DEPARTMENT OF THE ARMY
CORPS OF ENG!NEERS

JUL 21 1952
WOODS HOLE, MASS.

THE

BULLETIN

OF THE

BEACH EROSION BOARD

OFFICE, CHIEF OF ENGINEERS
WASHINGTON, D.C.

VOL. 6 JULY 1, 1952 NO. 3

DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS

TABLE OF CONTENTS

A Method of Separating Multiple Systems of Ocean
Waves for Detailed Study of Directions and Other

Properties COCCSHHSESHSTHFCTEHSHOHCSTESOHOSORHSHLEHTIDAE
Developments in the Science of Coastal Engineering «ssese

Notes on Determination of Stable Underwater Break-
water. Slopes COTCOROSCHRESHETHOSEHAESEHSCHOHOSHOSSFOHHOLOO

A New Method for the Graphical Construction of Wave
Refraction Diagrams COCTHSDOOOS HES OTIS CACHES TIOOOOOS

Beach Erosion StudieS ccccccsevccss20ceereccseeossersece

0 0301 OO449510 4

NANA OO

VOL. 6 July 1, 1952

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ERRATA SHEET FOR Vol. 6, No. 3 of THE BULLETIN OF THE
BEACH EROSION BOARD

All copies of the above issue dated July 1, 1952, should be marked
to indicate the following corrections:

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A METHOD OF SEPARATING MULTIPLE SYSTEMS OF OCEAN WAVES
FOR DETAILED STUDY OF DIRECTIONS AND OTHER PROPERTIES

by

H. A. WARD
Engineer, Reports and Publications Division

In past studies of water waves, primary attemtion has been given to the
measurements of individual wave trains and to refraction and diffraction
theory for a single system of waves. ‘Some attempts have been made to
determine the state of the sea for local areas through the use of stereo-
photogrammetric methods(1), but aside from this, little has been contributed
on the general make-up of the sea patterns.

Various organizations, including the Beach Erosion Board, maintain auto-
matic wave-recording devices that give a record of the change in water surface
on a height and time scale as waves pass the gaging point, but such records
give no data on the direction of approach, or on the several separate wave
systems which may be present at the time. Obviously, the energy value of
different systems that pass the gaging point, and their relative directions
of approach are of the utmost importance, since they may either augment or
oppose each other whereupon the algebraic values of the systems determine their
ability to transport material or produce other coastal phenomena of interest.

Where two or more systems of waves are present and the systems are
running at angles with each other, the record from the gages is confused
and erratic. For a period the waves may be regular, only to be followed by
a very irregular series, and occasionally out of a fairly rovgh sea, a flat
of considerable duration will appear. The study of multiple wave systems
has shown that data from a single gaging point is not enough to permit
evaluation of the forces, and because of lateral components resulting from
interference by companion wave trains, clapotis effects and flats will show
up on a record where to all appearances only generally wiiform systems of
waves are present. These lateral components have not been taken into con—
sideration in the theory of harmonic analysis for present methods of wave
recording .

Because of the irregularities shown on wave gage records, some have
concluwied what ocean waves do not conform to classical theory. However,
when the separate wave trains of a multiple system are examined, it is
found that they do conform to a surprising degree; but the crests must be
considered more in the nature of an undulating line whose full behavior

(1) Methods d'etude des Lames, M. J. Larras, Trauaux, Vol. 21, No. 58, 1937,
and Beach Erosion Board Bulletin, Vole 4, Noe 4.

cannot be recorded at a point. It is believed that clapotis groupings and
flats will average out to a uniform organization of the various systems com—
posing the state of the sea.

That wave systems do conform more closely to classical theory than one
might expect has important implications. Wave refraction theory, which is
based on a single system of waves of specific direction and period, is in
no way weakened by the knowledge that usually more than one system is present,
but instead the use of the theory is strengthened inasmuch as the various
systems can be analyzed separately and their net effects evaluated; a step
beyond present refraction procedures. This will require a reversal of
present processes; and to the betterment of the practice, refraction diagrams
may be drawn from the known inshore conditions seaward, rather than from the
computed or assumed offshore conditions to sometimes doubtful inshore results.

The development of refraction theory during the last decade is probably
the greatest contribution that has been made to coastal engineering, yet
little use has been made of refraction diagrams on the east coast of the
United States, primarily because the wide continental shelf with its many
irregular submarine features produces such complicated ray paths that they
go beyond present refraction procedures. Furthermore, the magnitude of
some of the diagrams is such that gross errors are introduced even over a
fairly uniform bottom. For example, to bring in a long-period diagram
from due east to the Long Island and Northern New Jersey cmsts it is
necessary to go some four-hundred miles offshore to the eastern edge of
Georges Bank, and even though the bottom were regular, the errors over this
distance would be considerable. Add to this the fact that the bottom
topography is most complex, causing the orthogonals to cross and sometimes
recross, any computations for values at the shore would be most unreliable.’

In view of the foregoing it is sufficient to say that present refraction
procedures are inadequate, and that attention should be given to the develop—
ment of more feasible methods of studying nearshore conditions. To that end,
the aerial photographs in the files of the Beach Erosion Board were studied
in detail, and as a result, the method of separating the wave systems and
determining their direction was developed. If accurate determination of
direction alone can be accomplished, (since indications are that even the
eye is unreliable in many cases) substantial progress will have been made,
but to be able to separate the various systems of waves that are present
and determine the directions and at least some of the other properties of
each, opens up a wide range of study for both the scientist and the coastal
engineer .

There is a wide conception that waves in deeper water are not long
crested, uniformly spaced, but are instead a series of short crests which
somehow miraculously unite in shallow water to form the breakers usually
observed. After examination of many aerial photographs this concept is
questioned. It is true that due to interferences of other wave trains:
the single crests show breaks at the instant of film exposure, such breaks

or family groupings are constantly changing position, though in general,
the wave systems maintain their organization remarkably well. When a
short-crested appearance is found, invariably two or more wave trains are
present.

While studying the aerial photographs some very interesting results were
obtained through the use of a mechanical aid in the form of a transparent
sheet on which parallel lines had been ruled, spaced about ten to the inch.
This was used to separate the individual wave systems appearing in the
picture and oftimes to the astonishment of the viewer, order appeared out
of a turbulent state of the sea that seemed devoid of orderly arrangement.

In mking the aid, fairly thin lines were ruled on clear cellophane
spaced as previously mentioned. In lieu of the above, a sheet of No. 79
Zip-A-Tone will give good results. In use, the sheet is rotated until one
train of waves appear, then aligned generally with the system viewed to
disclose the other. The same procedure is used with secondary systems
that are running with the primary systems. In some areas, such as the west
coast of the United States, long period swells may be running with the lesser
systems, but these will usually be obvious without an aid.

Photographs in which waves have only minor irregularities and the image
has the appearance of a single system should not be discounted. The smaller
the angle the crests make with each other, the more the wave pattern will
appear as a single unit, nevertheless, as long as the tell-tale interruption
of crests is present, multi-directional groups are indicated.

The accompanying photographs will illustrate the application of the
principles. Figure 1-A has two obvious wave trains, one a minor system
approaching from the upper left corner, and the other the more prominent
system which has the broken-crest characteristics. Figures 1-B and 1-0
show the latter to be two trains, each conforming to classical theory re-
markably well. Figure 2-A is an example of a turbulent condition of the
sea in which, although no wave patterns are clearly show in the offshore
area, two wave systems can be traced into the surf zone as shown in Figures
2-B and 2-C. Note particularly that each maintains its separate identity
through the surf, and that each produces littoral currents. In one portion
of the picture these currents oppose each other and in another portion they
augment each other.

