where transverse grooves are
cut in the partially consolidated material which is
exposed during the turning over of the wave. In
this respect waves of snow differ from those of
sand, for the resistance of the larger sand-grains
produces rippling on the surface of the sand-
waves.

On the prairie around Winnipeg, however, there
lay during January and February a good deal of
altered snow, composed of rounded icy grains,
which varied in size from 3, inch to 7 inch
in diameter, the former being the size of
somewhat coarse sand, the latter of the “lag
gravel,’ which is rolled along by wind but not
ordinarily thrown into suspension. This snow-sand,
as I shall call it, fell into ripples of great regu-
larity, much resembling those in sand. I lingered
on at Winnipeg in the hope of observing the for-
mation of this snow-sand, but was unable to do
so. It is, however, certain that it is sometimes
produced by the breaking up of the ice formed
by re-freezing of melted snow. The doubtful point
is whether there is any other way in which it is
produced. Snow merely consolidated by pressure
did not ripple. I watched the action of wind upon
the material when it was composed of fairly
spherical particles ;'¢ inch in diameter—i.e., of the

122 WAVES OF SAND AND SNOW

size of fine sand—but these particles were too
friable to maintain themselves intact as projections
upon the surface.

The almost icy crust formed during the night
upon the surface of the snow-waves would, I think,
when broken up form snow-sand capable of
rippling, and I have explained how this might
perhaps be produced without melting and re-
freezing.

On the afternoon of January 25th on the prairie
near Winnipeg much of the snow-sand was drift-
ing low over the hard, unlevel surface of the old
snow, never rising more than a few inches above
the ground. The temperature was about zero
Fahrenheit, and the wind had a velocity of 27 miles
an hour—i.e., that of a strong breeze. The
low sun, casting shadows from the steeper lee
faces, threw the ripples into relief. The drift-
ing snow-sand accumulated in the shallow de-
pressions in the surface of the old, hardened
snow. These deposits quickly fell mto ripples.
The increase of their wave-length was more
rapid than that of aeolian sand-ripples, and
their motion was also more rapid. In one of these
patches of snow-sand, ripples having a wave-length
of g inches advanced that distance in I minute
50 seconds—i.e., at the rate of 49 inches per

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LIPaiviad

123

SNOW-WAVES AND SNOW-RIPPLES 125

minute, whereas the aeolian sand-ripples of the
same wave-length which I observed in 1896
travelled under the action of a wind of the same
strength at the rate of o'5 inch per minute.

For a time all the ripples in the above-mentioned
patch of sand-snow grew pari passu, each ripple
of the group having approximately the same length
and height, but after a time this state of affairs
suddenly changed, the rear ridge—that is, the one
most to windward—beginning to increase in height
very quickly. I think the change began as soon
as the patch of drifted snow-sand rose above the
level of the surrounding hard surface. When the
windward ridge raised its crest above the others I
saw that the wind eddied in its lee, and observed
that some of the snow-sand in the centre of the
patch was travelling backwards towards the weather
ridge. The other ripples, hitherto so sharply
defined in the low sunlight, became indistinct and
were soon quite obliterated, except in two very
small areas on the sides of the drift at its lee
end. The patch of snow-sand had now become
crescentic, a space in the middle having been swept
bare by the return current. It had become, in
fact, a crescentic snow-wave or snow-barchan, and
the small areas where rippling remained were the
tips of the horns or cusps. At first the profile

126 WAVES OF SAND AND SNOW

of the barchan differed from that shown in the
preceding illustrations, the summit being near the
weather end ; but the position of the summit shifted
to leeward until there was a long, gentle weather
slope and a short lee cliff. By this time erosion-
grooves began to appear at the weather end, show-
ing that the patch of snow-sand, or rather so much
of it as was not required to fill up the depression
in the old, hard surface, was now travelling
forward (Figs. 7, 8, and 9).

The best measurements which I obtained of
ripples in snow-sand were those of the group
shown in Plate XV., which were taken after
the wind had ceased. They are as follows :—

No. of Ripple. Length. Height. Length.
Inches. Inches. Height.

I 2°025 0°09375 28

2 2°625 0'09375 28
3 2°562 0°09375 27°3

4 2°344 0°09375 25

5 2°062 0°0625 33

6 2°000 0°0625 32

The ripples of this group, which diminish slightly
in size from windward to leeward, covered a patch
of snow-sand which had filled a depression in the
surface of the old, hard snow.

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sojoiyied-mous Sunjiip

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SNOW-WAVES AND SNOW-RIPPLES 129

Fig.7
A patch of rippled snew, plan.
wind from the right hand.

Fig. 8.

Conversion of above toa Barchan early stage.

130 WAVES OF SAND AND SNOW

The forms Produced by Wind-erosion in Compact
Snow.

On the prairie near Winnipeg I measured series
of the transverse ridges which are formed when
wind is removing the upper layers of consolidated
snow. They are minutely grooved, or rippled,

Fig.9

The same at a later stage

owing to their stratification. Inasmuch as they
recede before the wind, preserving their relative
positions, they may be considered to be a group
of surface waves, but the movement is due solely
to a difference in the quantity of the material
removed from the two faces, there being no

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SNOW-WAVES AND SNOW-RIPPLES 133

adhesion of the drifted particles to the windward
cliffs and no accumulation of them on the lee side,
where there is but little shelter. Six transverse
erosion-ridges had an average wave-length of
13°75 inches, the wave-length being twenty times
the height. The average variation of wave-length
from one ridge to the next was 21°5 per cent.
In another case a single erosion-wave was measured
across seven sections, giving an average wave-
length of 12°95 inches, which was 15°62 times
as great as the height.

Four erosion-waves in unstratified snow on the
smooth ice of the Assiniboine River had an average
wave-length of 23°7 inches, which was 19°2 times
as great as their height.

In the following series, of which a diagram is
given showing the stratification (Fig. 10), the
length and height of each wave was measured :—

MEASUREMENTS OF A GROUP OF EROSION-WAVES IN
Compact SNOW.

Wave Length. Height. Taehe
Inches. Inches. Height.
29°750 1875 15°87
21°625 1°750 12°36
42°125 1°750 18°36
29°500 1°375 21°45
31°625 1°250 25°30

Average variation of wave-length = 20°2 per cent.

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SNOW-WAVES AND SNOW-RIPPLES 137

The four groups of erosion-waves referred to
above have an average proportion of length to
height of 18:225; é.e., their steepness is equal to
that of waves in loose sand but less than that of
the large ripples produced when the wind cuts down
into slightly coherent sand.

The erosion-waves in compact snow are, as I
stated when describing my observations in Scot-
land, an initial form which is finally replaced
by longitudinal ridges having a similar profile.
During the intermediate stage it sometimes happens
that the depressions and not the elevations of the
eroded surface are the most noticeable forms.
Sometimes these depressions are pits, roughly ellip-
tical in plan, and of which the profile has one
long and gentle and one short and steep slope.
They have therefore a resemblance to the pits which
I described in the loose sand at Helwan, but in
the erosion form the steep cliff faces the wind.
I have not been able to make out from the accounts
of travellers whether the sides of the fuljes, or
pits, in the sand of the Arabian Nefud are in-
variably composed of loose sand or whether it is

66 2?

sometimes ‘“‘set’’ and compacted. In either case
the profile due to wind action would have the two
characteristic slopes, one long and gentle, one short

and steep, but whereas pits left among accumula-
7

138 WAVES OF SAND AND SNOW

tions of loose sand would have their steep face
turned away from the wind, pits excavated in
cohering sand would have their steep side facing
the wind.

The last erosion form in snow to which I need
refer was an uncommon one of crescentic shape,
of which I give a drawing for the purpose of com-
parison with the form’ of the crescentic waves, or
barchans, in loose snow (Fig. 11). The cliff faces
the wind instead of being turned away from it,
and the gently sloping side is concave, instead of
convex, towards the sky.

Note on the Longitudinal Sand-dunes of the
Great Indian Desert.

I deal in this book almost entirely with what
I have myself observed in the field, but the
following paragraph relates to sand-dunes which
I have not seen but which have been elaborately
mapped and mineralogically examined.

The prevailing winds in the region of the Great
Indian Desert are south-west and north-east, of
which the south-west is the stronger. Far inland
the dunes are transverse to this common direction
and face north-east. Near the sea they consist of
very long ridges with equally steep slopes on either
side and trend from south-west to north-east. At

“MOUS OY} JO UOT}LOYLAYS
dU} SUIMOYS ‘[RUIPNLSUO] puv assoasuva} ay} UddAjzoq 9]¥IPoUTd}UT Sa.njon

Is UOISOIay

Sa licam

VId

139

SNOW-WAVES AND SNOW-RIPPLES 141

‘ydeuBojoud we wos ‘4 49] OU}
wouy puim'uBYyoueg e oF SNOZo]eUe WO} U0!SOIZ

Wt 3g

142 WAVES OF SAND AND SNOW

intermediate positions they have an intermediate
form, consisting of ridges transverse to the wind
with the weather slopes longitudinally furrowed.
There are minute shells of foraminifere, composed
of carbonate of lime, in the sand of these dunes.
The source of the foraminifere is the sand blown
in from the sea-shore. The percentage of
carbonate of lime in the sand decreases with
the distance from the sea.

My theory of the origin of the longitudinal
ridges, some miles in length, which occur near
the sea is as follows: viz., that when the sand
was loose it was laid down in transverse ridges ;
that the presence of a large quantity of minute
grains of carbonate of lime caused the sand to
consolidate or set under the action of moisture ;
that the wind then cut through the dunes, forming
longitudinal ridges; and that the sand removed
from the surface of the dunes collected from right
and left under the lee of these residual ridges and
finally united in sequence the longitudinal ridges
carved out of successive sand-dunes. The gradual
change in habit from longitudinal to grooved and
ultimately to transverse dunes in proceeding inland
I attribute to the recorded diminution in the per-
centage of carbonate of lime. I intended to have
tested this explanation on the spot, but have been

“MOUS JO UOTSO.ID Aq POWIO} SoINJONIYS [eUIpNyIsuo][—

co

aLVId

eae

peer

ices

145

are ary

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lp v

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> a vo A

i
%

cay oe Lense
; Mi a ty iq

thet
iy

47

‘a4 e

“SUOTJON.AYSGO JO PIeA\Id] OF MOUS Jo sosprs yeurpnyisuoJ—tz aivid

*

ERE:

uf

SNOW-WAVES AND SNOW-RIPPLES 147

unable to do so, and I hope that some one resident
in the neighbourhood will see if the explanation
of their origin as due to setting produced by
carbonate of lime will stand the test of a detailed
examination in the field.!

The Eddy Form of Snow-waves and Snowdrijts.?

On the lee of quickset hedges, of post and
rails, and of hurdle-fences snow accumulates in
drifts or banks. I examined many of these drifts
near Montreal in December, near Winnipeg in
January and February, and again in Montreal in
February and March. In the early part of the
winter at Montreal they had the form which is most
familiar in such accumulations, the profile being
somewhat similar to that of a water-wave about
to break, a moderately steep weather slope, with
a diminishing gradient near the summit, succeeded

« See Geographical Fournal, April, 1908, “ On the Observation
of Desert Sand-dunes,” by Vaughan Cornish.

2 “Tn the range of inorganic nature I doubt if any object
can be found more perfectly beautiful than a fresh, deep snow-
drift, seen under warm light. Its curves are of inconceivable
perfection and changefulness ; its surface and transparency alike
exquisite ; the light and shade of inexhaustible variety and
inimitable finish ; the shadows sharp, pale, and of heavenly
colour; the reflected light intense and multitudinous, and
mingled with the sweet occurrences of transmitted light”
(Ruskin, ‘‘Frondes Agrestes”’).

148 WAVES OF SAND AND SNOW

by the sharp edge of a cliff or, in damper snow,
an overhanging cornice with a steep and hollowed
lee side. As the winter wore on more snow accu-
mulated in the shelter of the fence. The bank
apparently soon attained its full height, its subse-

itl

Hall

eH

l (Mi ae WAH E ROSETTA P Py rete rrp terres
HN En ERAS TT ETT

FIG. 12.—FENCE AND COMPLETED SNOW DRIFT.

|

quent growth being by extension to leeward. The
cliff edge was, however, no longer at or near the
summit of the bank, and its height progressively
diminished as the bank extended to leeward. In
its final form the bank merged with gentle slope

JN kok
— ed
ee ae SR ee ~ =

Fic. 13.—STAGES OF GROWTH OF SNOW DRIFT FORMED BY A FENCE.

to leeward in the general level of the surrounding
snow surface, there being no lee cliff (Figs. 12,
13, and 14). This completed drift, though con-
taining more snow, was a much less conspicuous
object than the cusped bank produced after the
first snowfalls. In our own country, where snow

Peet ee

so

a MR incepta la in

‘[VIIJUOJ Iv9U ‘SSuTIVI JO OPIS 9d] OY} UO RJIIp-Mous v Jo ssuIUUIsOq—'te aALVIg

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149

‘OPIS 99] dy} UO r
Appo-purmM oy} Jo JuorInS preadn oy} Jo oAInD Surmoys ‘Kodg-uo-uMO}ULID IvaU jLIp-MouSsS—'Sz ALVIg

rs

152

SNOW-WAVES AND SNOW-RIPPLES 153

does not lie continuously throughout the winter,
it must be rarely that the drift on the lee side of
any large obstruction attains completion, the
amount of drifted snow not being as a rule
sufficient to fill the whole of the eddy-space, and
in all countries it is the incomplete snowdrift,
with its overhanging cornice, which attracts atten-
tion. Thus it was not until near the end of my
winter in Canada that I learnt what was the
completed form of a stationary snowdrift.

Ct i,

Fig 14
soe CC ag agree lg Selina

I drew the profile from my observations of
drifts on the lee of fences. I drew the plan, profile,
and cross-section of drifts caused by houses and
smaller buildings. I also drew the plan, profile,
and cross-section of the hollows kept open by wind
round tree-trunks in the loose snow of the woods
near Montreal. I also drew the profiles of trans-
verse travelling snow-waves, and the plan, profile,
and cross-section of the travelling crescentic snow-
waves, or snow-barchans. I was satisfied that
there was one kind of curve, which had a blunt

154 WAVES OF SAND AND SNOW

and a fine end, which was a containing, or
boundary, curve for all these structures, but that
for the stationary structures the curve had its blunt
end to windward and for the travelling drifts or
waves to leeward, at least as far as their vertical
profile was concerned (Fig. 15).

The stationary drifts, when complete, filled the
whole curve. The travelling drifts or waves
occupied only part of it. I was at first satisfied
by the mere fact that I had recognized unity of form
among the fantastic shapes assumed by snowdrifts

Fig. 15

The Fundamental curve of snow drifts.

at various stages of their growth in the neighbour-
hood of obstructions of diverse kinds, but I
presently realized that the general curve which I
had drawn so as to satisfy my eye had a wide
significance, that it was one familiar in other
aspects of nature than snowdrifts—that it was, in
fact, the containing curve of eddies. The recog-
nition of this fact made it much easier to under-
stand the mode of formation and the movements
of the structures I had been examining in both
sand and snow, particularly when extending their
study to three dimensions and not dealing merely

‘OPIS 9d] UO JOIUIOD SUISULYAIAO SULMOYS

WR
rere)

diuury ivou yylupMousg —"9z aLvTq

a

as

ree
oe

Oy, ¥ yt wry
¥ an ry

Ni
in |

+) a) : i * ey o ‘ ‘ : ;
4 ¥ ’ ie i ¢ ih: Oe ye ¥ i

f
ft
cae v

SNOW-WAVES AND SNOW-RIPPLES 157

with the profile, which is all that is generally studied
in waves.