Based on the many pictures examined, the conclusions are reached that
single wave trains are rarely found in the nearshore area and that multiple
systems are the rule. On the west coast of the United States the secondary
systems are often greatly overshadowed by the heavy swells which, of course,
are the more significant waves as far as coastal engineering is concerned.
Of the heavier swells, some approach from the northwest and concurrently
the southerly swells may be running, whereupon the condition is no different
than that of other coastal regions, and if net littoral forces are to be
determined the result must be the algebraic sum of the various systems. On
the east coast many of the pictures show waves that appear similar, which

suggests that they are crossed trains resulting from refraction of a single
deep water wave.

The use of this simple method of sorting the wave systems opens up
possibilities for greater use of aerial photographs as a basis for the study
of local areas. It will be noted that once separated, the wave lengths are
more measurable and therefore provide a good basis for various computations.
In such matters as the investigation of the formation of "finger shoals"
or the unusual concentration of wave action at one point, the contributing
factors can be traced from known conditions in the shore vicinity.

As a natural consequence of two or three trains running at an angle
with each other, they must at intervals synchronize and assume some harmonic
arrangement. Disregarding lateral components fer the moment, the determina—
tion ef this arrangement from a single gage record would require a slow,
costly analysis of the harmonic contents, which when completed would still
give no information on the angle of impingement on the shore. Where aerial
photographs are available or perhaps where the wave train directions and
length or period can be established by direct observations, or by recording
instruments developed for the purpose, a basis will have been provided for
a more simplified analysis, for then the major components of the record will
have already been set apart. Remembering that the appearence of the
individual system is such that a record of any one alone would be fairly
regular, the harmonic analysis of the group would be greatly simplified.

More definite knowledge of the complexities of wave patterns points up
some of the difficulties that have been encountered in attempts to develop
wave direction recorders,in particular, the attempt by the Beach Erosion Board
te use the Rayleigh Disk for that purpose(2). Under the influence of multiple
forces the disk attempted to align to momentary predominance or result ants,
therefore the desired result was not obtained.

At the present time no adequate method exists for the determination of
wave directions. It is even questioned whether present visual methods are
reliable, for in most cases they are made in connection with dye tests,
float runs, or some other activity, and are usually taken from some point
low en the beach. Scripps Institution of Oceanography madd a study of long—
shore currents(3) which disclosed unexplained behaviors that may have been
due to difficulties in determining the composition of the sea and the
direction of approach of the various systems. Commenting on the direction
observations the report states, "The field assistants who made most of the
observations, did not feel confident in all these observations since many
(2) "The Rayleigh Disk as a Wave Direction Indicator", Beach Erosion Board

Technical Memorandum No.°18.
(3) "Longshore Current Observations in Southern California", Beach Brosion
Beard Technical Memorandum No. 13.

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of them were made very close to sea level and the waves were often so much
confused that it was very difficult to be sure of the direction of approach
of the principal wave trains." Regarding unexplained current behaviors

it states; “....there appear to be a considerable number of appreciable
currents where the approach was normal and even a number of currents which
appeared to flow in the wrong direction so far as wave approach was con—
cerned." In view of their experience it is concluded that the determination
of the direction of approach of principal wave trains from a point low on
the beach is difficult, and that reliable observations for multiple systems
is practically impossible. In the subject study, the extent to which un-
recognized multiple wave systems may have influenced the results can never
be known, but it is noted that dual wave trains from the north were not
given recognition in an illustration used (aerial photo, Newport Bay, their
Figure 14).

In connection with a study by the Beach Erosion Board at Mission Bay,
Galifornia, it was found that of the several observational procedures, a
satisfactory method of determining wave direction presented the greatest
problem. A sighting bar(4) was devised for use with a transit and its
usé improved the results as far as the predominant waves were concernedo
Observations were made from the bluff, and no attempt was made. to separate
wave systems.

Every test made up to the time of writing indicates that the parallel
lines method is the most economical and convenient means yet devised for
determining directions, and for studying general sea surface conditions,
particularly for those who have a file of aerial photographs available.

Were it necessary to fly pictures for wave study alone the expense could
scarcely be justified, but since it appears that similar but limited results
can be obtained from photographs taken from some high point on the shore,
the method comes within the reach of all.

Figure 3 is an oblique photo showing good wave action at Jones Beach,
Long Island, New York, In the center and bottom prints, the two principal
wave trains have been separated, and it can be seen that each train has a
positive direction of approach that can be measured. Note how well the two
systems conform to classical theory. Furthermore, when the camera height
is know, the wave lengths can be computed and other data derived.

The illustration used has a fairly high oblique angle. Field tests
have not been made to determine how low the angle aan be and still give
satisfactory results, but judging from pictures taken from the pavilion on
the Steel Pier at Atlantic City, New Jersey, in connection with stereophoto—
grammetric wave measurements(5), which were relatively low in oblique angles,
the lower limit comes well within the heights of the usual vantage points
found on the seashore.

(4) "A Method of Estimating Wave Direction", D. R. Forest, Beach Erosion
Board Bulletin, Vol». 4, Noo 2.
(5) “Stereophotogrammetric Wave Measurements", BEB Bulletin, Vol. 4, Noo 4eo

12

Deep water wave have been separated in sea-rescue pictures in the files
of the Coast Guard which were taken from the Coast Guard Cutter, and were
probably lower in oblique angle than those from the Steel Pier. It is of
particular significance that deep-water waves as viewed from a vessel respond
to the parallel lines method, for now all that is needed to obtain a wide
collection of data is a simple method for making observations directly
without need for photography. Such a device is under development but must
still be tested under dynamic conditions where the wave systems are in con-—
stant motion, before it is known whether the present design will be adequate.

13

DEVELOPMENTS IN THE SCIENCE OF COASTAL ENGINEERING

by

Captain Peter Somers, Executive Officer,
Beach Erosion Board, Corps of Engineers

Geologists tell us that the approximate age of the earth is somewhat
more than two billion years, and that during the early part of that time,
in response to the pull of the sun the molten liquids of the earth's sur-
face rolled around the globe and that its atmosphere contained much hydro-
gen. Unlike the sun and her sister planets, our small globe had not enough
gravitational pull to retain the light and fast moving hydrogen molecules,
with the result that in a few thousand years, most of them had dispersed
into space, and the remainder combined with oxygen to form water vapor.

As the atmosphere cooled further the water vapor began to condense, ~
probably at first to be on the night-shaded side of the earth, Further cool—-
ing permitted the patches of condensed water to spread am increase in volume.
Based on the same theory, it is further believed that when the patches of
condensed water became permanent, the first ocean was born.

We are also told that the ocean contains an untold wealth of minerals
including silver aml gold, which can actually be ours if we can determine
how the sea can be made to yield its riches.

This promise of good fortumme however is of little comfort to the many
states, communities and individuals who find this very same ocean unleashing
with terrific fury its damaging forces against their worldy possessions,
the land adjoining the ocean and the structures provided to prevent the land
from eroding. Erosion is a natural agency which down through the ages has
been causing continual changes in land levels and shore lines.

The history of any shore line is one of continual mobility and change,
molded and remolded by the forces in breaking waves. Where shores are unde-
veloped, variations in the beach are not considered too important to local
interests, and recession of the shore line and mthods of preventing such
recession are of little concern. The problem becomes more acute however,
when intense development crowds the shore, amd property owners become aware
of the forces of nature. When the ocean begins to lap at their doors a
loud cry for immediate protection is raised.

The United States possess more than 20,000 miles of tidal shore line
(besides the shore of innumerable lakes and rivers) which include a large
number of beach areas of more than local significance. Such beach areas
are the popular holiday resorts of the nation. The habit of going to the
sea shore is so firmly established as a means of healthful recreation that
extensive development has resulted on many of the beach areas near popula—
tion centers.

14

There appears to be the universal desire to be close to the water.
The land closest to the water usually has the greatest value. Very little
consideration of the many forces involved in such areas is shom, in fact
the dangers are not actually known until the stability of the beach is up-
set by an attack of wind and waves.