The general form of an eddy can be observed
by fixing a board in a vertical position athwart a
stream, the board being just submerged. The con-
taining curve of the eddy is then easily traced by
the disturbance on the surface of the water.
There is seen to be eddying disturbance for a
short distance up-stream; its margin passes close
to the edge of the board in a direction slightly
inclined outwards, the greatest width of the eddy-
curve being a little to leeward of the obstruction.
From this position the border of the eddy closes
in very gradually, so that the tail of the disturbance
is situated far to leeward of the obstruction. The
distance from the shoulder, or position of
greatest width, to the tail is several times
greater than that from the commencement of
eddying on the weather side to the shoulder. The
outline as one looks down upon the surface of
the water is similar to that of fish as we see them
from above lying head up-stream. The eddy-curve
(on which, as I shall endeavour to show, sand-
dunes, snow-waves, and snowdrifts are moulded)
is the boundary-line on either side of the axis of
the eddy, the curve being precisely repeated, as
in a reflection, by the other side. When I refer

158 WAVES OF SAND AND SNOW

to the eddy-curve I mean therefore only one-half
of the curve which encloses the area where the
surface of the water shows eddying disturbance.
If we suppose the eddy-curve to be rotated about
its longer axis, it would trace out a cigar-shaped
form, which is that which, after much experiment,
was adopted for torpedoes. At first these were
driven with their sharp end foremost, although

‘
i]
i)
4
‘
\]
i}
‘
‘

MTA (eae
a ee

Fig.\16
Plan of snow drift caused by clump of bushes , wind from the left:

every seaman knew that a spar is best towed blunt
end foremost. They steered badly, and the form
was gradually changed until the head was blunter
than the tail. Professor Hele Shaw has proved
by experiment that cigar or torpedo-shaped bodies
have greater resistance if towed with their sharp
end first, and has shown that this is due to the
drag of the eddying wake formed behind the blunt

‘purm-dn Suryoo] Uayr} JJo] puv JYSLI WOT, AS1dAUOD YOTYAM syudsiNS
dy} UdAM}OG POUJOJ ‘Opis do] UO SSP [VUIpN}suoy [Pus YyAV

‘Q
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adiuury Jvou yylIpmMoug—"L7 aALvTd

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me

Writs
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7

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"MOIA OSIOASULI} ‘OPIS 99] UO ISplI [PUIPN}ISUO] []/PWS YPIA JJLIpMOUS OY. —'Rz ALVIg

Li ig

Hip | IN\[T Tiel

ame

SNOW-WAVES AND SNOW-RIPPLES 163

stern. If a wedge-shaped solid body has to be
driven through another solid the business end of

Fig. 17
Profile (dotted) and central ISigitudinel section of the same drift

the wedge is the thin end, but if a solid has to
be driven through a liquid the blunt end is the
business end.!

The plan of a snowdrift formed by a clump of
bushes, of which a photograph and drawings are

6

‘entrance ”

ee nN a

Fig.18
Section across the dotted line of Fig. 16

given, is the whole of the head or

and part of the “tail” or “run” 2 of the eddy-
curve (Fies, 16, 17, and.13).

* Thus the wings of birds have “thick leading edges”
(see Nature, June 19, 1913, Wilbur Wright Memorial Lecture
by Mr. Horace Darwin).

2 “Entrance” and “run” are terms used by naval architects
for the swelling fore part and the narrowing after part of a
ship. The lines of the submerged portion of a ship which
are integrated in the “curve of immersed areas” should have
a bluff entrance and a fine run, which is also the form given
to non-rigid airships.

1644 WAVES OF SAND AND SNOW

Small houses, nearly square in plan, situated.
on the prairie near Winnipeg, produced a remark-
able effect upon the extremely fine, dry, drifting,
snow (Figs. 19, 20, 21). The principal part of
the accumulation which they caused was a bank,
the plan of which had the form of a much elongated
horseshoe. It was high to windward of, and on

Fig 19

PLAN

of the principal snow drift around a heuse

on the prairie,near Winnipeg,wind from the

left.
either side of, the house, becoming gradually lower
to leeward, until it merged in the general level of
the old hardened snow at a distance to leeward
which was several times greater than the length or
breadth of the house. The broadest part of the
horseshoe was not far from the lee wall of the
house, from whence the sides closed in very gradu-

‘OPIS 99] dy} UO dINJON.AYs [eUIPNyTSUOT 9S1ey YAN

‘SadiuutAy Jesu yjlip

Mous—

6z aALVIg

16

SNOW-WAVES AND SNOW-RIPPLES 167

ally to leeward. The plan of the bank therefore,
as in the case of that formed by the clump of
bushes, comprised the whole of the head, or
entrance, and part of the run, or tail, of the eddy-

‘ (_______4

in BN Le 7
FIG. 20.—PROFILE AND CENTRAL LONGITUDINAL SECTION OF SAME
SNow DRIFT.

curve. Inside the elongated horseshoe bank the
ground was quite bare of snow, the black earth
of the prairie being visible, and this bare strip ex-
tended beyond the place where the horseshoe bank

Fig. <i

Tranéverse section of snow drift anlee side ofan outhouse onthe prairie.

merged in the general level of the hardened snow,
which lay on the prairie to a depth of a few inches.
When the wind was blowing’ I watched the
long wake of high-whirling snow in the lee of these

168 WAVES OF SAND AND SNOW

houses, the cloud of extremely fine particles
stretching to leeward beyond the tail of the horse-
shoe bank. .

In December the snow in the woods near Mon-
treal was neither the fine dust nor the sand-like
grains seen on the Manitoba prairies in January
and February, but seemed to consist of the original
flat crystals in which snow falls when the air is
moderately dry and cold, but more or less broken

Fig. 29
Plan of hollow round a tree, wind from the left.
up. The trees stood in many cases fairly far apart
with little or no undergrowth, and the wind swept
through the wood. The snow remained quite loose
and light, and had no crust upon the surface.
It embraced the saplings closely, but a space of
peculiar shape remained unfilled round each larger
tree, for the larger tree causes eddying motion of
such intensity as to toss away the snow (Figs. 22,
23, 24). Round the trunk from either hand the
wind sweeps in a spiral, or corkscrew, fashion,

*(qiutuns poyutod oy} WOIF DYOUIS DYIT papudsosey }I SUTJJIIP SPM MOUS dq}
JS[IYAV) ISNOY JO IplS dd] UO SUIDADAUOD S}UITINS UIIMJOq Pd}DI[[OD MOUS Jo YULq— Ol ALVIg

169

weesoonll

4 <
ig ‘

es ae Sg a one Me \ ye

SNOW-WAVES AND SNOW-RIPPLES 171

which gives great transporting power over snow-
flakes, which, owing to their slow rate of subsidence,
are very readily suspended, but which, as they,

lie close and flat, are not much exposed to the

Fig.23
Longitudinal section of the same.
direct current of wind as it flows parallel to the
surface. The hollow space round the tree has the
eddy form both in plan and profile, and corresponds
to the space enclosed within the bank of snow,

Fig.24

Cross section of the same. lee side.

which accumulates round the houses on the prairie
near Winnipeg. Similarly shaped hollows are kept
open where boulders project above the level of
loose-lying snow (Figs. 25 and 26).

172 WAVES OF SAND AND SNOW

Isolated mounds of loose snow or sand travelling
before the wind assume a crescentic form with
cusps, or horns, pointing to leeward—the form’ to
which the name “ barchan’”’ is given. What, then,

is the connection between the shape of a barchan,

Fig’ 25
Hollow ete cut by wind, from left, arounda stone,fram a
photograph taken in Scotland February 1900,

or crescentic mound, of particles drifting before the
wind, and that of an eddy space? When a patch
of loose sand or snow happens to form during drift-
ing upon hard ground it tends to grow, because
other particles driven by the wind have their pro-
gress retarded when they pass over the soft and
porous surface. The low mounds are at first
roughly elliptical in plan, with their longer axis
parallel to the direction of the wind, and are highest
near the middle; but eddy action soon occurs.
Its first effect upon the plan of the mound is to
truncate the lee end, which becomes a nearly
straight line transverse to the wind (see ante,

‘purm oy} Aq oivq ydams aords v Surtsopous atiiwaid oy} UO BsnoYy & PUNO! YlIp-MougS—IE aALVIg

SNOW-WAVES AND SNOW-RIPPLES 175

Fig. 6, p. 114). The concentration in the centre
of the eddies from the right and left hand, however,
sweeps the snow back more rapidly there, so that
the line becomes crescentic with the extremities
advanced to leeward. The plan of the crescentic
mound is not always the same in either material.
In some cases the cusps are short compared to the
fore and aft length of main mass, and sometimes
long. In the latter case the plan somewhat re-
sembled that of the elongated horseshoe-shaped
bank of snow formed around clumps of bushes or
around houses on the prairie. Owing, however, to
the retreat of the mound the lines of the weather
end remain finer, both in plan and profile, than

Fig. 26
Hollow cut by wind.From left, around aheap of manure
ona field, from a photograph.

those of a bank which occupies the eddy-space
of a fixed obstruction, but I think the whole space
occupied by the mound itself and the eddying wind
to leeward has generally, perhaps always, the bluff

head and fine tail arrangement, so that if it were
8

176 WAVES OF SAND AND SNOW

roofed over the cover would have the shape of
a sole, plaice, or other flat-fish lying head up-
stream.

In the case of both snow-barchans and sand-
barchans there is sometimes a longitudinal ridge
projecting to leeward from the middle of the cliff
(Fig. 27). When the barchan possesses this
adjunct it is more easy to realize its structural
similarity to the swirl left when an oar leaves the

Fig. 27

Longitudinal growth on lee side of a
travelling snow-drift.

water at the end of its stroke. The surface of
the water shows an eddying disturbance travelling
astern with a boundary convex to the direction of
its motion and on the bow side, or side towards
the oar, a right-handed and a left-handed spiral
or vortex in which the water revolves round a
vertical axis. A current is visible flowing astern
and entering the whirlpool between the right and
left-handed spirals, supplying water to replace that

‘asnoyjyno ue punol puta oy} Aq Mous Jo IvaTd day MoToYE]—'ze aLvig

Si

<a nae

ct

nies JE as
Tyke fina wa

SNOW-WAVES AND SNOW-RIPPLES 179

driven below by their suction. This current corre-
sponds to the ‘‘tongue”’ of the barchan, the right
and left-handed swirls to its cusps, and the convex
boundary sternwards to the convex boundary which
the mound of sand or snow presents to the wind.
It must be remembered that as the disturbance
from the oar travels astern, so also is the motion
of the barchan relatively to the wind in the direc-
tion of its convex front, although relatively to the
ground it travels in the opposite direction.

In foaming waves, nearly breaking, there are
numerous double eddies with a forward current
between, and as the wave passes on it leaves the
foam in the form of a squat figure of 8—i.e., a
double ellipse with a bridge of foam common to
both along the line of advance of the direct current.
This line of foam corresponds to the longitudinal
tongue sometimes formed on the lee of barchans
of sand and snow.

It is of interest to consider the profile of the
eddy-spaces left unfilled between the transverse
ridges of a group of travelling waves in sand and
snow. ‘These, it must be remembered, can only
have their truly typical form if there be a deposit
of granular material below the troughs, for, if a
hard floor be exposed, it necessarily interrupts the
vertical sinuosity of the aerial current. The direct

180 WAVES OF SAND AND SNOW

wind-current leaves the surface at the crest and,
descending, strikes it again somewhere on the
weather slope of the next ridge. The surface
current of the eddy sweeps backwards from that
point to the preceding crest. The steep lee slope
and the gentle weather slope of the sand surface
show the blunt head and the fine tail of the lower
half of the eddy. The measurements of sand-waves
and sand-ripples showed their wave-length to be
eighteen times as great as their height. If the
node, or point of divergence of the surface currents,
which is at the tail end of the eddy, be halfway
between the trough and crest, then the length of
the eddy is nine times as great as the height of the
sand-wave and, as the height of the eddy cannot
be much greater than the height of the sand-ridge,
the eddy must be about nine times as long as it
is high. The core of air which revolves under the
lee of each broad sand ridge has therefore a cigar
or torpedo-shaped profile, with its blunt end up-
wind. :

A group of snow-waves near Winnipeg, with
loose snow below the troughs, had a wave-length
fifty times as great as the height. The eddy-space
had a blunt head and fine tail form, and the length
of the eddy must have been about twenty-five times
as great as the height.

‘Sodiuura je osnoy ¥ Jo apIs 99] oy} JsuIeSe MoUs pojylIp Jo yuug—'Cl aLvIg

181

SNOW-WAVES AND SNOW-RIPPLES 183

On the Distance to which Hedges and Belts of
Trees Extend Shelter from the Wind.

The wind curves round the sides of a narrow
obstruction, and its direct horizontal movement is
therefore already felt not far to leeward. In the
case of a quickset hedge, or a wall, or a belt of
trees, the distance to which shelter extends depends
upon the height of the obstruction. In the snow-
waves the direct forward wind was kept away from
the ground for a distance twenty-five times as great
as the height of the ridge. ‘Applying this to the
case of fields enclosed by thick quickset hedges, I
conclude that a hedge 5 feet high would give
effective shelter from the wind to young growing
crops for a distance of at least 125 feet. Trees
planted in long, narrow belts, in the way more
common in Scotland than in England, must extend
effective wind-shelter for a considerable distance,
that for trees of 30 feet high being at least 750
feet or 250 yards.

On the Three Modes of Deposition of Drifted
‘Material Depending upon Rate of Subsidence.

The circumstance that size, density, and shape
each have an influence on the mobility of solid
particles under the action of a current of air or
water has hampered observers and writers in their

184 WAVES OF SAND AND SNOW

efforts to classify the materials whose drifting has
to be studied, classification by size being insuffi-
cient, owing to the fact that the greater mobility
of smaller particles may be compensated by higher
density or a more compact form. There is, how-
ever, a single constant which suffices for the classi-
fication of solid particles in the order of their
mobility of drift,! and this is their rate of subsi-
dence. All solid particles may thus be arranged in
three classes. There are first the least mobile
particles, whose rate of subsidence is so great that
they only travel on the surface and are never more
than momentarily suspended. In the desert this
order of material is represented by the gravel.
When dealing with the movement of detritus by
tides and waves it is represented by shingle. If
we care to study the way in which the winds of
autumn drift fallen foliage, we shall find that the
leaves of the plane-tree come in the same category.

Passing by for the moment the middle, or second,
class, we have as the third, or most mobile, par-
ticles those whose rate of subsidence is so slow
that they are held in suspension as long as there
is any upward movement of the encompassing fluid.

t See Geographical Fournal, April, 1908, pp. 421-2, remarks
by the author on Dr. J. C. Owens’ “ Experiments on the Trans-
porting Power of Sea-Currents.”’

‘pum oy} Aq MouS Wo.J 9915 Jday 99.1] ve IvoU sovdg—'bl aLVId

“<a ors

Ss

185

SNOW-WAVES AND SNOW-RIPPLES 187

The surface layers of a deposit of such material also
drift superficially before even a very slow current.
In the case of aeolian transportation this third or
most mobile class of particles is dust. In the case
of the movement of detritus by water it is mud.

The middle, or second, term of the series com-
prises particles which subside at a moderate rate,
and material of this order is called sand, whether
it be found on land or under water. It has in
different places a different mineral composition, but
on the whole its chief component is quartz, whose
hardness and texture are such that when the
diameter of the particles is from about 35 to
about ,3, of an inch their mutual attrition by
collisions when drifting is very slow.

When dry sand is drifting before the wind on a
beach where stones lie scattered on the surface,
a single tongue of loose sand deposits behind each
projecting stone, with a sharp crest or ridge exactly
in a line with the centre of the stone. Each side
of the ridge has a concave surface. It fills the
space of dead air between the right and left-
handed halves of the vortex or eddy produced by
the stone. Much sand is whirled in the eddy, but
some of it works its way out and drops in the dead-
air space. A similar ridge of sand collects behind
a walking-stick thrust into the beach. Neither

188 WAVES OF SAND AND SNOW

gravel nor dust collects thus, for the gravel is not
caught up by the eddy, and the dust which the eddy.
catches up cannot escape.

On the prairies of Manitoba in mid-winter J
found that a projecting lump of hardened snow or
a post in the ground had ¢wo tails of drifted snow
behind it, one on either side of the central line,
each having a gently convex surface. The drifting
material of which these tails were formed was a
fine powder or dust to which much of the snow had
been reduced. This conforms so precisely to the
movement of the eddying air that it can only deposit
during lulls or calm. The rapid setting of finely
powdered snow when lying in a heap helps to make
these two-tailed drifts permanent.

White steam issuing in large quantity from a
factory chimney forms a two-tailed streamer, and
the spiral motion of the condensed steam in each
half can be easily seen. As it leaves the mouth
of the chimney it rolls downwards and inwards
from either side. When once this dual motion has
been seen in white steam it is not difficult to detect
the double whirl in the single streamer of black
smoke issuing from the funnel of a steamer.

The action of a transverse barrier upon the drift
and deposition of dust is quite different from that
by which it arrests the superficial travel of heavier

‘O'g ‘OSNOY JaIDVTH ‘mous jo sassoq—'Sl aLvid

189

SNOW-WAVES AND SNOW-RIPPLES 191

bodies. The single track of the Canadian Pacific
Railway is slightly raised above the level of the
prairies. When i crossed these great plains they
were covered to a depth of some inches with snow,
but the railway line was clear. There was a rise
of the air in passing over the obstruction, and this
was evidently sufficient to carry the snow-dust clear
of the line. There must have been an eddy, with
horizontal axis and vertical whirling formed by
the obstruction, and it seems as if the snow-dust
must have travelled over it, borne along in the un-
broken sweeping curve of the main current of air.

Particles less fine, whose rate of subsidence was
the same as that of sand, would certainly have
formed some deposit on the lee side of the obstruc-
tion, for some of them would have subsided through
the eddy and been held back by its return draught,
which flows along the ground.

I also observed that the fine snow-dust of the
prairie used to fly quite over the city of Winnipeg.
Looking out from the suburbs to the prairie on
windy days, the snow was seen to be drifting there
so as to obscure the lower story of the farmhouses,
the upper story and roof standing out clearly. In
the streets of the city there were no flying particles
of snow, but high above the air was hazy with the
poudrette, or cloud of minute snow particles, which

192 WAVES OF SAND AND SNOW

formed a translucent screen upon which haloes and
mock suns were seen in beautiful opalescence.

The above observations bear upon the question
of the best form of fence for arresting drifting
snow. Fine drift which would be wafted over a
closed fence would quickly form a deposit in the
minor eddy spaces to leeward of an open fence.
Different forms of fence might ultimately collect
the same maximum quantity of snow, but the best
form would be that which collected it most quickly,
and this would be one with, so to speak, a fine mesh.

In the late autumn I have watched) the
drifting of the large leaves of plane-trees in
London. <As the leaf drifts. some part: ‘of )1tjas
generally in contact with the ground, and although
it is occasionally in the air its flight resembles
a jump or skip, the course of the leaf being, in
the language of golf, almost all “run” and hardly
any “flight.’”’ One day, with a southerly wind, I
saw these leaves banking up against a stone step
at one of the entrances on the south side of
Kensington Gardens. The _ obstruction quite
stopped their progress until a sufficient quantity
had collected to provide an inclined plane reach-
ing the level of the top of the step. Then, as other
leaves arrived, they glided up the slope, and, sliding
along the upper surface of the stone step, invaded
the gardens.

PLATE 36.—Bosses of snow, in a valley of the Selkirk Range, B.C.

198

SNOW-WAVES AND SNOW-RIPPLES 195

The next observation relates to the action of
the eddy with a vertical axis upon the drifting
leaves of the plane-tree. The place was the broad
pavement in front of the Imperial Institute. The
building projects at the principal entrance, on the
west side of which there are two high walls facing
south and west respectively. For some time in
the autumn I noticed every day a large circular
heap of leaves of the plane-tree within this angle,
the outer edge of the heap being several feet from
both walls. As other leaves arrived, gliding over
the pavement, they circled round nearer to the
walls, but, after a time, approaching the heap, they
were either deposited against its side or were lifted
and dropped more centrally upon it. The course
of events was clear. The leaves continued to travel
until they approached the centre of the eddy, where
the air, in order to escape, had to travel upwards.
‘Here the horizontal motion of the air ceased, and
the leaves, even if momentarily lifted by the upward
current during a gust, quickly settled.

This accumulation of heavy material is in a
position similar to that in which eddies of water
scour out circular depressions in a sandy bottom,
of which the particles are readily suspended. On
the pavement in Cromwell Road I found all the
plane-leaves banking against the high wall, but

196 WAVES OF SAND AND SNOW

there was a strip of road-dust composed of sand-
sized particles at a distance of a foot or two from
the wall. The reason of this is that the wind,
ascending when it reaches the wall, drops the heavy
leaves there, their motion ceasing where the hori-
zontal current ceases, but much of the finer material
is dropped outside the eddy.

The wearing of roads made with flints produces
a grit of the size of coarse sand. This collects
in two strips on pavement under a wall, a narrow
strip against the wall and a broad strip commencing
about a foot away from the wall. The former
lies in the dead air between the inner curve of the
eddy and the angle of wall and pavement. The
latter, I presume, lies outside the space where the
eddy-current sweeps the pavement.

I have not had an opportunity of observing
where the finest kind of dust would deposit under
such circumstances, but I think it would lie between
these positions, for it would remain entangled in
the eddy as long as the wind blew and then would
drop out, forming a strip below the line where the
eddy had been.

In dealing with the intricate phenomena of the
simultaneous transport of shingle, sand, and mud
by the sea I find it best to analyse the motion of
the water into its horizontal and vertical com-

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SNOW-WAVES AND SNOW-RIPPLES 199

ponents. Where change of their relative velocity
occurs there is a change in the proportion of the
three grades of material deposited.!

On “ Banner Clouds’ and on Sandbanks to Lee-
ward of Promontories.

The following remarks are in continuation of
what has been said of structures taking the form
of tails or streamers to leeward of a narrow
obstruction.

When wind blows over a peak on a mountain
ridge the eddy on the lee side brings up air which
is in a different condition as to temperature and
moisture from that which comes over the ridge ;
and when the two bodies of air mingle with one
another the chilling of the warmer part frequently
results in the formation of a cloud—the “ banner
cloud,” which is so often seen as a stationary
streamer stretching to leeward of a mountain peak,
revealing the long eddying wake left in the wind
byo) this’ )/projection: |, Although | the.) cloud! is
stationary in position, a whirling movement can
often be seen in its substance.

On the coasts of England are several sandbanks

t See “Waves of the Sea and other Water Waves” and
Fournal of the Royal Society of Arts, November 8, 1912, Cantor
Lecture by the author on ‘Ocean Waves, Sea-beaches, and
Sandbanks.”

200 WAVES OF SAND AND SNOW

which recall by their position relatively to a head-
land, and also by their shape, the banner cloud of
mountain districts, the difference being that the
sandbank is produced in the eddy formed by a
horizontal projection, the banner cloud in that due
to an upward projection. The Shambles Shoal,
near Portland Bill, is an excellent example of a
shoal analogous to the banner cloud. It is on the
east side of the promontory, which is the lee when
the current of the flood tide is running. There is
no corresponding shoal on the west side. The
same arrangement is found near Start Point, in
Devonshire, viz., a shoal on the east, but none
on the west. I have offered as an explanation
that when the current flows up-channel—i.e., east-
wards—it is for most of the time above mean sea-
level and carries much sand from the beaches with
which the water is then in contact and which are
then stirred up by waves. During most of the
time when the current ebbs westwards, down-
channel, the water is below mean sea-level, it is
not in contact with the thick and steep part
of the beach, and the waves beat less strongly
upon the flatter part which is submerged.!
Thus, as far as the formation of sandbanks is

* See ‘‘Waves of the Sea and other Water Waves,” by
Vaughan Cornish, Part II, p. 206.

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201

SNOW-WAVES AND SNOW-RIPPLES 203

concerned, the flood tide is far more effective than
the ebb.

On the Action of an Obliquely Crossing Wind upon
the Swell of the Sea.

My observations upon the different effects pro-
duced upon sand and snow by wind-eddies with
horizontal and vertical axes respectively led me to
notice certain effects of wind upon water waves.

The following observations relate to two different
conditions of the commencement of the wave-
making action of wind upon water; first when
there is a swell—i.e., pre-existing waves, already
running in the direction of the wind; second, when
the following wind blows obliquely across the
swell.

First Case.—On December 20, 1911, I was on
the P. and ©. §.s. Egypt, not far from Cape
Finisterre, homeward bound. There was a heavy
westerly swell, of which I took measurements at
3 p.m. Its length was 640 feet, speed 39°8 statute
miles per hour, and height about 20 feet. During
the ensuing night the wind came on to blow very
hard in precisely the direction in which the swell
was running. The force of the wind at 4 a.m. on
the 2Ist was between 9 and Io of Beaufort’s scale,
or 48°5 statute miles per hour. We were at this

204 WAVES OF SAND AND SNOW

time already in the Bay of Biscay. At 8 a.m.,
when I began observations, the wind had still a
force 9°25 of Beaufort’s scale,t and therefore a
velocity of 46°5 statute miles per hour. The sea was
running perfectly true; i.e., there were no cross-
ing waves, neither did I notice any waves longer
or shorter than the great billows which followed
one another in a procession of regular ridges. The
ship being hove-to on account of the violence of
the waves, I was able to measure their size and
speed with greater accuracy than usual. Their
height was approximately uniform, being rather
more than 31 feet from trough to crest, their length
was 933 feet from crest to crest, and their speed
47 statute miles per hour. The wind maintained
its direction unaltered throughout the morning, but
by noon its velocity had decreased to 35°5 statute
miles per hour. The waves by this time had
considerably diminished in height, length, and
speed. ?
The course of events is clear. ‘When the wind
came on to blow strongly it went into eddies having
long horizontal axes, on the lee side of the level-
crested ridges of the swells, which were the only,
waves running. As long as the velocity of the

* The numbers are the average of those given by different
officers observing at the same time.

‘MOUS UI

, woosysnw-u0}nq ,, y—'6L

aLv

Id

SNOW-WAVES AND SNOW-RIPPLES 207

wind exceeded that of the waves an eddy with
horizontal axis was maintained on the lee of
each, and the ridges were rapidly increased in
height.

Second Case.—During a voyage from Southamp-
ton to Colon and back in 1912 I carefully observed
the sea when the following wind blew obliquely
across the swell. I was much struck with the
extreme slowness with which new waves grew and
the small effect of the wind upon the height of the
swell. ‘When the swell and the waves which cross
it do not differ much in height there are no wind-
eddies with long horizontal axes, but on the con-
trary, the eddies are cut up into small lengths
and have their axes tilted. In this form they can
have little effect in raising waves, and, as far
as the circulation of the air is in the horizontal
plane, it tends to create whirlpool motion instead
of waves. |

When wind begins to blow upon the plane sur-
face of an enclosed sheet of water, its wave-making
action is at first slow but afterwards proceeds
quickly. The rapidity with which short but angry
waves are formed upon lakes is a matter of common
report. Whether this is appreciably increased by
the amount of disturbance reflected from the shore

I do not know, but the rapid growth of waves is,
9

208 WAVES OF SAND AND SNOW

I think, partly due to the fact that although in lakes
there is no concurrent swell to assist the action of
the wind, there is no crossing swell to hinder it,
as there usually is at sea.

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ALVIg

CHAPTER IV.
SNOW-MUSHROOMS AND CAHOTS

Snow-mushrooms.

Weather and snowfall in the Selkirk Mountains, B.C.—
Snowcaps on high stumps of felled trees at Glacier House
resemble large mushrooms—Diameter 9 feet—Weight about
1 ton—Shape due to bending under its own weight—
Mode of growth—Reason of their permanence.

On the Sparseness of the Falling Snowflakes.

Cahots, French name for undulations made by sledges in
snow—Formed on the ice of the St. Lawrence—In the
streets of Montreal—None in Manitoba during midwinter
—Similar undulations on an ordinary rough road at
Coniston, Lancashire, produced by a sledge. Experi-
ments with a small model sledge—The undulations are
produced without an initial inequality—And during slow
and steady motion—They are due to a loose but adhesive
condition of the road — Other examples of transverse
inequalities of roads.

On ‘Snow-mushrooms.
My Canadian tour was undertaken for the study

of the forms and movements imparted by wind
211

212 WAVES OF SAND AND SNOW

to drifting snow, but, as usually happens both in
travel and research, unlooked-for things forced
themselves upon the attention, and I shall deal
here with two of these. The first is the form
of snowcaps, determined, not by wind but by
gravity ; the second, the surface-waves on snow-
covered roads, which are made, not by wind but
by sledge traffic.

Travelling by train westwards from Banff, in
the Rocky Mountains, I noticed that the snow was
of the clinging kind and collected in protuber-
ances around the base of trees and in mushroom-
shaped caps upon broken stumps. It was in the
Selkirk Mountains, west of the Rockies, however,
that the forms of clinging snow were most
strikingly exhibited. Near Glacier House, the
altitude of which is 4,000 feet above the sea, the
railway traverses a forest composed of tall, straight
pine-trees. Great numbers of these on either side
of the railway have been cut down to provide
timber for the long snow-sheds which protect the
trains from avalanches. The base of the trunk
being tough, the trees are not cut through at the
level of the ground but at a height of about
6 feet above. The result is that there are on both
sides of the railway-line hundreds of wooden pillars
about 6 feet high and of a nearly uniform diameter

ere

PLATE 41.—A nine-foot snow-mushroom seen from below.

213

Nga oe }

SNOW-MUSHROOMS AND CAHOTS 216

of 2 feet. Upon their circular table-tops the
snow collects. When the tree-stump is shorter the
cap appears as a boss projecting above the general
surface. In such cases there is a hidden cave
beneath, into which one may easily fall, and from
which it is difficult to get out when hampered
by snowshoes (Fig. 28). The moist air from
the Pacific Ocean, rising to the summits of the

Snow Mushroom with hollow beneath,
From a photograph.

Selkirk Range, which attain an elevation of about
10,000 feet, deposits a vast amount of snow. On
February 4, 1901, the registered snowfall for the
winter already amounted to 25 feet, although this
had packed on the ground to a total thickness of
5 feet. The atmosphere of the valley at Glacier
House is very still, and there is no drifting. The
snowfalls are often very rapid, sometimes as much

216 WAVES OF SAND AND SNOW

aS 12 inches collecting in one hour. The tem-
perature, I understand, often rises at such times
to near the melting-point, and the flakes are then
very large, as well as being adhesive. I stayed
nine days at Glacier House, in order to study the
snow-mushrooms, or caps, upon the tree-stumps.
When I first saw them from the train I thought
they might at any moment break under their own
weight and that they would be readily dislodged.
In fact, after passing through Glacier House to
Vancouver, whither I was bound, I took the long
journey back by the next train lest I should lose
a transitory opportunity. I found, however, that
the caps were so firm upon their pedestals that I
could not dislodge them, and I was assured by
the railway and hotel people, who were the only
inhabitants of the district, that the caps remain
to the end of the winter. I noticed, too, the
singular circumstance that all these hundreds of
snowcaps were perfect, none having broken by
their own weight. Yet their weight was some-
times as much as one ton, as I found by taking
their measurement and determining the specific
gravity of the snow. On driving a pole into a
snowcap I found that the material was neither
loose on the one hand nor icy on the other, but
tough and tenacious, which accounts for the diffi-

welve-foot snow-cap ona broken tree
at Glacier House.

T

ATE 42.

4

ea

217

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“MOTIq WOIJ UdES dvd-MoUS JOOJ-dATOMT—' Eb ALVIG

220

SNOW-MUSHROOMS AND CAHOTS 221

culty in dislodging them. The circumstance that
the overhanging caps do not when overloaded
break off close against the tree-trunk is due to
the fact that the material which has accumulated
during many snowfalls is stratified, and that the
strata bend down steeply near the edge of the
cap. Thus if there be an overloading at the rim
or edge a small break occurs at once without any
extension of fracture to the main mass. Moreover,
the dome-shaped top is so steeply inclined at its
margin that an additional load of snow would
readily slide off. The photographs show clearly
the contrast between the smooth surface of the
upper stratum of snow, bent into a dome shape,
and the rough edges of the pendent strata below,
where the snow breaks away. The tree-stump
pedestals had generally a diameter of 2 feet, and
the caps were of the nearly uniform diameter of
9 feet—i.e., the snow projected 33 feet all round.
The depth of the snow upon the pedestal was about
43 feet. Perhaps the most striking of all the snow-
caps was one which had formed upon an unusually
large tree which had been broken off by lightning,
or some other agent, at a height of more than
20 feet above the ground. The diameter of this
tree where broken was about 4 feet, and the
diameter of the cap was about 12 feet. It must

222 WAVES OF SAND AND SNOW

not be supposed, however, that the larger the tree-
stump the more striking will be the appearance
of the snowcap. On the contrary, the remark-
able winter scene in the neighbourhood of Glacier
House is due to a chance proportion between the
size of the pedestals and the quantity of the
adhesive snow. Mr. Howard Chapman, of
Victoria, B.C., sent me photographs of snow-
caps upon the stumps of the giant red-wood trees
which grow farther west, and upon these snow
about 4 feet thick merely gives the appearance
of a white thatch with somewhat projecting eaves,
there being no mimicry of the mushroom. On the
other hand, snow cannot form a perfect, overhang-
ing mushroom top upon the stumps of small trees,
because the base is not large enough for the accu-
mulation of a deep deposit ; without depth there
can be no welding into a tenacious mass, and
without tenacity there can be no overhanging
eave.

It is obvious that the dome shape of the snow-
mushroom is due to the increased bending of the
material at a greater distance from the central
support, and it may not be without interest to
remark that many trees also acquire a dome-shaped
top owing to the bending of their boughs under
the action of gravity.

EG

PLATE 44.—Snow-cap formed upon the crosspiece of a telegraph pole
and upon the wires.

223

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‘sourm puv ojod ydessapo} v uodn deo-moug—'Sb anvid

226

SNOW-MUSHROOMS AND CAHOTS 227

On the Sparseness of the Falling Snowflakes.