The average engineer finds his interests far removed from the subject
of beach erosion until such times as he finds himself confronted with such
a problem; however, the engineer whose field of learning includes oceano—
graphy, coastal geomorphology, geology, meteorology, hydrology, soil
analysis and hydraulics, will find the study of shore phenomena a most
facinating and interesting subject.

The accumulated thinking and experiments of many generations to resolve
the physical laws that govern the natural forces affecting the loss of the
land to the sea have provided a large amount of knowledge to be utilized by
the research engineer of today.

The importance of coastal phenomena in connection with studies of
beaches and marine structures has long been known to the Corps of Engineers,
particularly in the realm of river and harbor works, and it is agreed that
while considerable advancement has been noted during the last two decades,
the scientific study of beach erosion and shore protection is just now
coming into its own.

Beach Erosion Board Problems

The shore problems studied by the Beach #rosion Board fall into three
general categories; (1) problems of stabilization and rehabilitation of beach
areas (these are the problems of beach loss or damage that occasioned and
justified the establishment of the Board originally); (2) problems arising
from the effects on adjacent shore lines of the provision of navigation chan—
nels from the sea or lake into rivers and inlets; (3) problem of shore con-
trol associated with harbor protective works.

The activities of the Board during the past twenty years lead us to be-
lieve that the solution to these problems requires adequate knowledge of six
cardinal elements of the material supply, energy and economic factors. These
ares

1, The sources and character of the shore mterial;

2. The rates of supply and loss of shore material to and from the
problem area;

3. The manner of movement of the shore material from the source
to the beach and from the beach to other areas;

4e The feasible methods of increasing the rate of supply to the
shore or reducing the rate of loss of shore material from the
shore;

5. The design requirements of the feasible mthods of modifying
rates of supply and loss of shore material;

6. The economic cost of each feasible method of modification.

15

The development of adequate knowledge of these six elements of any
specific shore problem constitutes the beach erosion control study or the
study of the shore effects associated with navigational improvement. The
determination of how to develop the knowledge required constitutes the gen—
eral investigation and research activities of the Board.

Goastal Physiography

The shore line of the United States is characterized by a diversity of
shore line forms. The New England shore line particularly north of Cape
Cod is found to be rather rugged with cliffs and headlands fronting directly
on the ocean and with rather short lengths of beaches caught between the
headlands.

The Atlantic shore line from Cape Cod south and the Gulf beaches are ~
characterized generally by long uniform beaches with the adjacent topography
lying only a few feet above high tide. Frequently, these take the form of
barrier beaches, separated from the mainland by salt water marshes or la-
goons. The Pacific shore line shows some of the characteristics of both the
preceding types of shore line with long sweeping beaches broken by bold
headlands.

The geologist tells us that the composition and origin of these beaches
and headlands started some two billion years ago when the molten mass of
the earth began to solidify and cool into igneous rocks. These original
igneous rocks have gone through various changes due to changes in weather,
environment, etc., so that the form and characteristics of many of them have
greatly changed. After all the weathering, frost action, glaciation, hydra—
tion, etc. we find that there are on shores several types of rocks and
minerals, the most abundant of which is quartz sand. The quartz reaches
the beach environment under the influence of gravity, by wind action, or as
water~borne detritus.

Natural Porces Affecting Beach Erosion

Changes of the shore or beach follow from natural physical causes
resulting from the interaction of the land, the sea, and the atmosphere at
the shore or beach. Changes in the shore line are usually the result of
sand movement due to the action of several matural forces. These forces
result from wave action, tidal action, and ocean currents, which act on
the shore in varying degrees depending on the coastal physiography. The
dominant force is the wind=generated ocean wave. These waves after being
generated by a wind disturbance, may leave the area of the disturbance and
travel for hundreds or even thousands of miles before being interrupted by
a land mass. Most of the waves noted along our shores are generated by
distant. storms.

Tides and Currents
The subject of tides has engaged the attention of mathematicians and

engineers for several centuries. The principal effects of the tides in

16

reference to beach erosion are generally agreed to be: (1) they shift the
zone of wave attack on the beach and (2) they set up currents that may
assist or oppose the movement of the sand particles which compose the beache

Gurrents resulting from tidal action are generally noticeable along
the coasts only in the vicinity of bays, estuaries, or inlets. The rise
and fall of the tide produces a flood and ebb of the current filling and
emptying the estuary. This current is uswally weak out can reach sufficient
magnitude in the vicinity of the estuary to cause erosion by its own action.
Where the currents are too small to causs movement of the beach sand alone
they can be effective by working in conjunction with the waves breaking on
the beach. Waves approaching the shore at an angle will produce a littoral
current substantially parallel to the shore.

Sand Movement

The effect of waves on the sand beaches is especially pronounced at
the breaker line, where comparatively large quantities of sand are thrown
into suspension, An angularity in the direction of wave approach frequently
results in a littoral current being set up substantially parallel to the
shore. This wave gemerated littoral current carries the suspended sand
alongshore.

The net effect of the action of waves and currents is to produce a
beach which may be accreting or eroding, may show cyclic or seasonal changes,
and is seldom if ever completely stable. It might be pictured as a river
ef sand whose direction and velocity are determined by the character of the
forces impressed upon it in the form of winds, weves, and currents.

It is well to remember that once a sand grain is put inte suspension,
the slightest movement of the surrounding water, will produce a corresponding
moverent of the sand particle. As long as the particle remains in contact
with the bottom, it will take currents of appreciable strength to move even
the fine sand. However, the almost unceasing wave action on the beaches con-
tinually keeps a substantial amount of sand in suspension. When the waves
approach normal to the beach, the sand movement would be essentially an
oscillation back and forth of the sand particles with little progressive
movement parallel to the shore. However, if even a slight littoral current
generated by tides or winds is present, the alongshore movement of material
can be relatively great.

To avoid confusion we mst remember that littoral current is the move-
ment of the water mass while littoral drift is the movement of the solid
particles. The coast in the vicinity of Senta Barbara, California, is com-
sidered to have a fairly large rate of littoral drift, the direction of
drift being from northwest to southeast, Here the average rate of drift is
about 300,000 cubic yards of sand per year. A rate of littoral drift rang-
ing from 20,000 to 50,000 cubic yards per year is considered relatively low.
Wind blowing over the beach can also be an effective agent in moving the
sand and should always be considered when making a study of a specific
locality .

Shore Protection Methods

Frequently we find that the natural conditions at a beach are not in
stable adjustment and that progressive erosion of the beach is underway.
In such cases it is sometimes found that the eroding condition can be ar—
rested by the construction of shore protection structures to check the re—
moval of material from the beach or by increasing the supply of material
to the shore.

Presently known feasible methods of modifying supply and loss rates
are limited with one exception to various types and placements of structures.
We know these by their designations as breakwaters, jetties, bulkheads, sea—
walls, revetments and groins; artificial nourishment is the non-structural
excdption .

Breakwaters as the name implies, are energy dissipating or wave inter—
rupting structures employed to break or dissipate water waves and thus pre-
vent their incidence on an area it is desired to protect. Their effect on
material movement arises entirely from modification, usually in the form of
reduction, of the incident energy of water waves.

Bulkheads, seawalls and revetments constitute a class of structures
whose chief function is to substitute non-erodible for erodible material and
concurrently provide for energy dissipation. Their effect on the movement of
material is direct, by the substitution of materials, and indirect, by the
modification, sometimes dissipative, of the energy in incident waves or cur-
rents. They are employed widely and are particularly suited for the preser—
vation of a definite land-water boundary at a given location. There is
almost always an increase in degradational action associated with their use.

Groins are structures designed and built to intercept and retain ma—
terial in littoral movement and thus modify rates of supply and loss of |
material directly. Their influence on the energy pattern is almost entirely
indirect, resulting from a reorientation of the shore line in a direction
more normal to wave approach. Accordingly, groins should be considered as
more than simple barriers to sand movement. Because of this action they
may cause an appreciable modification of the entire littoral regimen.