During a heavy snowfall the air appears thick
with snowflakes. When the fall is so heavy that
it accumulates to the depth of 1 foot in an hour,
as sometimes occurs at Glacier House, the air must
look so full of snow that the flakes would seem
to occupy a considerable proportion of the whole
space. I found, however, by timing the descent
of many snowflakes and taking an average, that
their rate of settlement was 2 miles per hour.
Therefore when snow collects at the rate of 1 foot
in an hour a column of the snowy air 2 miles,
or 10,560 feet, high and of 1 square foot section
only contains enough snow to form a deposit of
1 cubic foot in bulk. Thus the falling flakes
occupy less than one part in ten thousand of the
space in which they seem to be so crowded.

On ‘“ Cahots,” the Surface Waves Produced by
Sledges.

In December, 1901, I noticed that the snow
in some of the streets in Montreal and on the
driving track across the frozen St. Lawrence had
a remarkably undulating surface, obviously due to
the sledge traffic. The average length of these
undulations from crest to crest was 13 feet. The
length of the sledge-runners varies, but 5 to 6 feet

228 WAVES OF SAND AND SNOW

is a common size. The height of the undulations
varied considerably, 8 inches being, however, about
the usual height, reckoned from’ trough to crest.
The profile was symmetrical both in the single
track across the frozen St. Lawrence and in the
streets, where the track is double and the sledges
keep to the right-hand side. In the streets, how-
ever, the ridges were not quite at right angles .to
the course, the ridge being pushed slightly at both
ends in the direction in which the sledges are
driven, indicating a small amount of movement
since their formation.

These undulations are known by their French
name cahots, or jolts, which is the same word as

?

is used for “holes” in ordinary roads.

A long series of cahots was very quickly pro-
duced upon the frozen St. Lawrence in snow about
10 inches deep; indeed, it was surprising to see
how soon the flat snow surface overlying smooth
ice was thrown into waves by the sledge traffic.
In one of the streets of Montreal I saw the old
cahots being hacked up and the consolidated snow
relaid. It was, indeed, more like ice than snow.
At Winnipeg, during the great cold of January
and February, the snow did not form cahots, except
where, a snowdrift having consolidated, there were
one or two slight undulations, obviously made by

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SNOW-MUSHROOMS AND CAHOTS 231

the bumping of the sledges in passing over the
obstruction.

Those persons to whom I spoke about cahots
had no doubt as to their origin. The transverse
ridges and furrows, they said, were only produced
when some obstruction made the sledge bump. This
was usually hardened snow—e.g., a drift blown
across a road. Sometimes, however, the sledge
started bumping on account of a hole in the road-
way beneath the snow. I decided, however, to
examine for myself the conditions of their forma-
tion, both with respect to the movements of the
sledge and the character of the surface over which
it travels.

The motions of a sledge differ greatly from those
of a wheeled vehicle. The gliding runner meets
obstructions at a very slight, or grazing, angle, and
is very easily deflected from its course. If the
deflection be in a vertical plane, the sledge pitches
as a boat does. If the deflection be in a hori-
zontal plane, the sledge skids—i.e., swings sideways,
and is then apt to capsize. Both these pernicious
tendencies are minimized in carts by the rotation
of the wheel. The skidding, or swinging, of the
sledge is responsible for the fact that the undula-
tions produced by it are broad, instead of being
as narrow as the runners.

232 WAVES OF SAND AND SNOW

It is not only in snow that sledges produce
cahots, as I learnt after my return from Canada,
during a visit to Coniston, in Lancashire, in Sep-
tember, 1901. The road from Saddlestone slate-
quarry, on the hill called the ‘“‘Old Man of
Coniston,” is in places so steep that precautions
have to be taken in bringing down the slate.
Half the load is placed on a two-wheeled cart
and half on a sledge, which, being hitched on
behind the cart, serves as a drag for the steeper
parts of the track. When a gentler slope is reached
the sledge is run on to a wheeled truck. (Bie
steep parts of the road down which the sledge
passes are all in undulations of symmetrical pro-
file, having, like the cahots in snow, rounded crests
and troughs. The sledges pass over them in
only one direction—viz., downwards—the empty
sledges being taken up in the wheeled cart.

The length of the bottom of a sledge-runner
was measured, and found to be 4 feet 8 inches,
which is a little less than one-third of the wave-
length of the undulations, which was 14 feet
8 inches.

I arrived at Coniston on my second visit on
August 6, 1902, and occupied myself until
August 16th with a further examination of the
undulations caused by sledges.

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My first observation on ascending the steep
portion of the quarry road just above the railway-
station was that the undulations were of consider-
ably greater height, and that there were more
ridges in continuous series than was the case in
September, 1901. This I attribute to the circum-
stance that the summer of 1901 had been a dry
one, whereas that of I902 had been unusually
wet at Coniston.

Plate XLVII., from a photograph taken on
August 13, 1902, shows a series of the undulations.
The dimensions of the ridges, proceeding uphill,
were as follows, the height being taken at both
sides of the track :—

Wave Length. Height from Trough to Crest (Inches).

R.H. L.H. Mean.
a3) feet 3 -imehes ... pan OFF5 6°5 6°625
Maven CON Rk facet oh tee PTS Be |), Brae
Meh eee .) 45 ae ay eo) 70 7°00
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FOL. oS 4 are see O25 775 8:00
LOH © P ae ha OE 6:0 6°375
EDT set GE Miah “e es O75 75 8125

Mean length = 14 feet 9:2 inches. Mean height = 7°5 inches.
Wave-length divided by height = 23°685.
Wave-length divided by length of sledge = 3°165.
It will be observed that the length of the
undulations was practically the same as in 1go1,
the same sledges being in use.

236 WAVES OF SAND AND SNOW

On another side of the hill is a track from
another slate-quarry (Cove Quarry), on which
sledges are also employed. On this track also
I found undulations, but they were not so highly
developed as on the Saddlestone Quarry track. The
roadway itself was very loose, wet, and slushy.
A group of four ridges measured from crest to
crest 13 feet, 18 feet, 13 feet, and 15 feet, with
an average wave-length, therefore, of 14 feet
9 inches. The sledges were similar to those used
upon the Saddlestone Quarry track. The experi-
ments subsequently made convinced me that the
inferior development of the cahots on the Cove
Quarry track was due to deficiency of binding
power of road material.

Experiments upon the Production of ‘ Cahots.”

I proceeded to experiment upon the production
of cahots. Obtaining a large basket which had
a form something like a Laplander’s sledge, I
repaired to the little beach of sand and shingle
on the shore of Coniston Water, near the steam-
boat pier. Having weighted my “ sledge,’ which
was not on runners, and should, therefore, have
produced undulations more quickly, I hauled it
about on the coarse sand and fine shingle of
the highest portion of the beach, several feet

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SNOW-MUSHROOMS AND CAHOTS 241

above the level of the lake. It displaced the loose
material in a wave before its bows, but the track
which it made was flat.

I then tried the effect of drawing it backwards
and forwards over the same track, thinking that
in this way I might produce some undulation ; the
track, however, remained flat. I was careful
not to draw the sledge over my own foot-
prints.

Friends having come to my assistance, a higher
speed was tried, the sledge being dragged at about
8 miles an hour. I thought an undulation might
arise from the tendency of small inequalities to
make a sledge jump when moving rapidly, but
in spite of a good deal of hard work the track
of the sledge remained quite flat.

I had been trying whether undulations would
form upon a level surface, because my experience
with waves of sand and snow had shown me that
the formation of surface-waves does not require
the pre-existence of appreciable inequalities. How-
ever, as I had so far failed with the cahots, I made
a heap of loose sand, and the sledge was run
quickly over it again and again, always in one
direction. In this way an undulating surface of
regular wave-length was speedily produced by the
jumping and bumping of the sledge. First a

242 WAVES OF SAND AND SNOW

depression was scooped out to leeward of the initial
inequality, then a mound was thrown up to leeward
of the depression, and another trough was scoured
out to leeward of this, and so on, wave by wave,
the group of undulations continually extending.
There was, however, one important difference
between the experimental cahots and those usually
produced by sledge traffic. The former, as the
experiment was continued, became more and more
unsymmetrical in profile, with a gentle weather
slope and a steep lee slope, whereas the latter are
symmetrical.

I decided to change my model sledge, and
obtained a small mould, 9°25 inches long, used
for casting lead, which was very heavy, weighing
14 lb., and was suitably shaped, having the form
of a barge.

With this I began again, drawing it along slowly
and without the employment of an initial inequality.
The small, heavy sledge sank somewhat in the
loose, dry, sandy, or gravelly surface of the higher
parts of the beach, driving before it a mound of
loose particles, as in the former experiments. The
furrow quickly deepened as the sledge was drawn
backwards and forwards over the same track. My
back was turned as I hauled, so that I did not
see the sledge, but presently I noticed a change

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SNOW-MUSHROOMS AND CAHOTS 245

in the pull of the cord and, almost simultaneously,
a change in the sound made by the sledge. The
rattling over dry gravel had given place to a
muffled note, and the prow of the sledge had begun
to rise and fall. On turning to watch the sledge
the cause of this was immediately apparent. The
level of slightly damp, coarse sand had been
reached, and the pressure of the sledge soon
welded into a coherent mass the travelling mound
of material in front. The sledge then rode over
the obstruction, which after its passage was found
to be perfectly incorporated with the road-bed,
forming a gentle convexity of the surface. The
sledge at once began again to scoop up more
material and drive it in front. Presently it over-
rode the new obstruction, and a second wave-crest
was thus formed.

The undulations increased very rapidly in ampli-
tude, not only when the sledge was drawn back-
wards and forwards but also when drawn only in
one direction. The undulations were symmetrical
in profile, and similar in appearance and steepness
to the cahots of the quarry track. No appreciable
inequality was present to originate them, the speed
of the sledge throughout was only that of a very
slow walk—i.e., about 2} miles per hour—and the

pull was as steady as I could keep it. The
10

246 WAVES OF SAND AND SNOW

principal condition for the formation of an undu-
lating track by sledge traffic is, therefore, that the
material scraped from the road should be adhesive.
Neither pre-existing inequality of surface nor rapid
driving of the sledge is necessary for their forma-
tion. The undulations produced by dragging the
iron mould backwards and forwards over the same
ground averaged 2 feet 8°52 inches in length from
crest to crest, 7.€., 3°52 times the leneth ofiehe
sledge. The cahots on the quarry track were 3'225
times as long as the sledge.

In order to ascertain if the ridges on the quarry
track travelled downhill I put in iron pegs to mark
their position, hoping that observations could be
made after my departure; but the pegs could not
then be found. The opinion of the manager of
the quarry is that the ridges do not travel; he
says they become “too hard to move, being all
as if crusted and cemented together.’’ The road,
he informs me, has to be remade from time to
time, the ridges being hacked up, with considerable
labour, and the material strewn in the hollows.
The symmetrical form of the ridges supports the
impression of their immobility, particularly as the
sledge only traverses them in one direction. It
must not be forgotten that the condition of the
track varies with the weather. When the road is

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SNOW-MUSHROOMS AND CAHOTS 249

wet the cahots might at first travel, but when dry
weather supervenes the ridges would set in a hard
mass and become stationary.

Other Examples of Transverse Inequalities of Sur-
face in Roads and Paths.

The principal inequality produced by wheeled
iraiie)on a. Soft road’ or track is, of course, the
rut, or longitudinal furrow, but in harder roads
small transverse inequalities are often produced,
although I have never seen them attain regularity.
On macadamised roads the first step in their forma-
tion seems generally to be the kicking out of a
stone by the horse’s hoof. The wheel soon enlarges
the hole, and when the inequalities thus produced
are examined it is seen that they are generally a
succession of arcs of wheel-tyres separated by a
rather large stone firmly wedged. If an initial in-
equality be caused in a wood pavement by a bad,
soft block, this is speedily multiplied in both direc-
tions by the bumping of the wheels.

The action of a wheel to make holes in a stony
Hoadudis\ exactly, the reverse..of that: of 'a, roller
employed for smoothing out the inequalities of
paths. The roller, however, is drawn slowly. It
is reasonable to assume that the depressing effect

250 WAVES OF SAND AND SNOW

of a wheel or roller upon a projecting stone is pro-
portional to its weight and to the time it remains
upon the excrescence ; that is to say, it is inversely
proportional to the speed, whereas the impact against
a projecting stone will increase, I presume, as the
square of the speed. Hence the effect of slow,
heavy wheeled traffic and of light, rapid traffic will
be different in respect to the production of ruts
and of transverse inequalities respectively, the latter
being produced chiefly by rapid driving. The
difference would be more noticeable but for the
fact that vehicles used for rapid driving are gener-
ally provided with better springs than the heavy
wagons which go mostly at a foot’s-pace.

While these matters deserve attention, it must
be well understood that wheeled traffic does not
produce large and regular undulations like those
formed by sledges.

A slight transverse undulation in footpaths,
such as the Broad Walk in Kensington Gardens,
has not necessarily any connection, except that of
form, with waves. This path is highest in the
centre, so that rain runs off transversely to its
length, making transverse grooves. The places
first lowered are thus kept damper, and therefore
softer, than the intervening) spaces, so that the
hollows wear away more readily than the convexi-

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SNOW-MUSHROOMS AND CAHOTS 253

ties, and the tendency is for the path to acquire
a slightly undulating surface.

Muddy lanes are sometimes trodden into trans-
verse furrows by cattle, the intervening ridges being
separated by a uniform distance, which is equal to
the length of stride of the beasts. I have come
across several examples, the best of which was on
the track to a pond where the cattle drank, but I
have not watched the process of treading. I pre-
sume, however, that the cattle, seeking the firmer
ground, tread where their predecessors trod, thus
deepening and regularizing the troughs and leaving
the weaker ridges untrodden.

PART III

SUB-AQUEOUS SAND-WAVES

CHAPTER, V
RIPPLE-MARK AND CURRENT-MARK

Ripple-mark.

Sir G. H. Darwin’s experimental reproduction of ripple-
marks—My measurements of natural ripple-mark—Osborne
Reynolds’ experiments.

Current-mark.

In very slow streams with a smooth surface—Effect of
making the course of the stream straight—Action of current
upon a body projecting above the bed of the stream—
Current-mark in shallow streams with a waved surface
and a velocity of 1°5 feet per second—Moving down-stream
—The same in a stream with a velocity of 2:2 feet per
second move up-stream—Dr. Owens’ experiments on the
diminished rate of settlement of sand in sandy water—
Explanation of the up-stream movement of the current-
mark or sand-ripples in a shallow stream with a rapid
motion — Effect of progressive water-waves upon the
current-mark of streams—Ratio of length to height of
current-mark compared with that of ripple-mark.

Ripple-mark.

THE best known example of a sub-aqueous sand-

wave is the ripple-mark of the sea-shore, produced
257

258 WAVES OF SAND AND SNOW

by the alternating currents of the swell. If the
bottom of any vessel be covered with sand sub-
merged by water, similar ripple-marks are produced
almost at once when the vessel is rocked. The
late Sir George H'. Darwin ascertained the motions
of the water during this process by observing the
convolutions and dispersion of a dark, heavy liquid,
a kind of ink, in fact, of which he introduced a
small quantity into the water.! In these experi-
ments the time of a complete oscillation of the
water was about one second, which is nearly that
of the smallest waves formed by wind, and less
than that by which the natural ripple-mark is
usually formed, the period of the swell of the sea
being usually from about three to twelve seconds.
In Sir George Darwin’s experiments the ripples
under the action of rapidly alternating currents
could be seen to be built up from both sides by
eddies which acted in quick succession, first on one
side and then on the other, a very different action
from that of a simple current. The ripples formed
in a trough are symmetrical, as are those produced

* Mrs, H. Ayrton used, instead of ink, well-soaked ground
black pepper, from which the finer particles had been washed
away. This showed the eddying during violent motions which
would have dispersed the ink. See “The Origin and Growth

of Ripple-mark,” by H. Ayrton, Proceedings of the Royal Society,
Ser. A, 84 (1910).

PLATE 53.—Symmetrical ripple-mark produced by waves of the sea ;
at Montrose.

PLATE 53.—Unsymmetrical ripple-mark produced by waves of the sea.
259

RIPPLE-MARK AND CURRENT-MARK 261

by the swell of the sea in pools off-shore or where
the waves are not near the breaking-point. Both
are steeper than the sand-ripples formed by a
simple current. I measured a series of eighty-six
consecutive ripple-marks formed by waves on the
flat shore of the Mawdach estuary in North Wales,
and found that they had an average length of 1°99
inches and height of 0°36 inch, so that the length
was only 5°53 times the height. The measure-
ments were made after the water had receded, and,
as the ridges had not preserved the sharp crests
which they have when under water, I presume that
the height had been originally somewhat greater.
The ridges extended in broad, straight lines, and
the wave-length had an appearance of almost per-
fect regularity. The measurements gave IO per
cent. of the mean wave-length as the average
difference between the length of succeeding waves.

At Felpham, near Bognor, on the Sussex coast,
I found almost symmetrical ripple-marks left dry
on a plank. Seven ridges had an average height
of 0534 inch and an average length of 3°24
inches, so that the length was 6°07 times as great
as the height.

The late Professor Osborne Reynolds in his
working models of estuaries used “tides” with
periods of from thirty to sixty seconds, which is

262 WAVES OF SAND AND SNOW

considerably greater than those of the waves of
the sea. When the model estuary was symmetrical,
the oscillating currents, which represented natural
tides, followed the same course during ebb and
flow. In channels wholly submerged even at low
water they produced ripples in the sand which were
similar to the ripple-mark of oscillating sea-waves
in being symmetrical—i.e., having equal slopes on
either side ; but they were not so steep, the length
being twelve times as great as the height.

Current-mark.

The miniature sand-waves seen at the bottom of
clear streams have been called “ current-mark.”

I have made numerous observations of the sand-
ripples in a little stream which flows across a sandy.
beach close to where I used to live on the Dorset
coast, between Bournemouth and Poole Haven, and
have from time to time verified these observations
in other places.

The stream issued from a culvert, and flowed
at first at a speed of only 0°63 foot per second, with
a depth nowhere greater than two-thirds of an
inch. The surface of the water here was smooth
and unrippled. The sandy bottom was irregular,
having pools in places with little cliffs on their up-
stream side one-third of an inch in height. The

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RIPPLE-MARK AND CURRENT-MARK 265

distances from one cliff to another were irregular,
and although there was some approach to trans-
versality, yet in this respect, as in that of wave-
length, they did not satisfy the ideal of ripples or
waves. Two opposing influences seemed to be at
work, one trying to make transverse, the other
longitudinal cliffs. The surface of the sand was
compact and firm.

In a deeper stream which makes its way through
the sandy beach at Mundesley in Norfolk, the
velocity where it issues from its culvert was about
the same as in the last case, viz., 0°54 foot per
second, but the depth was greater, viz., 5 to 6
inches. In this stream the cliffs were at intervals
sufficiently regular to give the impression of ripples
or waves, and the average wave-length was 5°5
inches. There was a position to leeward of the
deepest places from which I could see the sand
departing in two directions, backwards towards the
foot of the preceding cliff and forwards towards
the brow of the next. The approach to each cliff
from the up-stream side was by a slope so gentle
as to be hardly perceptible. The surface of the
stream was perfectly smooth and the water quite
clear. No sand could be seen in suspension except
a little which was churned up in the pool or trench
on the lee of each cliff.

266 WAVES: OF SAND AND SNOW

The last case which I shall cite of one of these
very slow streams is that of the upper part of the
Bourne, the little brook which gives its name to
Bournemouth. This has been canalized where it
flows through the Pleasure Gardens. In the upper
part, beyond the gardens of the Corporation, where
the stream flows through the Durrant estate, there
are some reaches where the bottom is covered with
clean sand. In one of these the course of the:
stream is perfectly straight, and it flows between
perpendicular banks about seven feet apart. The
depth was 3°75 inches, and the current flowed at
the speed of 0°85 foot per second. The sand was
in ripples of the form just described—i.e., with
broad and nearly flat crests, and were not only
fairly regular in wave-length but stretched almost
the whole way across the stream in continuous
ridges at right angles to the banks. Forty-six
consecutive ripples had an average wave-length of
6 inches, and an average height of approximately
0°35 inch. I saw these in 1911, fifteen years alien
I first observed the same type of sand-ripple in
winding channels. Not until I saw the regularity
of the ridges in the canalized stream did I realize
that so slow a current could produce such regular
ripples. I had noticed, however, something of the
same kind with regard to water-waves. I have

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PLATE

RIPPLE-MARK AND CURRENT-MARK 269

pointed out elsewhere! that a winding course is
inimical to the formation of river waves of fixed
position and size, because the lower layers of water
do not flow in the same vertical plane? as the
upper, so that there is always a tendency to set up
whirlpool motion instead of wave motion.

The presence of bottom currents crossing the
direction of those of the surface is likewise inimical
to the formation of transverse sand-ridges.

I was at first much puzzled by the fact that
although the sand ripples in the Bourne were so
numerous, regular, and _ well-developed, they
appeared to be scarcely stirred by the water. I
put sticks into the sand at the edge of the little
cliffs, and after a quarter of an hour I found that
the cliffs had not moved. Now, the sand ripples in
the Branksome brook had moved half an inch per
minute under the action of a somewhat slower
current. I came to the conclusion that the current
of the Bourne had had time and opportunity to do
all it could to the sand. The troughs were covered
with coarse-grained material. The broad, nearly

* See “The Travels of Ellen Cornish” (published by W. J.
Ham-Smith, 1913), p. 134, on the waves of the whirlpool rapids
of Niagara.

2 See James Thomson “On the Winding of Rivers in Alluvial
Plains,”

270 WAVES OF SAND AND SNOW

flat crests had a very smooth surface of close-lying,
fine-grained, clean yellow sand. The slow current,
flowing with a close approximation to absolute
steadiness, both of velocity and direction, could
only move material on the nearly flat summits or
crests by pushing it along the surface. Now, it is
an accepted fact that the film of water next a solid
is almost stationary, and such must be nearly the
state in this case where the surface of the sand
is so smooth and compact. Only larger grains
projecting from the surface into the region of
appreciable current would be pushed along. This
process I conceive to have already gone on until
all the available larger grains had been rolled over
the cliff, where they had formed a covering to
the surface of the succeeding pool.

Now, in the pool to leeward of the cliff the
straightforward movement of the current is stopped,
being replaced by a gentle pumping action. The
power of the eddy to remove the sand depends,
therefore, upon the slowness with which the sand-
grains subside—i.e., for any particular kind of sand
upon its fineness. The eddy could not toss away
the coarser materials which the direct current had
rolled over the cliff, nor even raise them sufficiently
to get at the underlying finer material. The very
slow current appears therefore to be only able to

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RIPPLE-MARK AND CURRENT-MARK 273

make and move the ripples for a time, both pro-
cesses coming to an end owing to a redistribution
of material. I have not yet been able to test
the above explanation by further observations.
Returning now to the Branksome brook, I will
describe the ripples in the lower part of its course
across the sandy beach, where it flows more swiftly.
Where the velocity attained 1°5 feet per second
the surface of the water was in waves 3 inches
in length and of no great breadth of front, and
under each was a sand-wave with a rounded crest
and nearly the same profile as the water-wave.
The sand-waves had a height of 4 inch. They
travelled down-stream at the rate of 1 inch in
33 seconds, or ‘024 foot per second, the sand con-
tinually pouring over from the weather to the lee
side of the crest. This progression was, I thought,
due to that of the superincumbent water-waves,
although these were of the form called stationary,
or standing, waves. The circumstance that the
water-waves themselves travelled down-stream was
apparently due to erosion at the place of their
origin, where the sandy bank or bed was eaten
away by the action of the undeflected current.
Accordingly, when I produced a train of water-
waves by placing in the stream a stone too heavy

for the current to move, the sand-waves which
am

274 WAVES OF SAND AND SNOW

formed beneath the stationary water-waves did not
move, although the sand-grains could be seen
to travel pretty freely over their corrugated
surface. Where these things happened, with a
current of 1°5 feet per second, the water was
quite clear.

On some days it happened that the stream
acquired in its lower reaches a higher velocity,
and churned up the sand so as to form a turbid
current. Whenever this happened a train of water-
waves, each with an underlying sand-wave, imme-
diately arose. Unlike the waves last described,
their fronts quickly broadened until they extended
across the whole width of the stream. These waves
were formed when the velocity of the current was
2°2 feet per second. Their length on different
days was from 6 to g inches. The following is
the most complete measurement which I obtained
of one of the sand-waves and its superimposed
water-wave. The length of both was 9 inches.
The height of the sand-wave from trough to crest
was ? inch, which is ,, of the length. The
height of the water-wave from’ trough to crest was
1 inch. The depth of water was 13 inches on ©
the crest of the sand-wave and 1 inch over the
trough. The trough of the water was therefore
+ inch higher than the crest of the sand. It 1s,

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RIPPLE-MARK AND CURRENT-MARK 277

however, difficult to be certain of the exact level
of the surface of the sand, for below the turbid
water the superficial layers of sand are gliding
along. The superposed water-wave is, unlike the
standing waves, usually formed in natural streams
in that its front extends in a straight line quite
across the stream at right angles to the current.
It evidently owes its existence to the sand-wave,
and not vice versa. The reason why these sand-
waves suddenly arise when the velocity of the water
is sufficient to throw large quantities of sand into
suspension is, I think, revealed by a discovery made
by Dr. J. C. Owens.!' He found that sand-grains
settle more slowly in sandy water than in clear
water. Thus wherever erosion of a sandy bottom
becomes so rapid as to make the water thick the
rate of settlement is thereby diminished. Now,
the level of a sandy bottom affected by the action
of a current is only maintained constant when the
amount of erosion and deposition are equal. It
appears, therefore, that the velocity at which large
quantities of sand are thrown into suspension 1s
a critical velocity at which any minute depression
due to erosion will be immediately deepened. If
the sand, or some part of it, be heavy enough to

x Dr. J. C. Owens on “ Experiments on the Settlement of
Solids in Water,” Geographical Fournal, January, 1911.

278 WAVES OF SAND AND SNOW

stand in a ridge against the horizontal thrust of
the current, as is the case with the sand of the
Branksome brook, ripples or waves will imme-
diately form. If the sand be too light, the level
of the surface of stationary sand will be uniformly
lowered, and above it there will be a stratum of
water heavily charged with sand in suspension.
The most remarkable property of the sand-waves
produced in very shallow water when the velocity
attains about 2:2 feet per second is that they travel
up-streaam. This I have observed in the Brank-
some brook ; at Mundesley, in Norfolk; at Grange,
in Lancashire ; at Torquay, at Cannes, and in other
places. These sand-ripples which travel up-stream
are indeed formed wherever tidal waters make
their way swiftly through sand in a shallow current.
The rate of up-stream motion in the case of the
sand-ripples of the Branksome brook, of which
the dimensions have been given, was o'4 inch
per second, or 2 feet per minute. It is very curious
to see a group of these sand-ripples moving in
procession up-stream against the current which pro-
duces them. The sand can be seen tobe accu-
mulating on the up-stream face of each, whilst
the down-stream face is scoured away. If a stone
be placed in the trough between two ridges, it is
soon covered by the advances of the ridge below

RIPPLE-MARK AND CURRENT-MARK 279

it, and presently will be uncovered as the ridge
passes on up-stream. The up-stream sand-ripples
occur, as I have said, in groups, and each member
of the group moves up-stream, but the first member
—viz., that which is exposed to the undeflected
current—is being flattened out all the time and
soon disappears, number two succeeding it as the
head of the group. This in like manner continues
to travel up-stream, but its life is short, for the
current planes off the top, making the ridge flatter
until it vanishes.

I have already put forward an explanation of
the origin of these sand-ridges in a current of this
velocity. I proceed to offer an explanation of their
up-stream motion.

The shallowness of the stream causes the surface
of the water to rise at once in standing waves, and
there is no eddy on the side of the ridges, a sort
of stream-line motion being substituted. Thus the
weather face of the ridges is exposed to a shower
of the subsiding particles from the turbid liquid
denser than that which falls upon the lee side. This
is one-half of the process of up-stream motion.
The other half is, I think, due to the circumstance
that below the sandy water is a stratum of watery
sand, which is just visible and appears to be
dragged along. The firmly bedded sand, with only

280 WAVES OF SAND AND SNOW

stagnant water in its interspaces, is lower down and
cannot be seen.' Now, the superincumbent water,
being in standing waves, flows almost exactly
parallel to the surface of the sand-ripples, so that
the watery sand must be dragged up the weather
slope more slowly than it slides down the lee slope,
and there is no eddy to bring it back on the lee
side. Therefore, both on account of the sand which
travels in suspension and on account of that which
travels superficially, the ripples grow on the
weather side and lose on the lee side, consequently
advancing up-stream.

I do not think that up-stream sand-waves
would be formed in deep water, for unless the
water surface were in waves there would be an
eddy on the lee side of the sand-ridges which
would ensure a down-stream motion.

In mountain torrents I have often seen progres-
sive waves assisting in the formation of the sand-
ripples called “‘ current-mark.” The broken water
of a waterfall descends intermittently, each lump
of descending water sending out a travelling wave,?

« T examined a sample of firmly bedded sand taken from the
bed of a stream where the velocity was only 054 foot per
second, and found the volume of the interstices to be # that of
the real bulk of the sand-grains—.e., 8; of their apparent bulk.

2 See “Waves of the Sea and other Water Waves,” by
Vaughan Cornish, p. 346.

RIPPLE-MARK AND CURRENT-MARK 281

and in each pool among the boulders the whole
body of water can be seen to be heaving. On
the little beaches in backwaters the progressive
waves become steep-faced, with straight, broad
fronts, and can be seen charging obliquely upon
the shore in rapid succession. In this position the
sand-ripples are almost entirely due to the pro-
gressive waves. Thus in a backwater below Spey
Bridge, near Grantown, in Scotland, when the river
was swollen during a rapid thaw, I observed pro-
gressive waves coming in upon the shore, thirty-
four to the minute, making sand-ripples. These
were parallel to the shore, with a steeper front on
the shore side, but I could see the sand-grains
drifting with the current along the ridges, parallel
to the shore. This existence of the two modes of
motion in the sand, one general, parallel to the
ridges, the other differential, at right angles to
them, is a good illustration of the fact that sand-
ripples, though passive, are truly waves.

Except near the shallowing shores the progres-
sive water-waves in rapid rivers travel in the
direction of the river and not athwart it. They.
are not very noticeable, but can often be detected
by half-closing the eyes so as to blur the outline
of stationary bodies such as standing waves, a
device which brings moving objects into relatively

282 WAVES OF SAND AND SNOW

greater prominence. When the current and the
progressive water-waves are in the same direction
the latter no doubt assist in producing the un-
symmetrical sand-ripples called current-mark, and,
I expect, make them a little steeper than they
would be if formed by current alone. In a shallow
rock basin in a mountain torrent in Switzerland
I found a patch of rippled sand left bare. From
its position I could be sure that the ripples had
been produced by a throbbing and pulsating
current. The sand was sufficiently tenacious to
stand vertically, so that I was able to cut a longi-
tudinal section and make an impression of the
profile on paper. I found that eleven consecu-
tive ripples had an average wave-length of
0'443 inch and an average height of 0'057 inch,
the length, therefore, being 7°8 times as great
as the height, which, though less steep than the
ripple-mark of the sea-shore, is steeper than the
ripples and waves which I have measured in
steadier currents.

At Grange, in Lancashire, I measured unsym-
metrical sand-ripples still covered to a depth of
2 inches by water. The water was then stagnant
owing to the subsidence of the tide, but the ripples
had been obviously formed in a current, and the
situation was such that there was probably some

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RIPPLE-MARK AND CURRENT-MARK 285

co-operation by progressive waves. Fight ripples
had an average length of 6°156 inches and height
of o'61 inch, so that the length was Io‘! times
the height. They were sharp-crested, and there-
fore of a very different appearance from the sand-
ripples of the same length formed in the creeping
current of the canalized Bournemouth brook, which
had almost flat summits, and were only about half
the height. On the sandy road on the top of the
East Cliff at Bournemouth I found current-mark

ee DN ue aera art We ay) i
a Enso Ce

FIG, 29.—CURRENT-MARK ON ROAD AFTER THUNDERSTORM.

left after a thunderstorm. Where a pool had
formed the ripples had a wave-length of 3 inches,
and the ratio of length to height was 12°41;
but where the water had run off instead of escaping
by subsidence the ripples were left flatter, the wave-
length being 16°80 times the height. Fig. 29
shows four consecutive ridges.

In many clear rivers which have a sandy bottom
sand-ripples are a noticeable feature, ranged in
long series, sharp-crested, with gentle slope on
the weather side and steep on the lee. I may

286 WAVES OF SAND AND SNOW

recall their appearance to the memory of many
readers if I mention particularly the rippled bed
of the Tiber at Rome and of the Arno at Florence.
At Innsbruck I saw them grouped in an interesting
way on a sandbank to leeward of a broad pier
of the bridge. In this backwater the current
flowed towards the pier, and then, turning,
bifurcated and made its way to right and left
to the main streams on either side of the pier.
All these complicated currents were faithfully
recorded in the direction of the current-mark of
the sands.