_detties are multi-purpose structures, whose functions may include those
of breakwaters, groins and bulkheads. Although they are usually associated
with navigation improvements at inlets, river mouths or harbor entrances,
they frequently result in major physiographic changes. Analysis of the
effects of jetties on shore lines is one of the most difficult of shore
problems to solve in detail, the ease with which general features of the
effects can be predicted belying the difficulty of a detailed analysis.

Artificial nourishment is adequately described by its name as a method
of supplying beach material additional to that available naturally. It is
useful for rehabilitating or rebuilding beaches, for maintaining a desired
existing beach condition, or for improving to a large or small extent exist—
ing conditions, Although gaining in popularity as a shore control method,

18

little authoritative data on its requirements or performance are available.

In many instances it will be found that alternative solutions of shore
problems are indicated by the analysis of the physical problem. In other
instances there will be a unique solution. When a choice is possible the
problem analysis should include information on the comparative economic cost
in sufficient detail to permit final selection of a plan of solution on the.
basis of economic advantage between otherwise equal plans. It may be found .
that two or more plans are feasible but not equally desirable from a physical
viewpoint. In mamy cases economic cost may be the controlling item dictat—
ing the selection of the plan, even at the expense of desirable physical
advantages.

It is recognized by engineers in this field that many aspects of
coastal processes are not clearly wnderstood, and several institutions have
undertaken research programs to improve present knowledge of the various
processes.

Research is conducted in the laboratories of the Beach Erosion Board
(and in the field) and is designed to improve knowledge of physical laws
pertaining to shore processes and design of shore structures for use of the
engineering profession, and to compile general information regarding shores
of the United States and the forces acting thereon to aid in the solution
of engineering problems at specific locations.

Projects in progress include: (1) s study of the direction and velocity
of littoral currents generated by waves, with secondary data on how groins
modify littoral currents; and (2) a study of methods of by-passing sand at
inlets, which is contributing information on how sand builds up at a jetty,
the tidal currents in a jettied inlet, the wave climate in the area, the
daily, weekly and bi-monthly changes in the shore line position and bottom
topography, the amount of sand transported by waves, and data for relating
littoral currents to the generating waves, Laboratory studies include
measurements of wave forces against structures with high speed photographs
for the study of breaking waves. Another laboratory study is the development
of factors that affect the equilibrium profile of beaches. This same data
is used to determine the feasibility of using models to study beaches.

Over the course of many years the Board has amassed a large amount of
basic data on the character of United States shores. Such information con—-
Sists chiefly of the geology of the shore, the wave and wind climates, data
on the shore material, and the historical record of changes in shore position
and condition. It is planned to continue the collection of this background
information, which serves as a reservoir of data available for use in beach
erosion control studies, thus reducing their cost and the time required for
their completion.

19

NOTES ON DETERMINATION OF STABLE UNDERWATER BREAKWATER SLOPES
BY

Kenneth Kaplan, Engineering Division

The method of determining underwater stone sizes and stable slopes
proposed by Iribarren and Nogales (1) contains certain inherent weaknesses:
first, the Airy wave relationships commonly used for waves moving up a
gradual ly sloping beach are considered to apply at points over a breakwater
slope. Second, it is assumed that waves will break in a depth of water
equal to their breaking wave height. Third, and perhaps most important,
the cause of stone removal both above and below the water surface is con-
sidered the same. That this last does not hold may be seen by referring
to the force diagram from which the basic Iribarren equation is derived En 9
in which an intermittent "flow-no fluid" is considered to be the basic
cause of stone removal above still water level.

It would seem that a more realistic approach would be one in which
use is made of the currents caused by wave action. To this end, the re—
lationship derived by Blanchet (3) dealing with the destruction of stone
masses by currents may be applied. That is

— waK f28% (dD ysinta-a,) (1)

in which v is the critical current velocity for stone mound disintegration;

K is a complex non-dimensional coefficient, but one which should
be fairly constant for stones of the same form;

D is a characteristic dimension of the stone; ,

Gand % are the specific gravities of the stone and fluid of immersion

respectively;

@ is the angle the mound makes with the horizontal; and

@, is the angle of repose of the constituent stones »

The weight of each stone may be written as
—- W=he% aD? (2)

in which W@ is the mit weight of fresh water. From this

3/ YS
theo D= Ew a (3)

The maximum current due to wave action which would exist at depths
below still water in the absence of the breakwater is given by

1 TQ ca cosh cosh 2n(d-Zf
DP oS 1 sinh 274), (4)

20

This will not be the current velocity which exists when the breakwater is in
place, but if we propose that a measure of this current is the v' of
equation (4), , we may call

ae ra TA
wx Kaus Hs + (5)

Substituting equations (3) and (5) in equation (1) and collecting the
coefficients gives

sin(a-@,) = Ha [4% (wr Jee) ?| (6)

W4L7

from which we may find the stable slope for stone of weight W under wave
attack of height, iH ang Ronan fT at a depth of approximately 2 (better at
a depth, z - H” ae oy f=)9 in which the constant K (or K,) must be
sinh 276
Z
empirically determined. However if the above development is substantially
correct, K should remin fairly constant for any one type of stone.

In the report by Iribarren and Nogales (1) a table of stable slopes
is given for the breakwater at Argel measured after wave attach had _
"shaken down" the slopes. : Though the upper face of this breakwater consists
of artificial blocks, below the depth of 11 meters the armor stone is
natural quarry stone. The maximum wave attack immediately before the
structure is given as 6.45 meters in height with a period of 13.75 seconds.
The breakwater itself is founded in a depth of 35 meters. At the depth of
11 meters the stone weight is 4 metric tons and the EOE is lonil1e5. The
value of "a" may be found’from equation (4) (d - 2 = 21 Meters) by use of
tables of hyparbolic functions (5). Solving equation (6) for K (assuming

a, = 45) a tentative value of K = 1.15 is established.

In an attempt to verify this value the results of model studies per-—
formed in 1948 at the Waterways Experiment Station (4) were used. In these
tests prototype waves with a height of 15 feet and a length of 270 feet
were directed at a breakwater founded in a depth of 60 feet, The tests
were continued until the breakwater slopes attained stability. Two depths,
10 feet and 25 feet were chosen at random at which the average stone weights
were 10 tons and 1 ton respectively. Stable slopes were then calculated
and compared with those found in the model tests. At the 10-foot depth ‘the
calculated slope was 1 on 1.46 and at the 25-floot depth the calculated
Slope was 1.0n 1.52. The actual slope at both these depths was 1 on 1.5-

Though these values indicate substantial agreement with the preceding
theory, further studies are necessary specifically to determine the value-
or range of values - of K. In addition prototype data of existing structures
should be analyzed to verify model conclusions.

(1)

(2)

(3)

(4)

(5)

BIBLIOGRAPHY

Iribarren Cavanilles, Ramon with the collaboration of Casto Nogales
y Olano: "Generalization of the Formula for the Calculation of
Rock Fill Dikes and Vertification of its Coefficients", Review
of Public Works, May 1950, Madrid, Spain. (translation published
in the Bulletin of the Beach Erosion Board, January 1951).

Iribarren Cavanilles, Ramon; "A Formula for the Calculation of Reck—
fill Dikes", Revista de Obras Publicas, July 1938. (translation
published in the Bulletin of the Beach Erosion Board, Vol. 3, Now l,
January 1949).

Blanchet, Ch.; "Formation and Destruction of Stone Masses by a Water
Current", La Houille Blanche, New Series, No. 2, March 1946.
(translated by W. W. Geddings, Jr., Waterways Experiment Station,
Vicksburg, Mississippi, 1950).

Waterways Experiment Station Bulletin No. 31, "Empirical Verification
of Transference Equations in Laboratory Study of Breakwater
Stability", Mississippi River Commission, Corps of Engineers.

Bulletin of the Beach Erosion Board, Special Issue No. 1, July 1948.