In the Leven, in Lancashire, I saw current-mark
arranged in regular ridges at right angles to the
course of the river and extending from bank to
bank. The place was where the railway crosses
the tidal river on the way from Ulverston to
Windermere. I was myself a passenger in the train
and unable to reach the sands, but I judged the
wave-length of the current-mark to be about
g inches.

I am not able to establish by observation the
continuity between current-mark having a wave-
length of about 9 inches or 1 foot, which is com-
monly seen in clear, shallow streams, and the
larger sand-waves, which are generally unseen
during their growth owing to their situation or to

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287

RIPPLE-MARK AND CURRENT-MARK 289

the depth or turbidity of the water. The shortest
of these which I have measured had an average
wave-length of 4 feet. Most of my observations
of these larger sand-waves have been on sand-
banks which dry out at low water in tidal estuaries.
Their situation was generally such as to show that
they were produced either by the current of the
flood tide or by that of the ebb, and their un-
symmetrical form supports this conclusion. In
deep-water channels up and down which the tides
flow and ebb the alternating currents form, we
are told, large sand-waves of symmetrical form ! ;
but I have not had an opportunity of examining
these submerged ridges.

The question I should like to answer somewhat
more definitely than I am able is whether the
smaller current-mark and the larger current-formed
sand-wave grow at the same time and place, as
do ripples and waves formed by the action of wind
in dry sand. When one examines the larger sand-
waves on the dried-out sandbanks of tidal estuaries
one sees them rippled over with the current-mark,
and this led me to think that pulsations of the

t See Osborne Reynolds in Reports of the Committee of the
British Association appointed to investigate ‘‘the Action of
Waves and Currents on the Beds and Foreshores of Estuaries
by means of Working Models,” 1889-91.

290 WAVES OF SAND AND SNOW

current were producing the small ripples at the
same time that the large waves were being formed
by the general drift. I find, however, on re-
examination of my photographs that the current-
marks occur close to the lee of the cliff of the
large sand-waves, and that even here they face
with the direct current. But if they were formed
while the eddy was active they would, I suppose,
face towards the cliff—i.e., in the direction of the
return current. The current-mark left on the dried-
out sand-waves may therefore only be what is
formed during the subsidence of the water when
the depth is insufficient for the growth of the larger
sand-waves, and when they are, on the contrary,
being flattened out. If so, the sand-waves may
perhaps have an unrippled surface during their
growth. Further observations are required on this
point, to which my attention was called by Dr.
J. ‘C.Owens.

CHAPTER VI

SAND-WAVES IN TIDAL CURRENTS

The Mawdach Estuary, Barmouth, N. Wales, its drying sand-
banks and their waved surface—Measurements of length
and height—D shape of estuaries, influence on course of
tidal currents and effect in producing unsymmetrical sand-
waves upon the drying sandbanks—Measurements showing
how far these sand-waves depart from uniformity—Ratio
of length to height—Sand-waves in the estuaries of the
Findhorn and South Esk—The estuary of the Severn:
smooth sandbanks at Severn Bridge, waved sandbank
near Severn Tunnel ; explanation of the difference—Sand-
waves in estuary of the Dovey, North Wales—Stakes fixed
in sandbank and measurements of size and movement of
sand-waves during seventeen days—Effect of velocity of
current and depth of water upon the sand-waves—Sand-
waves upon the North Goodwin Sand—Pools left after
partial obliteration of sand-waves, similarity of their form
to that of the pits called fuljes which occur in sandy
deserts.

Sand-reefs in the Mississippi.

Their size and movement — Not true transverse waves—
Their formation in freshly deposited sediment—How the

size of the sand-grains limits the size of the sand-wave—
291

292 WAVES OF SAND AND SNOW

Suggested effect of greater heterogeneity of material to
increase the limiting size of the sand-wave—On the relation
of velocity of current to size of sand-wave in water of
sufficient depth.

WHEN visiting Barmouth, North Wales, in Decem-
ber, 1899, I was struck by the appearance of the
sandbanks left exposed at low water in the lower
portion of the Mawdach estuary. Their surface
was in waves, the length of which was generally
about 20 feet from crest to crest. The ridges,
which were sometimes nearly straight and some-
times sinuous, extended in broad wave-fronts, and
the number which followed one another in un-
broken series was often large. The variation of
length from one wave to the next was generally
about one-quarter of the average wave-length. An
unbroken series of forty-five waves was measured
on January 9, 1900, on the shoal above the railway,
bridge. The waves had their steeper face in the
direction in which the flood tide runs. The greatest
wave-length was 29 feet, and the least 8 feet.
On January 11th eleven consecutive waves were
measured on the same shoal below the railway
bridge. These also faced in the direction of the
flood tide. They varied from 21 to 34 feet in
length, and the greatest height was 2 feet 2 inches.
This part of the shoal is 2 feet lower than the sand

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293

SAND-WAVES IN TIDAL CURRENTS 295

above the bridge, the greatest depth of water upon
it, according to the chart, being 5 feet at high
water of neap tides and 9 feet at high water of
spring tides. The thickness of the sandbank itself,
or at all events of the soft deposits overlying rocky
bottom, is here about 60 feet, as has been proved
in sinking for a solid foundation to the piers of
the railway bridge.

Similar sand-waves were seen on the shoals ex-
posed at low tide on each side of the narrow low-
water channel between the island of Ynys y Bawd
and the town of Barmouth, but whereas on the
town side the ridges faced with the flood, on the
other side of the channel they faced with the ebb.
The Mawdach estuary has a very narrow entrance,
but when the tide has risen above the level of the
sandbanks it spreads over a wide interior basin.
Another character of the estuary is that a shingle
spit has grown out from the south, which is the
side on which there is the more open expanse of
sea, forcing the low-water channel close against
the hills on the north. This shape of estuary is
connected with the formation and preservation of
sand-waves upon the drying shoals, for it has the
effect of checking the current over them during the
first part of the flood tide and last part of the
ebb, allowing the currents, however, to flow strongly

296 WAVES OF SAND AND SNOW

when the shoals are covered by a considerable
depth of water.

Shortly after my visit to Barmouth I went to
Scotland in order to take advantage of a spell
of severe weather for the study of snowdrifts.
When the thaw came I sought upon the map of
Scotland for estuaries of a form similar to that of
the Mawdach, and visited those of the Findhorn
River, and of the South Esk, at Montrose, which
were shown to have the required shape. In both
estuaries I found drying sandbanks covered with
the large kind of sand-waves. In the wide in-
terior basin of the estuary at Montrose some of'
the drying banks were covered with mussels, whilst
others were of clean sand. Of the latter, one,
near the main channel by which the tide ebbs, was
in large waves, facing with the ebb—i.e., seawards.
I measured here on ‘March 6, 1907, ‘a)'senes
of fifteen waves, which had an average length of
13 feet 2°4 inches and an average height of
11°83 inches. The variation of length from one
wave to the next was 22°3 per cent: ofthe
average wave-length, so that their departure from
perfect regularity was about the same as that of
the sand-waves upon the shoals of the Mawdach
estuary at Barmouth.

The mean difference between the heights of con-

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297

SAND-WAVES IN TIDAL CURRENTS 299

secutive sand-waves was 23°57 per cent. of their
average height.

The following table shows the details of the
measurements :— |

SERIES OF FIFTEEN SAND-WAVES IN THE ESTUARY OF THE
SoutH Esk aT MONTROSE, PROCEEDING DOwNwaARDsS—
1.£.. IN THE DIRECTION IN WHICH THE WAVES FACE.

Wave-Length. Height.
18 feet 8 inches... ae fOObT i? neh
17 y) 10 ” I ”) I ”
12 yy oO ) oO ”) Il yg”
14 ” 9 bb) O y) T0’5 ”
Tf ”” 8 ) I ”) I ”
II ” O y) I ”) Oo ”
14 bb 3 ” Oo yd) Io ”)
12 pb) O ” O ” 10'5 ”
12 ” 3 ” O ”? Ir’5 ”)
12 ”) I ” I dg” I'5 ”
18 ” 6 yf I ” 6 ”
15 ” It ” Oo ” 9°5 ”
io, It ” QO) Ys, » FO! 4
se Weir ee ee oa Sosy SOW age bik Oud oe
19 ” Oo ” ° I ” 2 ”

Average ratio of length to height = 14°76.

‘All my measurements of these large sub-aqueous
sand-waves have been made after the tide had
wholly receded and left them bare. The last
runnings of the ebb over the crests (which I
observed from, a boat to be rapid) probably

12

300 WAVES OF SAND AND SNOW

flattened the waves somewhat by ploughing off the
crests and depositing sand in the troughs. On the_
other hand, the final escape of the water is by a
current which flows laterally along the troughs and
may perhaps deepen them.

The rate of advance of three of the ridges was
measured with the aid of stakes driven deeply into
the sand. Between March 7th and 8th—i.e., as
the result of two ebb’ tides—the ridges had advancea
25 inches, 25°5 inches, and 27°5 inches respec-
tively—i.e., an average of 13 inches during one
ebb tide.

During April, 1900, I went to see the sandbanks
in the estuary of the River Severn. The first which
I examined were those just above Severn Bridge,
more particularly the shoal nearest the west bank
which is named on the ordnance map the Waveridge
Sand. Its surface when left dry was almost smooth,
except for the minute ripples called “ current-
mark.’’ On April 26th, at the time of spring tides,
I watched the commencement of the flood from
the Severn Bridge, which is nearly 100 feet
above the water. The Waveridge Sand has on its
west side the main channel followed by the ebb
current and on the east a blind channel, or swash-
way, between it and the Ridge Sand. I could see
the first rising of the water progressing slowly up-

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304

SAND-WAVES IN TIDAL CURRENTS 305

stream below the bridge. The ebb current in the
main channel under the west bank, flowing swiftly
on a steep bed, was not stopped by it, but, on the
contrary, turned it aside, and the flood waters pass-
ing under the bridge filled up the blind channel
on the east of the Waveridge Sand. Everything
went quietly until the critical moment when the
incoming tide, having filled the blind channel to
the brim, overtopped the Waveridge Sand. Then
suddenly a broad sheet of water swept laterally
over from the blind channel to the main channel,
covering the shoal so quickly that the air in the
interstices of the dry sand was trapped, and could
only escape by flinging up jets of water which
spouted with great violence from all over the shoal.
Thus the flow commences as a swift current from
side to side across the shoal. Ata later stage when
there is deep water the flood tide is free to travel
longitudinally over the shoal.. As the tide at
ordinary springs rises 27 feet at Sharpness, just
below the bridge, the depth on the Waveridge
Sand at high water must be somewhere about
20 feet. During the early stages of the ebb I
watched the water flowing quietly over the shoal,
but later, when there was less water upon it, the
ebbing current rushed violently across stream over
the shoal with much noise, the surface of the water

306 WAVES OF SAND AND SNOW

being moreover in waves. Thus the circum-
stances of the flow and ebb of the spring tide over
the Waveridge Sand are such as to leave it nearly
smooth, although the currents are strong and the
waters deep. The circumstances to which atten-
tion should be chiefly drawn are the steep gradient
of the river, or estuary, and the presence of a side
channel into which the flood tide is diverted at
its commencement.

The sand or shingle spits outside the estuaries
of the Mawdach, Findhorn, and South Esk prevent
the flood tide there from finding an alternative
channel.

Lower down the estuary of the Severn, where
the Severn railway tunnel has been made, there
is a rocky shoal called English Stones, which com-
pels the incoming tide to stem the current of the
ebb and follow the principal channel under the
right bank. Thus the reach of the Severn im-
mediately above the English Stones resembles the
estuaries of the Mawdach and South Esk. The
gradient of the channel in this part of the Severn
is also much less than at Severn Bridge. A little
higher up than English Stones is the shoal called
Dun Sands. Hearing that this, unlike the
Waveridge, was often in large waves, I went down
by boat next day, April 27th. I passed many

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307

SAND-WAVES IN TIDAL CURRENTS 309

sandbanks in that part of the Severn below the
bridge where the gradient of the channel is steep,
all of which had dried out with a smooth surface.
The Dun Sands, however, was all in large sand-
waves. A series of fifteen had an average length!
of 37 feet 81 inches, and an average height of
I foot 11°22 inches, the length being, therefore,
19°49 times as great as the height. The mean
difference between the lengths of successive waves
was 26°4 per cent. of the average length, and the
mean difference between successive heights was
37°7 per cent. of the average height. These ridges
had somewhat undulating crests and sinuous fronts,
and in many places pools of water are left in the
troughs, where, my boatmen told me, salmon are
sometimes impounded. This state of things is no
doubt due to a current which sets across this part
of the shoal after the higher south-west part un-
covers during the ebb. In some places there were
two sets of ridges of almost equal size crossing
one another. The fact that the variation of height
is much greater than the variation in wave-length
is probably due to the effect of the cross current.
Its action, I think, would be more to scoop out holes
in the troughs than to raise peaks on the crests.
I was on the Dun Sands at noon. At 2 p.m.
the water began to rise. I left for the western

310 WAVES OF SAND AND SNOW

shore at 2.20 p.m. and watched from Beachley
Point. The sands were covered by 3.45 p.m., but
the English Stones were not covered until nearly
an hour later. A local pilot told me that the sands
were in an “ eddy tide”’ during the commencement
of the flood, and that at high water on this day
there would be a depth on them of fully twenty:
feet. Thus the tide covers, and, I think, leaves
the sands gently. The situation, the depth of water,
and the low gradient of the channel are such that
there must be fairly strong currents on flood and
ebb running over the sands for a considerable time
when the water is deep. Thus they are thrown
into the larger kind of sand-waves which are not
obliterated when the water leaves them.

The estuary of the River Dovey in North Wales
has extensive sandbanks, many of which are
covered with the larger kind of sand-waves. I
made observations here from May 31 to June 20,
1900. The tidal entrance clings to the north
shore of the valley, a long spit of sand and shingle
having grown out from the southern side. As in
the case of the estuaries at Barmouth and Mont-
rose, the spit formed by littoral drift has grown
from the side exposed to the longest stretch of
sea, and behind it the estuary has partially silted
up. These estuaries may be classed as D-shaped,

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311

PLATE 66.—Tidal sand-waves of which the daily
movement was measured ; Dovey estuary.

PLATE 66.—Tidal sand-waves with current-mark in troughs ;
Dovey estuary.
314

SAND-WAVES IN TIDAL CURRENTS 315

the tidal entrance being up the straight stroke,
while the space enclosed by the bow of the letter
is encumbered by sandbanks which are covered
and uncovered during the rise and fall of the tide.

From the high hills on the north shore a good
view is obtained of the whole estuary, and at low
water the arrangement and direction of the sand-
waves on the surface of the shoals is so clearly seen
that they form an excellent map of the strength
and direction of the tidal currents above low-water:
mark. The sand-waves which face with the flood
have generally broad, straight fronts, those facing
with the ebb are more sinuous.

On a sandbank called Traeth Malgwyn, in a
position bearing south from the north end of the
Pier and north-east-by-east from the Refuge, I
pegged out a plot 60 feet square, putting in five
rows of stakes parallel to the ridges, four stakes
in each row, driving them 3 feet into the sand.
Threads, stretched from stake to stake at the two
sides of the plot, were used for the measurement of
the height of the waves from trough to crest, and
also served as a datum by which to ascertain
whether there were any change in the mean level
of the sand surface. The height and length of
the waves were measured when the sands were
uncovered from June Ist to 17th inclusive, a period

316 WAVES OF SAND AND SNOW

extending from one set of spring tides to the next
with the time of neap tides between. At this time
of year, however, the spring tides are of smaller
range than near the Equinoxes. The tables
(pp. 322-5) show the results of the measurements,
and should be consulted before the reader proceeds
with the text.

On comparing the table on p. 189 with the first
it will be seen that the slight diminution in average
length between June Ist and 4th was due to the fact
that the front ridges moved more slowly than those
at the back. The ridges were not contour lines, as
the ridges of swell-formed ripple-mark usually are,
but lay along a slope inclining downwards to a low-
water channel on the north-west, so that the last
runnings of the water from the plot were along the
troughs of the waves—i.e., in a direction at right
angles to the current which produced the waves.
As the tides diminished after springs, the length
of the waves diminished very slowly, but their
height fell off rapidly, and at the time of neap
tides they were nearly obliterated, the surface of
the sandbank being almost smooth. The average
level of the sandbank was, however, unchanged.
When the tides increased after neaps, well-defined,
steep sand-waves were again formed, which grew
in height and length.

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320

SAND-WAVES IN TIDAL CURRENTS 321

ee oe ere eto

FIG. 30.—PLAN OF FIVE RIDGES SHOWING POSITIONS ON FourR
SUCCEEDING Days, Dovey Estuary. SCALE, 1” =16’.

WAVES OF SAND AND SNOW

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SAND-WAVES IN TIDAL CURRENTS 323

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WAVES OF SAND AND SNOW

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SAND-WAVES IN TIDAL CURRENTS 325

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326 WAVES OF SAND AND SNOW

In order to examine the effect of the currents
of the sea in forming the larger kind of sand-
waves I visited Mundesley, on the north coast
of Norfolk, where owing to the form' of the coast
the tidal currents might be expected to run strongly
parallel to the shore. On April 15, 1900, with
a light off-shore wind, the sands exposed at low
tide were mostly smooth, but in the “low,” or
narrow, depression parallel to the beach there were
well-preserved sand-waves, the crests of which were
at right angles to the shore, whereas the crests of
ripple-mark formed by waves are parallel to the
shore. The length of the sand-waves was 4 feet.
During the afternoon the wind came on to blow
with moderate force in a long-shore direction, and
next day the sand-waves in the “ low ”’ had a length
Of aditeet: (6 aches:

The large sand-waves on the North Goodwin
Sands are evidently formed by currents, not by,
swell. I visited this sandbank on May 12, I9goo.
The ridges faced in a northerly direction—i.e., were
opposed to the waves and to the light wind pre-
vailing at the time. The reason why they faced
with the flood and not with the ebb was evidently,
that the higher sands to the north were uncovered
three and a half hours after high water, whereas
the ebb current does not commence until four and

PLATE 69.—Tidal sand-waves at right angles to the sea shore
in a “low,” or depression ; at Mundesley.

A pale Ea, TES O

PLATE 69.—Tidal sand-waves partially obliterated on the
sea shore; at Mundesley.

327

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‘UIMpOOL) Y}ION OY} UO SOAvA-pULs [epl}—OL ALVId

330

SAND-WAVES IN TIDAL CURRENTS 331

a half hours after. Thus the ridges are sheltered
from the ebb current which runs to the south-west.

There were two sizes of large sand-waves super-
posed ; three succeeding ridges with wave-lengths
of 66, 88, and 642 feet had upon their weather
slopes smaller waves of about 15 feet in length.
The larger waves were apparently much flattened,
and their height was only about 1 foot 10 inches.

On one of the sandbanks in the estuary of the
River Dovey there were ridges which reminded
me by their size of the large ridges on the
Goodwins. I found them to be almost immobile,
the sand having become set. There are three con-
ditions of the mobility of sand—quicksand (of
which I shall have something to say later), ordinary
loose sand, and sand which has set. Sub-aqueous
sand-waves, even those which are periodically un-
covered, are less liable to setting than the sand of
dunes.

A process occurs in the obliteration of tidal sand-
waves which is of interest in connection with the
study of dunes. I refer to the formation of pools
by the washing of portions of the crest into the
trough during the recession of the tide. The
longitudinal section of the pools, with the long,
gentle slope on the one side and the short, steep
slope on the other, is that of the peculiar hollows

332 WAVES OF SAND AND SNOW

among the aeolian sand-waves called /uljes,
which I described in a previous chapter (see
Plate LXX1.).

Sand-reefs in the ‘Mississippi.

The engineers of the Mississippi River Com-
mission have made many observations upon the
ridge-and-furrow formation of the sandy bottom
of the Mississippi near Bullerton and Fulton, where
the waters of Mississippi and Ohio are not com-
pletely blended, although the distance below their
junction is about 100 miles. These ridges or reefs
are not exactly at right angles to the current,
neither do they progress without change of form.
They are, therefore, hardly to be considered as
truly waves.

“The wave (as the sand-reef is termed by the
engineers) retains its position until some change
in velocity disturbs or displaces the eddy, when
its rapid destruction, either partial or total, follows,
after which a new wave is formed under the new.
conditions . . . motion rarely takes place except
during the obliteration of the wave, when a part
of the material scoured from it is deposited imme-
diately below, thus flattening the front slope and
carrying the crest down-stream. After the wave
has under this action entirely lost its original

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SAND-WAVES IN TIDAL CURRENTS 335

form, the whole profile may gradually move down-
stream. ne

The average dimensions of the sand-reefs are

as follows :—

At Bullerton (Wide River). At Fulton (Narrow River).
Height of reefs .... 4°4 feet 4°7 feet.
Distance apart’ ... 300 i 600 *

Daily motion bee ES ‘ 22 ss
Depth’ of water”... 10 to 30 ,, 45 60 001),
Velocity of river ... 3°5 feet per second 5°8 feet per second

On the nearly flat tops of these reefs series of
regular sand-waves of about 15 feet length are
often observed, and these are at right angles to
the current.

Although the travelling reefs, wholly or partly
on account of the windings and the irregular cross-
section of the river, are not true groups of travelling
waves definite in length and permanent in form,
yet the detailed examination to which they have
been subjected throws light upon some problems
of sand-waves. The engineers report that it seems
probable that the reefs are forms which freshly
deposited sediment tends to assume under the action
of a current of sufficient velocity. The heavier
portions of the eroded material taken from their
weather slopes are deposited on the lee of the

* Report of the Mississippi River Commission, 1882, p. 108.

13

336 WAVES OF SAND AND SNOW

crests, and remain there until the progression of
the reef once more exposes them to the direct
current. But the upward currents on the lee of
the ridges carries away the lighter materials in
suspension.

These conclusions at which the engineers of the
Mississippi Commission have arrived help us to
understand how the size and weight of the particles
limit the height of sand-waves.

General Conclusions as to the Conditions of the
Formation and Growth of Sub-aqueous Sand-
waves.

Let us suppose waves in sand of uniform size
to grow in a stream of sufficient depth under the
action of a current of a certain velocity. What
property of the sand itself will ultimately stop the
growth of the waves? If the uniform sand be
light—i.e., the particles be small—the limit will
be reached owing to the inability of the upper
layers at the crest of the waves to withstand the
horizontal thrust to which they are subject between
the direct current behind them and the eddy in
front. Growth will therefore cease when the crests
are ploughed off.

On the other hand, suppose the uniform sand to
be heavy—i.e., the particles large—then for a

SAND-WAVES IN TIDAL CURRENTS 337

current of a given velocity the pumping action
of the eddy will become too weak before the direct
current becomes too strong. Therefore the growth
in height of the sand-wave will be arrested when
the upward velocity, or pumping action, of the
eddy in the trough is not greater than the rate of
subsidence of the sand-grains. If this reasoning
be correct, the large heights which the cliffs of the
Mississippi sand-reefs can maintain is partly due
to the heterogeneity of the material, hence their
being characteristic of recent sediments.

The measurements which I have made are suff-
cient to give a rough indication of the relation of
velocity of current to the length of the sand-waves
which it produces. The measurements about to be
quoted are those where there is sufficient depth
of water to admit of full development of the waves.
For two slow streams, taking the mean, I found that
a current of 0o°695 foot per second produced waves
with a length of 5°75 inches. In the estuary of the
Dovey a current of 2°93 feet per second produced
waves with a length of 124°8 inches, so that the
increase in length was much more rapid than the
increase in velocity. The length of the sand-waves
in the estuary was 21°7 times as great as that
in the slow streams. If the length increased pro-
portionally to the square of the velocity, then the

338 WAVES OF SAND AND SNOW

speed of the current required to produce waves
124°8 inches long would be 3°24 feet per second
instead of 2°93 feet per second.

The longest waves which I have measured were
on the North Goodwins, which had a length of
847 inches.

Sand-waves 1248 inches long in the Dovey
Estuary were formed by a current of 2°93 feet
per second. If the length be proportional to the
square of the speed of current, then the sand-
waves on the North Goodwins would require for
their formation a current of 7°6 feet per second, or
4°52 knots, which is somewhere about the strength
which would be met with at spring tides in such a
situation.

The group of steepest sand-waves measured on
a dried-out sandbank had lengths almost exactly
fourteen times as great as their height. If the
longest sand-waves measured on the Goodwins have
at their full development the same shape, their
height would be 5 feet. I do not know if heights
as large as this have been recorded. The Rev.
John Gilmore, in a book called ‘* Storm Warriors,”
relating to lifeboat work on the Goodwin Sands,
speaks of the lifeboat continually grounding on
“ridges 2 or 3 feet high.”

The sand-reefs of the Mississippi are not groups

SAND-WAVES IN TIDAL CURRENTS 339

of waves with definite length, and the ridges are
separated by a distance which is often one hundred
times as great as their height. It is of interest,
however, to note the height of these ridges in
relation to the speed of the current. Taking an
average of the values found for the wide and
narrow parts of the river respectively, we find that
a current of 4°65 feet per second, with an average
depth of 36 feet, maintained ridges of a height
Of 4 feet 6 mches; A. velocity of 2°93, feet per
second observed in the River Dovey gave a height
of sand-wave 9°7 inches, so that, reckoning the
height as proportional to the square of the velocity,
a current of 4°65 feet per second should give a
height of only 2 feet. The greater height of the
sand-reefs in the Mississippi is, I think, mainly
due to their not being true waves but ridges not
at right angles to the current. Thus they are main-
tained partly by lateral scour, and are not wholly
dependent for their upkeep upon the pumping
action of an eddy with horizontal axis.

CHAPTER, Vit

ON THE SMALLEST DELTA, ON THE COMPOSITION
OF QUICKSAND, AND ON “MACKEREL SKY”

On the Transverse and Longitudinal Ridges formed in the Flow of
Watery Sand, and on the Smallest Delta.

Settlement of sand through water and subsidence of water
through sand—Transverse and longitudinal ridges formed
during the latter process—Rapid deposition of the small
longitudinal ridges in radiating branches—Their diameter
equal to that of a fully grown drop of water.

On the Composition of Quicksand.

Observations of Mr. C. Carus-Wilson on presence of marsh
gas—Experiments of Mr. C. E. S. Phillips on effect of
included gas—Author’s observations on effect of imprisoned
air—On the effect of some finer earthy particles to prevent
the escape of air from sand—The three kinds of fluid:
gaseous, liquid, and granular, and suggestion that an emul-
sion of all three produces a quicksand.

On the Rippled Clouds called ‘‘ Mackerel Sky.”

Ruskin’s remark—Mathematical investigations by Helmholtz
and others—Sir G. H. Darwin’s description—The author’s
observations—Shape of the clouds—Their wave-length—

Description of author’s photographs—The positive and
340

341

.
I

ist Cliff, Bournemouth.

¢

PLATE 72.—A fan-shaped deposit of sand, showing a stream of water which soaks into the porous material
at the foot of the E

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1dJWM JY} JO 9OUNpIsqns u

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s jo sansuo,— tL aLvig

344

ON THE SMALLEST DELTA 345

negative compared—The former shows the white clouds,
the latter the blue sky—It is the latter which has the form
of ripple-mark in sand—The clouds correspond, not to
ripple-mark but to the eddies of water which make the
ripple-mark.

On the Transverse and Longitudinal Ridges formed
in the Flow of Watery Sand, and on the
Smallest Delta.

THE great variety in the position, shape, and super-
ficial inequalities of submerged sandbanks is due
to the circumstance that sand can be carried in
suspension, but that it does not follow the line of
flow of the water. Wherever the current is checked
or deflected the sand tends to collect in a heap.

In their lower course sandy streams often dry
up owing to the escape of water by percolation.
On the large scale and with gentle slopes this
process forms deltas. On the small scale, with
streamlets on steep slopes, the deltaic deposits have
curious ridges which are somewhat analogous to
the transverse ripples and longitudinal ridges
formed on the beds of sandy streams. The ridges
of these deltille, or miniature deltas, are due in
the first stage to the quick subsidence of sand in
water, but in the final stage to the rapid subsi-
dence of water through sand. These forms are
produced very imperfectly or not at all in mud-

346 WAVES OF SAND AND SNOW

flows, the separation of mud and water being too
slow.

My observations of the ridges formed in
miniature deltas were made on the Bournemouth
cliffs between Canford Cliffs, on the west, and
Southbourne, on the east. At the western end I
noticed chiefly the deposits, of which a photograph
is reproduced (Fig. 74), where during rains a tem-
porary stream had carried a large load of sand over
a steep and porous slope. The stream had appar-
ently been subject to rapid fluctuations of speed.
Whenever the speed slackened sand deposited at
the end, raising the bed and lowering the gradient ;
and presently the water subsided through this sand,
leaving it in a weald or ridge. Each succeeding
effort of the failing stream seemed to have ended
in a repetition of the process, but at a position
higher up, the final result being a long tongue of
sand transversely barred by wealds. I have not
had an opportunity of watching the process actually
at work in these tongues of sand quickly produced
during heavy rain, but the longitudinal sand-ridges,
prettily arranged like the fronds of seaweed, I have
often seen in actual formation. They are not found
on the western part of the Bournemouth cliffs, but
begin east of the Bournemouth pier and extend
beyond the Boscombe pier. They occur where

PLATE 74.—Deposit of cliff-sand, containing an admixture of fine
particles, left after subsidence of water, showing transverse
ridges ; at Bournemouth.

347

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puvs-yI[9 Jo psodaq—SZ axvig

350

ON THE SMALLEST DELTA 351

rain-water, percolating through the sandy cliffs,
reaches a layer of clay, or rather hardened mud,
which here les above the level of the beach. The
streamlet becomes reduced to a thread-like trickle,
having only the thickness of a finger, but it con-
tinues to flow for days. When it emerges at a
moderate gradient it deposits an alluvial fan, but
when it overflows the bed of clay and descends
very steeply it deposits its burden of sand in a
different manner. The stream is subject to fluctua-
tions both of velocity and direction. Diminution
of speed is immediately followed by the deposition
of a little tongue of sand at the extremity of the
stream, and the thread of water is instantly
deflected, darting out in another direction, where
another tongue of sand is quickly formed. The
process goes on very quickly, the thread of water
darting this way and that like a living thing, the
tongues of sand being built up with such quick-
ness that in quite a short space of time a very
pretty frond-lke structure is produced. The whole
process, indeed, goes on so rapidly that it would
make a good cinematograph, even if the instrument
were worked, and the picture reproduced, so as
to show the real rate of operation.

The size and shape of the tongues of sand are
of interest and significance. The surface of the

352 WAVES OF SAND AND SNOW

tongue of sand is strongly curved, and its tip is
often distinctly drop-like. The diameter of the
tongue is commonly # inch, which I find is about
the width of the larger drops in which rain collects
on the under side of the sash of a window. The
size and form of the thread-like stream of water
is, in fact, due to capillarity, and the size and
cross-section of the little tongues of sand which
it deposits are therefore determined by the same
force. The breadth of the smallest delta is there-
fore the diameter of a full-sized drop of water.

On the Composition of Quicksand.

A quicksand is one which readily swallows any
heavy body placed upon it. Dr. J. C. Owens has
shown experimentally how this condition can be
brought about by allowing water to flow upwards
through the sand.t_ Since, he says, a grain of
siliceous sand of ;!; in. diameter settles through
water at the rate of little more than o-2 foot per
second, a very slight velocity of current is capable
of lifting the grains out of contact and keeping
them separated by layers of water, so that they
will not bear weight. In Nature, Dr. Owens says,
such quicksands are due to springs finding an outlet

1 “The Transport and Settlement of Sand in Water, etc.,”
Section 9, British Association, Birmingham, 1913.

SOSPLI OS IOAsSULI] OU SUIMOYS

‘

‘yyNowouInog 4
Joye Aq WILD 9Y} UMOP pores puvs Appnut jo psodaq-——‘oL aLVvIg

358

THE COMPOSITION OF QUICKSAND 355

underneath a bed of sand. Mr. C. Carus-Wilson
has shown that there are also quicksands in which
there is no upward or other current. They are
produced by the inclusion of gas in wet sand.
Such quicksands are found in Morecambe Bay
where cockles and other organisms are present in
numbers sufficient to produce during decomposi-
tion large quantities of gas.

In a lecture upon some properties of sand
delivered at the Royal Institution Mr. C. E. S.
Phillips illustrated the effect of included gas in
quickening sand. He had two beakers con-
taining sand, to one of which water only had been
added, to the other a little carbonate and hydro-
chloric acid also. When the point of the finger
was pressed upon the surface of the sand which
contained water but no gas it penetrated only a
short distance, after which the material offered solid
resistance. When the point of the finger was
pressed upon the surface of the wet sand in the
other beaker (in which carbonic acid had been
generated, some of which was still enclosed in the
wet sand) there was no stiffening of the material,
and the finger could be pressed down without
increase of resistance.

There are three kinds of fluid—viz., gaseous,
liquid, and granular—and such a statical quicksand

356 WAVES OF SAND AND SNOW

is an emulsion of all three. I think it is probable
that the inclusion of ordinary air often makes wet
sands unable to bear a load.