22

A NeW METHOD FOR TH# GRAPHICAL CONSLfRUCTION
OF WAVE RaFrRACTION DIAGRAMS

by

Tf. Saville, Jr. and Kk. Kaplan
Staff, Beach Erosion Board

In comection with the preparation of a design manual for shore
Ssorvuctures Shee sah 1) being prepared by the Beach Brosion Board, a re~
examination of the methcds and validity of the various means of obdtveaininz
refraction characteristics became necessary. Tnis reexamination has shown
that the error. involved in the use of the crestliess method for drawing
orthogenals devised by Isaacs(1)(2) and in general use throughout the tnited
States, may become cuite significant when larse angles of incidence or
large contour intervals are used -- in eXtreme cases errors in sxcess of
5 to 6 degrees in direction and 10-to 15% in refraction coefficient being .
possible. This error is introduced into the scales devised by Isaacs by
the assumption that the change in angle, Aq , is small in comparison to
the angle of incidence, q , so that sin(a -4a ).= Sin a@ ,

However, this assumption is not necessary to the derivation of the
eavation expressing the angle change, and more accurate equations may be
derived in a manner similer to” that of Isaacs. The basic assumptions Sor
this extension of the original theory remain the same: namely that the
velocity varies linearly between contours, that the radius of curvaturs
of the orthogonal between contours is constant (a circular arc), and that Aa
is small so that tan Jda= = sin 4a2zAc.

Referring to figure la 5 oe and do, £1 and og, ere the depths and vel—
ecities respectively at contours 1 and 2.- If dj is greater than 42, then
e2, and in moving from A to B an orthogonal will follow a circular arc
tangent at A and B to OA and OB respectively. Similarly another orthogonal
a ditferential distance d away from AB is tangent at A' and B! to OA’ and 02
respectively, Since d is a differential distance, AA'~00'=BB'=d. ee
If Ris the distance of wave advance during a time SESE eds t, then RyekSeABy
and Ry = A'B'. By construction the angle BY BB! = Ag , and af Ag is
considered less than 13 degrees, (for two ciNee acouraeehs tan Avssinda=- Aa,
then.
Bo. Ra=k,

AG TAIPAGe =
¢ ANAK Baas coi (1)

Since the velocity is assumed to vary linearly between contours, the average
velocity between A and B is

C'= Gt Se, (2)

to

and if t is the time interval required for the wave front to move from A 4!

23

24

d sin(a-Ac)

Contour Q@ do

Contour

to B BI,
tos (3)

The rate of change of velocity with distance across the contours is 4 -“s

where J is the distance between contours, and therefore the velocity 63!
at A' is greater than that at A by the amount ¢, -¢2 d sin @ ;

Similarly the velocity Cg' at B' is greater than that at B by the amount

5 -& dsin (@-4a). The velocity C" between A' and B' is therefore
Eg

, , ,
0% LE at fo, 48 dana + 2 g sin (a-tea)] (4)

and, as before

: Mae =c"t (5)
From equation (1)
4a= “24 oo te aa t[ sin arsin(a- ~4a)] (6)
From equation (2) and (3), a rf ee
é 2

Aan) rar] | Lat saae€ BeIsinat sin(a- 4a)] (7)

It may be noted that if sin(a-Aq) is assumed approximately equal to sing ,
the equation derived by Isaacs results. However , with the more accurate
approximation ef sin(«-dq@) = sin @& cosd4a- cos @ sin 4a = sina-da cos a 5
then Aa Yecomes

aN SE ee 4a cos a)
daett Fe (sing Se coea 8)
lay J ae (
Now angle 0" AQ = a and from triangle A O"J
es aa\_ / (9)
at aee ifn ye |

203 a+ 42 sin a

Substituting into equation (8) and reducing terms, then

daa 4h 2tana-ha (10)

—

Lav, 2*+datmnae

Letting fe = K and ies for Jae

ie Ages a(ae)+ Va+k)*+ Bk tan2ae. a (12)

2tana -
25

Graphs or overlays may be made up from this equation, or somewhat more
easily, from the solution for q@ :
/ C2rk)aa
COP Gow Baie 12
2N-4aé re
One such overlay is shovn in Figure 24.

If the orthogonal is being drawn from shallow to deep water (e.g.
pest a shoal, or from shore seaward), a’ may be defined ag the angle.
between the wave crest and the first contour crossed (at which tha velocity
G,} will be less thanC 9). In this case 4& will be turned in the opposite
direction, and a derivation similar to that above gives

yep Sten ttha _ (2-K)-VQ-K)—8ihtanZa' — 3)

“-Aa tan a’ Z tan a’
and
Yb GOAN | :
hana eee Co

An overlay based on this solution is shown in Figure 2b. This overlay
should be used whenever the orthogonal is being drawn from shallower to
deeper water.

If a derivation by the Isaacs! method is made for an orthogonal
being drawn from shallow to deep water the form of the solution for 4@ is

4a=K tan a’

For a particular orthogonal, as @-4da bub since Isaacs' original derivation
gave for Ac:

4a=kK tan

this could never hold.

Indeed, a measure of the accuracy of the new deriva tion is that for
equation (21) and (13), or (12) and (14) @'very nearly equals &-dq 4»
and, to the limit of accuracy of the overlays, (2 does equal qQ- Aes

The solutions presented will be applicable in,all ordinary cases.
However, the application of these solutions is limited by the necessity of
keeping 4@ small so that the distance between contours becomes small as «
aoproaches 90 degrees. Equation {8) also represents a valid solution,,.
however, and, for practical reasons of workable distances between contours,
it is desirable to use this equation wherever @ exceeds about 80 degrees.
vor large values of @, sinq@ and cos @ do not vary appreciably and the
values for @ = 85° may be chosen as representative of the range between
80° and 90°. Equation (8) may be solved to give

He Sere S/n a (15)
R 1
CP CO SICG
26

nv

og ODIs

YSIVM YSMOTIVHS GYVMOL ONIGSSOO¥d YOS GSASN WVYOVIG 4O NOILYOd 40 INSWS9YV INS

ND

YSLVM YSMOTIVHS OL YSdSaSq WONS IWNOSOHLYO ONIMVYC NSHM GaSnN 3a O1 WVHYSVIC

AD 5
AAW

$O SvO vO SEO £0 seo vO Sto SO

IS =
4

DV

27

3
c|

qz Old

MALVM UMadaad GYvVMOL ONIGAZS00Nd YO4 GASN WVHOVIG 4O NOILYOd 40 LNAWS9NV INA

: ‘AD 5

TV
900 +00 200 (0) zoo vOO 900
soo £00 loo 100 £0'O SOO io 00 £10

il
a FEEE

YaLVM Yadaadq OL NSMOTIWHS WONS TWNOSOHLYO ONIMVYG NSHM GASN 3a OL WVHUSVIC

800

20:0

‘AD 7
1V
5 100 10°0
0 Sb0 v0 seo ¢0 Szo 20 20 szo ¢0 s¢0 0 Sv'0 Ke
L =
dt
£ | +
Vv! 3 7
S = _ =
9 - = —
2 Seq = ~ —
8 5 =
6/ Bay S ==
to] =a Za =e =
ut ae = ~ — =
2 saat o—-
eit = L. — ==
S0:G eG 1g SO:

nv

mA-OMar ONTMNA—

28

oe aE:
Curves showing this variation of da with Tat, and 4 for a=85 are also
av.

shown in the overlay in figure 2a.

When either the wave direction, or the direction in which the orthogonal
is being drawn, is from shallow to deeper water, the direction of turning is
opposite and equation (15) becomes

R ‘ ! ‘
— S/7
De ern aa tal Sst ame (26)
Z=K- Cos a"

Curves showing this solution are included in the overlay in figure 2b.

These two overlays may be used either as ordinary graphs, or in con—
junction with a drafting machine in the same methed as the original
Isaacs' overlay. In the past, the turning point for the changes in angie
(Aq@ ) has been assumed to be at the mid-contour. However, the correct
orthogonal (circular arc) is not tangent to two straight lines that meet
at the mid-contour, but to two lines that meet some small distance above
(toward deeper water from) the mid-contour (see figure 3). The ratio
f the distance of this point from the deeper contour to the full distance
between contours is given by

Lon — tan Bz

Q- A,
2

tan a, —- tan A,
If, for example, a, =60° ard @=55"°, this ratio is 048 instead of 0.5,
and if @=603 a=50° , this ratio is 0.42 instead of 0.5. The magnitude
of the error in the distance along the contours is given by the difference
between the tangent of the average angie (the exact solution) and the

average tangent of the two angles, (i.e. tan BGs ss fan Oot 2G

The accuracy is improved considerably by taking the turning point not at

the mid-contour, but at a point toward deeper water, such that, in Figure
3, the distance AO = 0B. This point my be estimated by eye with sufficient
accuracy o

A direct construction of Rj,,may be made with a drafting machine by
changing the direction of the orthogonal by 42% once at the first contour
and again at the second contour, rather than once by the full value of
4a at the mid-contour. The angles being correct, this construction
will define the position and direction of the orthogonal at the second con—
tour o

However, it is not felt that the increase in accuracy which would re-
sult from this procedure warrants a change in the standardized method of
constructing orthogenals using one angle change. Rarely are contours
defined accurately, and the modified procedure suggested, in requiring two
angle changes instead of one, complicates the mechanics of orthogonal con-
struction. It is thought that sufficient accuracy is obtained by making
the one angle change at a point estimated by eye such that the distances
OA and OB are equal.

Mean Contour

Figure demomstrating inaccuracy involved in using the mid—contour
(0') as the turning point rather then the correct turning point
O, such that OA =0OB. The distance OC is given by the expression ,
tan (a - aa) — fan ( x - Aa)

2 ey

fan o— tan (a= Aes

where Ay is the distance between the contours d, and d3-

FIGURE — 3

30

SP odl D ‘S\4

\\ \ Es
x-0 4 — ‘swy 2 =|
_ \ : “Suy © - = } =
yo - ‘swy G — (,02 2.18 =»°%) .08*SWOHiv4 19
iv HOWONddY 4O S3T9NV HLIM AVM
GNOOSS 21 4YOJ NMVYQ WVYSVIO NOILOVYsay
a suy 2 -
A I—-w-S *
ys = cp Gy 4-S GNV MV1 S77aNS)

SX sovvs] v
D - ‘sw SI

WG SANIVA 40 NOSIMVdWOo LOSwiId YO4 | 378vi O1 yadau
+>0— Db ‘sud OZ 7 |

SHNOLNOD TATIVYVd GNV LHSIVYLS |
Meee 4YO4 MV1 STTSNS HLIM STIVNOSOHLYO |
Rs & —— ONIMVEG JO SGOHLSW SNOINWA 3O NOSINVdWOOD >

‘sy OS

sw} 19

31

A hypothetical case of refraction over straight, parallel contours is
shown in Figure 4. The parametric equations for the orthogonal given by
Arthur and Munk (3) are

fae cos Bi B =e sin SB; ZB sin 8 SE COs es

These may be solved by simple separation of variabies for a velocity field
which is a function of y alone. (Here G=90~—a@ ). In particular, for a

field which varies linearly with y, c = co(l - ay) the solutions for x and

y are

Me ees 1 (cos a-COS X,) BNA fx
asin &, x

which are the parametric equations of a circle of radius

asia, (SIN & 5/4} a)

ziNioie jig 4 /
pa VSP FZG +4 and center at. |<= = Dy hiS car
ASINZ A, 2SNZA, a
The solution for y may be put in the form
; A VAG
— _ = a aoe | fa
SI X= sin (a-4a) (/ es ) in Q,

which is Snell's law.
From these, exact values of 4a and x at any point in the field may be
found.

The values for the particular case chosen are compared with values
obtained from Isaacs! equations and the ones contained herein. This com—
parison is showm in Figure 4, and also in Table 1, where both values of the
change between contours and cumulative values are given. Jt may be seen
that angular values obtained from the new equations agree almost exactly
with those determined from Snell's law, and are considerably more precise
than those obtained from the original Isaacs! equation. Distances along
the contours are still somewhat in error if the mid-contour is used as the
turning point (as in the Isaacs' case), though not nearly as greatly in
error as obtained from the Isaacs! method (see column S-K-I). If the
turning point is selected so that the segments of the tangent lines within
the contours are equal, then the result is almost identical with Melli's
Law. This is shown under "S—-K".

It is concluded that these new protractors, or overlays represent
@ considerable advance over the original Isaacs! protractor, in
that they approach much more closely exact valuese

it may be noted that a paper by Arthur, Munk and Isaacs recently
presented at the May 5 meeting of the fmerican Geophysical Union, but
not yet published, has considered the equations of the wave rays, or
orthogonals. Solutions of these equations using essentially the same
assumptions as used in the geometrical derivation herein, give for

ine Aen \ a LL SU ZA oat
a = sin If 1+ sin | a= sin’ |(£E2 ) sina —a

32

(Zathoms)
61
50
40
30
25.
20
15

10

E
BY

«040

2094
0155
~150
2150
237
2194

© 235

TABLE 1

Comparison of Angles and Distances as Orthogonal Crosses
Specific Contours for the Various Methods of Drawing
Wave Period is 20 seconds

Snell's
Law

(2°

77O
(4°

73°
(CHE

B82.

28°

22°

(Oe
129

80°

Ha)

Aq!
5")

42!
O')

La!
Si)

De!
49°)

As
BD)
i

45")

16!
29!)

47!
11")

36!
261)

10!
04')

06!
18' )

48!

Orthogonals.

S-K
0°
(2° 13")

T° 2
(4° 6!)

TB ohlt
(7° Of)

66° 41!
(4° 49')

el 530
(5° 52")

56° 1!
G2)

48° 57)
(8° 45!)

40° 121
6° 281)

BD Ah!
(5°, 12")

280 32!
(6° 261)

BIO hi
(ALG /#»)

18° 03!
Gers)

IZ 15

Tsaacs
g0°
(2 Ze")

Tie Bust
(G2 42")

72° 491
(ES Gy)

53° 43!
(7 21")

46° 22"
(Oo de)

Bye!
(69 30")

BORE 3!
(Bo 2")

25° 29!
(6° 281)

19° OL!
(3° 50")

15° 11!
(3° 20)

g° 59°

Bie

Snell's
Law

0.00
(5 0926)

5 20926
(3.9382)

9.0308
(2.7842)

11.8150
(2 075))

13.8865
(1.6605)

15.5470
(1.3061)

16.8531
( .9876)

17 «8407
( 27538)

18.5945
( .6022)

19.1987
( eFI52))

19.6739
( 3667)

20.0406
( .2765)

20 3171

shel
0.00
(5.1448)

5 lLLAS
(4.0170)

9.1618
(2.8682)

12.0300
(2.0559)

1401259
(GL S772)

15.-S031L
(LS SWS)

He 7
( -9967)

18 .1143
( 3 7564. )

18.8707
( 6052)

19 4759
( 4750)

19.9509
( Pirlayoll )

20 3170
( -@ifell, )

20.5931
#2760

+1.36%

Isaacs

0.00
(5.0941)

50941
(3.8753)

8.9694
(2 ° 6731)

11.6425
(1.9147)

13.5572
(1.5396)

15.0968
(1.2051)

16.3019
( .9014)

17.2033
( 6776)

17.8809
( .5334)

18.4143
( 4106)

18.8249
(. .3080)

19.1329
( 22)

19.3566
- +9605
4 013%

o-K

0.00
(5.0929)

5.0929
(3.9223)

9.0252
(2.7750)

11.8002
(2.0760)

13.6762
(1.6608 )

15 5370
(1.2981)

dle Sul
( .9850)

17.8201
(7526

18.5727
( .6041)

19 .1768
( .4732)

19.6500
( .3656)

20.0156
( 755)

20.2911

0.13%

for proceeding from deeper to shallower water. These will be recognized
as a rearrangement of Snell's Law, and would result in protractors
identical with those contained herein for angle changes up to about 13°.