I made the following observations upon the
air imprisoned in wet sand at the foot of
the East Bournemouth cliffs when I was examining
miniature deltas and mud-flows. In one place
somewhat muddy sand had flowed, with production
of wealds or transverse ribs, and had come to rest.
The surface was dry, but quaked under foot. I
found an empty beer-bottle lying on the beach,
and, holding it by the neck, I used the bottom
as a plunger, inserting it in the sand and pushing
it up and down without withdrawing it. Numerous
large bubbles of air came up, and after a time
the bottle was gripped and held pretty tightly by
the sand. Near by was an alluvial fan, or delta-
like deposit, where the sand was purer, containing
much less admixture of fine, earthy particles. It
had flowed with less formation of broad wealds
and more of the longitudinal ridges already de-
scribed, which are due to the rapid separation of
sand from water. In this deposit I inserted the
plunger and worked it up and down as before.
Some bubbles of air came up, but they were few
in number and small in size. I should add that
in both cases the working of the plunger produced

PLATE+77.—Rippled cirrus cloud, seen from Branksome Chine,
near Bournemouth.

“MACKEREL SKY” 309

some separation of sand from water, the upper
parts becoming more watery.

Near by I found a mass of wet mud which had
flowed down the lower slopes of the cliff as far
as the beach, where it had come to rest with a
sloping surface. I inserted the plunger and worked
it up and down as before, but no air-bubbles came
off and there was no separation of the water from
the earthy matter.

When sand dries, air enters its pores which, if
the sand be pure, readily escapes when it is again
wetted, but an admixture of fine earthy particles
prevents or retards the escape of air. The tenacious
character of the sands of Morecambe Bay (where
the neighbouring rocks are of limestone) doubt-
less causes the retention of the gases evolved by
decomposition of the cockles. It may also cause
an imprisonment of air during the rapid rise of
the tide, thus co-operating with the upwelling of
the water to deprive the sands of the power to bear
a load. I have already described a case in which
the flood-tide entrapped the air in a sandbank, and
in all such cases the sands would become unstable.

On the Rippled Clouds called ‘* Mackerel Sky.”

Ruskin wrote of ‘‘ mackerel ’’ clouds that “ the
vapour’...,.. falls ito; ripples like sand,” An

360 WAVES OF SAND AND SNOW

explanation of the mode of formation of these
clouds has been given by Lord Kelvin, von
Helmholtz, and Sir George H. Darwin in almost
identical terms. The last named includes a short
treatment of the subject in the paper on “ Ripple-
mark ”’ to which reference has already been made,
and the subject has frequently been treated since
in a theoretical way. The explanation is that when
a “temperature inversion” occurs in the atmo-
sphere—i.e., when a layer of warmer air lies upon
a bed of colder air—then, if there be relative move-
ment, the surfaces become waved or rippled. Sir
George Darwin writes, in the paper already cited :—
“The layer of transition between two currents
of fluid is dynamically unstable, but if a series of
vortices be interpolated, so as to form friction-
rollers, as it were, it probably becomes stable.
If one of the currents of air be colder than
the other, a precipitation of vapour will be caused
in the vortices and their shapes will be rendered
evident by clouds. . . . If one of the currents
veers, the axes of the vortices are shifted. The
existing clouds will be furrowed obliquely and the
vortical stratum will be cut into diamond-shaped
spaces determined by the intersection of the old
and new vortex axes. This would explain the
patchwork arrangement commonly observed in
mackerel sky.”

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Ays Joloyovul ,, W—"

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ALVTq

“MACKEREL SKY” 363

I have often watched mackerel clouds, which
is best done with the aid of dark glasses. It is
usually the thin white clouds of the upper air
which are rippled, but in stormy weather dark, low-
lying clouds sometimes go into parallel bars trans-
verse to the wind. In the mackerel clouds formed
at great altitudes a distance of one or two degrees
of arc from bar to bar is a common size for the
smaller ripples. This, with a distance of 30,000
feet, means a wave-length of from’ 250 to
500 feet. In stormy weather wave-clouds of much
greater wave-length are often formed in which the
scale is so large that a few of them cross the
whole sky, so that they do not produce the familiar
“miackerel-skin’’ appearance. The bars of the
ordinary mackerel clouds are generally unsym-
metrical in profile, as is shown by their being denser
in appearance on one side than the other. This
shows that, like the eddies of air or water on the
lee of sand-waves, they have a thick and a thin
end. Usually they drift with the thick end up-
stream, but occasionally I have seen them going
with the thick end foremost. Sometimes they are
produced by the furrowing of a continuous layer
of cloud, but I have also seen them forming, bar
by bar, in clear blue sky, and on looking one
wave-length ahead of the last-formed member of

364 WAVES OF SAND AND SNOW

the group I have been able to see the beginning
of the formation of a new member of the series.
The perfect bar-like form, with straight edges, does
not impart the impression of a swirling motion, but
I have often seen them begin as separate circular
or oval whirls of cloud, each like a puff of smoke,
the whirls in each transverse row growing in size
so that they come closer together until the
transverse row of whirls becomes a continuous
bar.

The best photographs which I have taken of
these clouds were obtained on August 5, 1900,
at Branksome Chine, near Bournemouth. The
barometer stood at 29°7 inches. At 8 a.m. the
sky was clouded and the air exceptionally clear,
indicating that rain was near at hand. The rain
began at 9 a.m. and continued until 3:30 p.m.
At 4.30 some blue sky was visible, some low,
drifting clouds, and higher cirrus cloud. I noticed
the latter beginning to fall into ripples, so I went
indoors and got my cameras. On coming out I
found that the ripples were already finely formed,
low down in the west. Later on the rippled clouds
spread up to the zenith, and by 6.30 p.m. they
were low down in the east, the sky overhead and
to the west being now all clear blue. Thus the
area of rippled cloud moved east before the west

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‘puvs jo y1eul-o]ddri oy} soquiesas
AJoso[o a10ur YOTYM pnoyo oy} you pue Ays onyq oY} St Wt yey} Surmoys “Yep spnoypo yy
puv jySy savoddv Ays onytq oy} YOTYA ur ‘spnofo-aaem jo ydessojoyd oy) Jo saAlwSON—og ALVId

368

“MACKEREL SKY” 369

wind. Most of the time the individual transverse
bars of cloud travelled fairly fast with the wind.

la Plates LXXIX. and’ LXXX. I have had
a photograph, which was taken looking south
at/.5-15 p.m., reproduced twice,:once in the
ordinary way as a positive print, once as a nega-
tive. The former shows the clouds as they actually,
appeared. They were drifting rapidly, and this per-
haps accounts for the fact that they are symmetrical.
The shadow of each roll of cloud is thrown on
the next cloud to the left. In the negative the
clouds appear dark, and the eye, following as it
is compelled to do the high lights, sees a different
pattern. This is the pattern of the blue sky, which
by this device stands revealed in its true form.
The blue sky is thus seen to be standing up in
sharp-crested ridges, which fit in between, and keep
apart, the whirling air, filled with particles of mist
which constitute the clouds. Thus the blue sky,
not the cloud, is the true aerial ripple-mark, the
clouds corresponding to the eddies of air or water.
But in order that the true aerial ripple-mark should
be manifest, it is necessary to adopt my device of
reversing the light and dark parts. The junctions
of the ridges are particularly deserving of notice
as showing the completeness of the similarity

between the ripple-marks of sky and sand.
14

APPENDIX

APPENDIX

CATALOGUE OF ORIGINAL PAPERS BY THE
AUTHOR ON THE SURFACE WAVES OF THE
ATMOSPHERE, HYDROSPHERE, AND _ LITHO-
SPHERE

1. ON THE FORMATION OF SAND-DuNEs. Geographical Fournal,
March, 1897.
A paper read before the Royal Geographical Society,
January 19, 1897, being an extension of a paper read
to Section E, British Association, Liverpool, 1896.

2. ON SEA-BEACHES AND SANDBANKS. Geographical Fournal,
May and June, 1898.
A paper read before the R.G.S., March 16, 1808.

3. ON KUMATOLOGY, THE STUDY OF THE WAVES AND WAVE-
STRUCTURES OF THE ATMOSPHERE, HYDROSPHERE, AND
LITHOSPHERE, Geographical Fournal, June, 1899.

The abstract of a paper read before the R.GS..
March 27, 1899.

4. ON THE APPLICATION OF THE STUDY OF WAVES TO GEO-
GRAPHY. Report of the VIIth International Geographical
Congress, held at Berlin, 1899.

A paper read at Berlin, 1899.
373

374 APPENDIX

5: ON DeEsERT SAND-DUNES BORDERING THE NILE DELTA.
Geographical Fournal, January, 1900.
A paper read before the R.G.S., November 27, 1899.

6. ON THE FORMATION OF WAVE SURFACES IN SAND. Scottish
Geographical Magazine for January, 1901.
Contains positive and negative photographs of
‘mackerel sky,” showing the pattern of the blue sky
as the true aerial ripple-mark.

7. ON SAND-WAVES IN TIDAL CuRRENTS. Geographical Fournal,
August, 1gol.
A paper read before the R.G.S., June 10, Igor.

8. CINEMATOGRAPHING THE SEVERN Bore. Geographical
Fournal, January, 1902.
A short paper read before the R.G.S., November 25,
1gOl.

g. ON SNow-Waves AND SNow-DRIFTS IN CANADA, WITH
NOTES ON THE SNOW-MUSHROOMS OF THE SELKIRK
Mountains. Geographical Fournal, August, 1902.

A paper read in part before the R.G.S., May 12, 1902,
and in part on June 10, Igor.

10. ON THE DIMENSIONS OF DEEP-SEA WAVES, AND THEIR
RELATION TO METEOROLOGICAL AND GEOGRAPHICAL
ConpiTIons. Geographical Fournal, May, 1904.

II. PROGRESSIVE AND STATIONARY WAVES IN_ RIVERS,
Engineering, 1906.
These articles are included in Part III. of the book
on “ Waves of the Sea” (vide post).

APPENDIX 375

12. PROGRESSIVE Waves IN Rivers. Geographical Fournal,
January, 1907.

13. ON SuRFACE WaAvEs PRODUCED BY SLEDGES. Proceedings
of the Dorset Field Club, 1907.
The substance of this paper was communicated to
Section G, Mechanical Science, of the British Association,
Belfast meeting, 1902.

14. THE JAMAICA EARTHQUAKE (1907). Geographical Fournal,
March, 1908.

A paper read before the R.G.S., December 9, 1907,
giving an account of the author’s experiences at Kingston
during the earthquake, and of a subsequent visit to the
island, with a map showing the distribution of damage
done by the earthquake, and the probable positions of
the areas from which the shocks came. The character
of the surface waves which overthrew buildings is
described.

15. ON THE OBSERVATION OF DESERT SAND-DUNES, Geo-
graphical Fournal, April, 1908.

A short paper of suggestions to travellers in desert
regions. It contains also the author’s theory of the
mode of formation of the longitudinal dunes of the
Great Indian Desert.

16. THE PANAMA CANAL IN Ig10. YFournal of the Royal Society
of Arts, December g, 1910.
A paper read to the Royal Society of Arts, December 7,
Igio, containing an account of the author’s examination
of the landslides accompanied by upheaval in the
Culebra Cut.

376

APPENDIX

17. ON THE CAUSE OF THE JAMAICA EARTHQUAKE OF JANUARY 14,

1907. Geographical Fournal, September, 1912.

Shows how the distribution of the damage can be
explained on the supposition that the observed redis-
tribution of load by the rivers which rise near
Hardware Gap, and the neighbouring “ gaps,” caused
subsidence and elevation in the regions burdened and
lightened respectively.

18. OCEAN WAVES, SEA-BEACHES, AND SANDBANKS. fFournal of

the Royal Society of Arts, November 1 and 8, 1912.

Two Cantor lectures, of which the first contains a
formula, based upon observations at sea, for the relation
between the velocity of the wind and the velocity,
length, height, and steepness of the waves which it
finally produces.

19. THE PANAMA CANAL AND THE PHILOSOPHY OF LANDSLIDES.

Edinburgh Review, January, 1913.
Contains a history of the landslides accompanied by
upheaval which have occurred in the Culebra Cut.

20. ON THE PANAMA CANAL AND THE FORMATION OF GRAVITA-

TION WAVES IN THE CULEBRA Cut. Geographical
Fournal, March, 1913.

A short paper on the same subject as the last, but
containing figures showing cross-sections of the Cut.

21. ON A SIMPLE METHOD OF DETERMINING THE PERIOD

OF WAVES AT SEA.

A paper read before Section A, British Association,
Birmingham Meeting, 1913.

The above papers contain the first full account of
new matter on surface waves published by the author,
with the following principal exceptions, viz., that the

APPENDIX Ol7

book on “ Waves of the Sea and other Water Waves,”
published by T. Fisher Unwin, 1910, contains in Part II.
the first account of the author’s explanation of the pre-
dominant action of waves and tides to drive shingle
and sand farther in the direction of their advance than
of their recession ; and “ The Travels of Ellen Cornish,”
published by W. T. Ham Smith, 1913, contains in the
chapter on ‘ The Falls and Rapids of Niagara”’ original
matter concerning the relation between wave motion
and whirling motion in rivers.

22. ON LANDSLIDES ACCOMPANIED BY UPHEAVAL IN THE
CULEBRA CUT OF THE PANAMA CANAL.
A paper read before Section G, British Association,
Birmingham Meeting, 1913, and printed in The Engineer,
October 17, 1913.

INDEX

Aeolian sand-ripples—
Always present on the waves, 75
Experimental reproduction of, 88
Measurements of, 81
Rate of advance, 82
Sorting of grains during rippling, 83
Aeolian sand-waves—
Angles of weather and lee slopes, 35
Height and length of, 37, 38
Mode of origin, 54, 58
Peaks and saddles on the ridges, 58
Rate of advance, 54
Ayrton, Mrs. H. on ripple-mark, 258 note

Blunt, W. S., 49

Barchan, 50, 52, 53

Barmouth, sub-aqueous sand-waves at, 292

Bournemouth, observations in neighbourhood of, 79, 262, 266,

340, 364

“Cahots,” or undulations produced by sledges, 227 ef seq.
Experiments with model sledge, 236 ef seq.
Carus-Wilson, C., 355

Cattle, treading of, produces tranverse furrows, 253
379

380 INDEX

Clouds—

‘‘Banner-clouds,” 199

Rippled, or ‘‘ mackerel sky,” 359 et seq.
Coniston, Lancs, use of sledges at, 232
Current-mark, 262 ef seq.

Travelling up-stream, 278

Darwin, Sir G. H.—
On ripple-mark, 39, 258
On rippled-clouds, 360
Delta, the smallest, 340
Dovey, river, sand-waves in, 310
Drifting materials, rates of subsidence of, 183

Eddies, 39, 46, 147, 157, 172, 176, 179, 187, 195, 203, 360,
369
Eddy-curve—
In relation to forms of fish, 157
Of ships and torpedoes, 158, 163
Estuaries, D-shaped, 310

Findhorn, sub-aqueous sand-waves at, 296
Floyer, E. A.,' 73

Foam, pattern on water-waves, 179
Fuljes, 49, 52, 332

Glacier House, B.C., snow-mushrooms at, 212
Goodwin Sands, sands-waves on, 326
Grange, Lancs, sand-ripples at, 282

Helwan, aeolian sand-waves at, 31, 41, 42
Hyde Park, snow-ripples observed in, 96

Ichthyomorphism, of snow-drifts, 157
Ismailia, sand-dunes near, 73

INDEX 381
Leaves, drifting of, 192

Medano, 50

Montreal, snow-waves near, IOI

Montrose, sub-aqueous sand-waves at, 296
Morecambe Bay, sands of, 355, 359
Mundesley, sub-aqueous sand-waves at, 326

Oar, eddying disturbance caused by, 176
Owens, Dr. J. C., 184, 277, 290, 352

Phillips, C. E. S., 355
Quicksand, on the composition of, 355

Reynolds, Osborne, 261, 289
Ripple-mark, 257 et seq.
Roads, transverse inequalities in, 249

Sand-banks, to leeward of promontories, 199
Sand-dunes—
Dew upon, 69
Effect of moist ground on formation of, 70
Illusion of great height, 66
Longitudinal, of the Great Indian Desert, 138
On route to El Arish, 61
With crest reversed, 65
Sand-grains—
Effect of electrification of, 73
Interstices between, 280
Rate of subsidence, 41
Sizes of, 32, 74
Two modes of motion of, 54
Sand-reefs in the Mississippi, 332

a

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UNWIN BROTHERS, LIMITED

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