REFERENCES
(1) Isaacs, J. Doe, Memorandum on Drawing Refraction Diagrams Directly by
Orthogonals, Univ. of Calif., Fluid Mech. Lab., Rot HE-116-47,
1944, (unpublished).

(2) Johnson, Jo. We, Mo Pe O'Brien, and J. D. Isaacs, Graphical Construction
of Wave Refraction Diagrams, H. 0. Publ. 605, 1948.

(3) Munk, W. He and R. S. Arthur, Wave Intensity Along a Refracted Ray,
Symposium on Waves, National Bureau of Standards, 1951, in press.

Ls)
ix

BEACH EROSION STUDIES

The principal types of beach erosion control studies of specific
localities are the following:

a. Cooperative studies (authorization by the Chief of Engineers
in accordance with section 2, River and Harbor Act approved
3 July 1930).

be Preliminary examination and surveys (Congressional author—
ization by reference to locality by name).

c. Reports on shore line changes which may result from im-
provements of the entrances at the mouths of rivers and
inlets (Section 5, Public Law No. 409, 74th Congress).

d.- Reports on shore protection of Federal property (author-
ization by the Chief of Engineers).

Of these types of studies, cooperative beach erosion studies are
the type most frequently made when a community desires investigation of
its particular problem. As these studies have greater general interest,
information concerning studies of specific localities contained in these
quarterly bulletins will be confined to cooperative studies, Information
about other types of studies can be obtained upon inquiry to this office.

Cooperative studies of beach erosion are studies made by the Corps
of Engineers in cooperation with appropriate agencies of the various
States by authority of Section 2 of the River and Harbor Act approved
3 July 1930. By executive ruling the cost of these studies is divided
equally between the United States and the cooperating agency. Information
concerning the initiation of the cooperative study may be obtained from
any District Engineer of the Corps of Engineers. After a report on a
cooperative study has been transmitted to Congress, a summary thereof is
included in the next issue of this bulletin. A summary of a report trans-
mitted to Congress since the last issue of the Bulletin and lists of
authorized and completed cooperative studies follow:

SUMMARY OF REPORT TRANSMITTED TO CONGRESS

a a A A NS NN

STATE OF CONNECTICUT-CONNECTI CUT RIVER TO HAMMONASSET RIVER

The area studied comprises the shore of Long Island Sound between the
mouths of Connecticut River and Hammonasset River. It includes the shores
of the Towns of Old Saybrook, Westbrook, and Clinton, a total length of
about 12.5 miles. This shore area is about 30 miles east of New Haven
Connecticut, and about 100 miles east of New York City. It is extensively
developed as a resort and residential

35

area, with improvements ranging from cottages to small estates. The permanent
population of the three tows is about 6,500. The summer population is more
than 3 times as great. A mmber of small town cwnedbaaches are included in the
area o

Long Island Sound is a tidal arm of the Atlantic Ocean. Tides are semi-
diurnal, the mean range increasing gradually from 3.5 feat at Saybrook to 407
feet at Clinton. Spring ranges are respectively 4.2 and 5.5 feet at these
locations, Maximum tide of record at Saybrook was 9.9 feet above mean high
water. Tides 3 feet or more above mean high water occur about once a yea.
With a tidal stage of 3 feet above mean high water, the maximum height of
breakers landward of the low water line is about 5 feet at the east end
of the study area and 6 feet at the west end. Larger waves can reach the
shore only during infrequent higher tides.

tue sole
cause of ae ee wave action. ae eee pecan f > littoral
movement and offshore less of beach material. Absence of ewer probably
precludes the possibility of return of waterial from offshore by wave action.
The greater fetch and wind movement from the west and southwest account for
the general predominance of eastward and northward littoral drift depending
on shore alignment, Waves caused by easterly storm winds cause reversals of
drift direction. Where sections of the shore are protected by islands or
structures from waves from the west, westward littoral drift is predominant.

The sbudy area is characterized by headlands of wacensolidated glacial
material with some rock outcrops, between which wave-built bars have been
formed and the landward areas generally have filled «and become marshy. ‘The
headlands formerly supplied ample material 4o the intervening beaches, but
the headlands are now generally protected by seawalls and ravetments.

The supply of material is thus reduced or eliminated and consequently the
beaches have slowly detericrated. Groins have been found to be capable of
eausing minor accretion areas and stabilizing a narrow band along the upper
portien ef the beach, but the natural supply of material is insufficient for
the formation ef adequate protective beaches. Tha building and maintenance
of adequate beaches may be accomplished by artificial plecement of sands

The prospective low rates of Llosa of beach material, based on past experience
of shore Line reesssion, are insufficient to warrant the eoustinee oe of
epesues except where nesessary to prevent the shoaling or closing of inlets
or drainage channels,

The Board concluded that the best methods of protection and improvement
ef beaches within the study area ars as follows:

a. Borough of Femrick (West Part) — Gonstruction of a dumped
riprap wall along the high water shore line;

®

be Plum Bank Beach - Direc mens of a Bre eee sand beach
in front of the sea walls and cottages, and construction of an impermeable
groin at the north limit of the Dili;

oe |
» PLAS

ce Great Hammock Beach ~ Direct placemant of a protective sand
beach or dune in front ef the cottage development.

de Saybrook Manor, Chalker Beach and Chapman Beach — Direct
placement of a protective sand beach in front of the cottages or
residential developments;

e. West Beach — Direct placenent of a protective sand beach
in front of the sea wall along the west snd of the public beach and in
front of the cottage development west of and adjacent to the sea wall;

f,. Grove Beach = Construction of an impermeable groin at the
east end of the beach.

It is also concluded that projects for Plum 3ank, Great Hammock, Saybrook
Manor, Chalker and Grove Beaches appear to be justified by evaluated
benefits. The Board also believed that the pudlic ownership and inberess
in the projects are insufficiet to warrant federal aid under the policy
established by Public Law 727, 79th Congress. The Board recommended that
local authorities consider adoption of mrojects for pretection and
improvement of these beaches at lecal expense, substantially in accordance
with the foregoing plans. The Board considered it advisable, however,
for loeal interests to make independent evaluations of prospective benefits
from these projects in determining justification for their construction
at local expense.

In accordance with existing statutory requirements the Board stated its
opinion that:

ae It is inadvisable for the United States to adopt projects
authorizing Federal participation in the cost of protecting and improving
the shores within the area studied;

be The public interest involved in the preposed measures for
these shores is small; and

c. No share of the expense should be borne by the United

States.
COMPLETED COOPERATIVE BEACH ZROSION STUDIES
Location Completed House Doc. 2ress
MAT NE
Old Orchard Beach 20 Sep 35
NEW HAMPSHIRE

Hampton Beach 15 Jul 32

South Shore,Cape Cod (Pt, Gammon to Chatham )
Salisbury

Winthrop Beach

Lynn-Nahant Beach

Revere Beach

Nantasket Beach

Quincy Shore

RHODE ISLAND

South Shore
(Towns of Narragansett, South Kingstown,
Charlestown & Westerly)

CONNECTICUT

Gompo Beach, Westport

Hawk's Nest Beach, Old Lyme

Ash Creek to Saugatuck River
Hammonasset River to East River

New Haven Harbor to Housatonic River
Conmcticut River to Hammonasset River
Pawcatuck River to Thames River

NEW YORK
‘ Jacob Riis Park, Long Island
Orchard Beach, Pelham Bay, Bronx
Niagara County
South Shore of Long Island
NEW _JERGEY

Manasquan Inlet & Adjacent Beaches
Atlantic City
Ocean City

VIRGINIA
Willoughby Spit, Norfolk

Colonial Beach, Potomac River
Virginia Beach

NORTH CAROLINA

Fort Fisher

Wrightsville Beach

Kitty Hawk, Nags Head & Oregon Inlet
State of North Carolina

26 Ang 41
26 Aug 41
12 Sep 47
20 Jan 50
12 gan 50
12 dan 50
2 May 50

4 Dee 48

18 Apr 35
21 Jun 39
29 Apr 49
29 Apr 49
29 Jun 51
28 Dee 51
31 Mar 52

16 Dee 35
30 Aug 37
27 Jun 42

6 Aug 46

15 May 36
li Jul 49
15 Apr 52

20 Nov 37
24, Jan 49

25 Jun §2

10 Nev 31
‘2 Jan 34
1 Mar 35
22 May 47

Fd,
134
167

145

454,
47h

397
450
a71

Ts
538

482
333

204
218
155

763

80
62

81

74
75

75
él

75
81

72
73
"he
86

SOUTH CAROLINA

Folly Beach . 31 Jan 35 156 74
Pawleys Island, Edisto Beach &
Hunting Island 24 Jul 51
5 GEORGIA
St. Simon Island 18 Mar 40 820 76
FLORIDA
Blind Pass (Boca Ciega) 1 Feb 37 187 15
Miami Beach 1 Feb 37 169 75
Hollywood Beach 28 Apr 37 253 75
Daytona Beach 15 Mar 38 571 75
Bakers Haulover Inlet 21 May 45 527 79
Anna Maria & Longboat Keys 12 Feb 47 760. 80
Jupiter Island 13 Feb 47 7655 80
Palm Beach (1) 13 Feb 47 Ti2 80
MISSISSIPPI
Hancock County 3 Apr 42
Harrison County - Initial 15 Mar 44
Harrison County -— Supplement 16 Feb 48 682 80
LOUISIANA
Grand Isle 28 Jul 36 92 75
TEXAS
Galveston 10 May 34 400 73
Galveston Bay, Harris County 31 Jul 34 74 1h
CALIFORNIA
Santa Barbara — Initial 15 Jan 38 552 75
Supplement 18 Feb 42
Final 22 May 47 761 80
Ballona Creek & San Gabriel River (partial) 11 May 38
Orange County 10 Jan 40 637 76
Coronado Beach 4 Apr 41 636 Hil
Long Beach 3 Apr 42
Mission Beach 4 Nov 42

(1) A cooperative study of experimental steel pile groins was also made, under
which methods of improvement were recommended in an interim report dated
19 Sep 1940. Final report on experimental groins was published in 1948
as Technical Memorandum No. 10 of the Beach Erosion Board.

39

Point Mugu to San Pedro Breakwater
Carpinteria to Point Mugu

PENNSYLVANIA
Presque Isle Peninsula, Erie
(Int erim)
(Final)
OHIO

Erie County - Vicinity of Huron
Michigan Line to Marblehead

Cities of Gleveland and Lakewood
Chagrin River to Fairport
Vermilion to Sheffield Lake Village
‘Fairport to Ashtabula

Ashtabula to Pennsylvania Line

ILLINOIS
State of Lllinois : 7
WISCONSIN
Ii lwaukee County
Racine County, Wisconsin STO.
PUERTO RICO

Punta Las Marias, San Juan

ia,

27 dun 51
4 Oct 51

3 Apr 42
23 Apr 52

26 Aug 41
30 Oct 44
22 War 48
22 Nov 49

24 Jul 50°
1 Aug 51

1 Aug 51

8 Jun 50

21 May 45
5 Mar 52

5 Aug 47

220

177,

502

596

526

769

719
719
81
81

79

80

AUPHORIZED COOPERATIVE BEACH ZROSION STUDIES
NEW HAMPSHIRE

HAMPTON BEACH. Cooperating Agency: New Hampshire Shore and Beach Preserva—
tion and Development Commission

Problem: To determine the best method of preventing further erosion
and of stabilizing and restoring the beaches, also to
determine the extent of Federal aid in any proposed plans
of protection and improvement.

MASSACHUSETTS
PLUM ISLAND. Cooperating Agency: Department of Public Works

Problem: To devise effective means of preventing further erosion of
the shore.

PEMBERTON POINT TO GURNET POINT. Cooperating Agency: Department of Public
Works.

Problem: To determine the best methods of shore protection prevention
of further erosion and improvement of beaches, and specifical—
ly to develop plans for protection of Crescent Beach, The
Glades, North Scituate Beach and Brant Rock.

CONNECTI.CUE

STATE OF CONNECTICUT. Cooperating Agency: State of Connecticut (Acting
through the Flood Control and Hater Policy Commission).

Problem: To determine the most suitable methods of stabilizing
and improving the shore line. Sections of the coast are
being studied in order of priority as requested by the
cooperating agency until the entire coast has been included.

NEW YORK
JONES BEACH. Cooperating Agency. Long Island State Parks Commission
Problem: To determine behavior of the shore during a 12-month cycle,
including study of littoral drift, wave refraction and
movement of artificial sand supply between Fire Island and
Jones Inlets.
NEW JERSEY

STATE OF NEW JERSEY. Cooperating Agency: Department of Conservation and
Economic Development.

Problem: To determine the best method of preventing further erosion
and stabilizing and restoring the beaches, to recommend
remedial measures, and to formulate a comprehensive plan for
beach preservation or coastal protection.

NORTH CAROLINA
CAROLINA BEACH, Cooperating Agency: Town of Carolina Beach.

Problem: To determine the best method of preventing erosion of the
beach.

FLORIDA
PINELLAS COUNTY. Cooperating Agency: Board of County Commissioners.

Problem: To determine the best methods of preventing further re-
cession of the gulf shore line, stabilizing the gulf
shores of certain passes, and widening certain beaches
within the study area.

LOUISIANA

LAKE PONTCHARTRAIN. Cooperating Agency: Board of Levee Commissioners,
Orleans Levee District.

Problem: To determine the best method of effecting necessary repairs
to the existing sea wall and the desirability of building
an artificial beach to provide protection to the wall and
also to provide additional recreational beach area.

TEXAS

GALVESTON COUNTY. Cooperating Agency: County Commissioners Court of
Galveston County.

Problen: To determine the best method of providing a permanent
beach and the necessity for further protection or extend-
ing the sea wall within the area bounded by the Galveston
South Jetty and Eight Mile Road.

To determine the most practicable and economical method of

preventing or retarding bank recession on the shore of

Galveston Bay between April Fool Point and Kemah.
CALIFORNIA

STATE OF CALIFORNIA. Cooperating Agency: Division of Beaches and Parks
State of California.

Problem: To conduct a study of the problens of beach erosion and
shore protection along the entire coast of California.
The current study covers the Santa Cruz area.

WISCONSIN
KENOSHA. Cooper ating Agency: City of Kenosha.

Problem: To determine the best method of shore protection and beach
erosion control. .

OHTO

STATE OF OHIO. Cooperating Agency: State of Ohio (Acting through the
Superintendent of Public Works).

Problem: To determine the best method of preventing further erosion
of and stabilizing existing beaches, of restoring and creat—
ing new beaches, and appropriate locations for the develop-
ment of recreational facilities by the State along the Lake
Erie shore line. Sections of the coast are being studied
in order of priority as requested by the cooperating agency
until the entire coast has been included.

TERRITORY OF HAWAITL

WAIKIKI BEACH

WAIMEBA & HANAPEPE, KAUAI. Cooperating Agency: Board of Harbor Commissioners,
Territory of Hawaii.

Problem: To determine the most suitable method of preventing erosion,
and of increasing the usable recreational beach area, and to
determine the extent of Federal aid in effecting the desired
improvement »

43

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