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TP 77-4

Sediment Suspension and Turbulence
in an Oscillating Flume

By
Thomas C. MacDonald

TECHNICAL PAPER NO. 77-4
APRIL 1977 |

Approved for public release;
distribution unlimited.

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U.S. ARMY, CORPS OF ENGINEERS
COASTAL ENGINEERING
RESEARCH CENTER

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Department of the Army position unless so designated by other
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REPORT DOCUMENTATION PAGE

1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER

TR. 774

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

SEDIMENT SUSPENSION AND TURBULENCE IN AN
OSCILLATING FLUME Technical Paper

6. PERFORMING ORG. REPORT NUMBER
HEL 2-39

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
Thomas C. MacDonald DACW7 2-71-C-0024

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
1 1 i H AREA & WOR Ti
University of California ORK UNIT NUMBERS

Hydraulic Engineering Laboratory

Berkeley, California ~94720 D31193

CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Department of the Army April 1977

Coastal Engineering Research Center (CERRE-CP) 13. NUMBER OF PAGES

Kingman Building, Fort Belvoir, Virginia 22060
- MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report)

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SUPPLEMENTARY NOTES

KEY WORDS (Continue on reverse side if necessary and identify by block number)

Oscillating flume Sediment suspension Turbulence Waves

20. ABSTRACT (Continue on reverse side if necesaary and identify by block number)

An experimental study measured suspended-sediment concentrations and tur-
bulence above the bottom of a specially designed oscillating flume. A total
of 73 concentration distributions was measured for a single fixed-bottom
roughness and the same specific gravity (1.25) of sediment. Three different
sediment sizes were used, 65 experiments with the same size, These experi-
ments show a simple exponential distribution, except near the bottom, as
previously found by other investigators. The slope of the concentration

Continued

DD en, 1473 Evrtion oF 1 Nov 65 1s OBSOLETE UNCLASSIFIED

ee eee
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distribution is in the range of -5 to -15 per foot (-16 to -50 per meter)
for the experiments. For the limited data on other sizes, the slope of the
concentration distribution becomes more negative as fall velocity increases.

Turbuieut velucity fluctuations measured with a hot-film anemometer are
normally distributed with mean zero for measurements at two elevations above
the bed, well outside the viscous boundary layer. The root mean square of
the velocity fluctuations decreases exponentially with distance above the

bed, and at the bed, increases approximately linearly with increase in flume
velocity.

When extrapolated to typical field conditions seaward of the breaker,
these experiments demonstrate the importance of fall velocity, maximum wave-
induced bottom velocity, and turbulent velocity fluctuations in controlling
Sediment suspension by shoaling waves. However, comparisons of data obtained
with the lightweight sediment in these experiments and the probable motion of
quartz sand in the field suggest that sediment suspensions caused by shoaling
waves offshore of the breaker are likely to be limited.

UNCLASSIFIED
ga Ee ES (Ea ete baad stem hotels BANS Ye WEE
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PREFACE

This report is published to provide coastal engineers with an analysis
of data on suspensions of sediment produced by oscillatory motion in a
specialized laboratory facility at the Hydraulic Engineering Laboratory
(HEL), University of California, Berkeley. The work was carried out

under the coastal processes program of the U.S. Army Coastal Engineering
Research Center (CERC).

The report was prepared by Dr. Thomas C. MacDonald, a former graduate
student at the Hydraulic Engineering Laboratory, and now an engineer with
Leeds, Hill, and Jewett, San Francisco, under CERC Contract No. DACW72-
71-C-0024. The report is a modification of report No. HEL 2-39 which was
originally issued by the Hydraulic Engineering Laboratory.

The author acknowledges with sincere gratitude the active supervision
and counsel of the late Professor H.A. Einstein, the advice and the
opportunity to participate in this project provided by Professor J.W.
Johnson, and the assistance of Professors J. Harder and L. Talbot during
the experiments and in the preparation of the report. The cooperation
and assistance of the staff of the Hydraulic Engineering Laboratory are

gratefully acknowledged, especially W.A. Hewett, J.C. Allison, and R.W.
Cambell.

Dr. M.M. Das, former Hydraulic Engineer in the Coastal Processes
Branch, and Dr. C.J. Galvin, Jr., Chief, Coastal Processes Branch, were
the CERC contract monitors, under the general supervision of R.P. Savage,
Chief, Research Division.

Comments on this publication are invited.

Approved for publication in accordance with Public Law 166, 79th
Congress, approved 31 July 1945, as supplemented by Public Law 172,
88th Congress, approved 7 November 1963.

JOHN H. COUSINS
Colonel, Corps of Engineers
Commander and Director

CONTENTS

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI)

SYMBORS PANDY DEESINTMTONSHieinearensciucl oneien uiebiton tone

I INH NODUWICI MONG 8 G66 ood 0 0 6 0-500 6 0.0 G0

II CONCENTRATLONE DRS TRIVBUTUONS iciereimet te lea outs i Montell tellne

iG
Bo
Ne
4.

EXpenimentalaeAppiaralteuS) mete sihcmleelren telltemnep te
ExperamentalyshroCe duels: o tenbeiiiou re) cnwel el le)
RESWULCS G66 Gyo! OG) Ba 60 67 OO 06,0156 0

Experiments Using Sediments of Different
Sewuilimnye: Weloesdtedles 4 (4 io 6 6 0) 66 6 Go Svc

Summary of Experimental Results. ......

III DISTRIBUTIONS OF TURBULENT VELOCITY FLUCTUATIONS.

iG
Ze
3
4.

EXpendmential App aacatcUs ic inveii fai ceueiion etal el ter ie
Experaimentailg pO Ceduceutiemcdich lent ciitentenceiaten ts
ISSMIESo |G) 6 9 006 66 a 616 G6 6 6 6 BONS
Summary of Experimental Results. ......

IV THE SUSPENDED LOAD IN OSCILLATING FLOW. .....

Suspended-Load Theory in Unidirectional Flow

Similarities Between Oscillating and
Unaidatire ctvonalGplOws tic touaey vou cenlews ermieiinen. tellne

Sediment Suspension in an Oscillating Flow .
Hite Bases Concentratvonl | C7 soi. stiedrs te Wleunedle
Net Transport of Sediment in the Ocean...

Additional Investigations Needed to Complete
Che wSuSpPenSHonwene OiGyeaepc eo sete mrse lon eere ae

ConicluSTOnsi aaaw ce ceptors, se cecuret Kal Layee ets

IIE VNU RUS (CINE S. Gl Gio oe old) G 6.04.0 Ol Gand Glco

ARPEND XGaE Cee RaIMEN AU aD ADAGtor irene uiteletureitotilelivel Nei toinioiirswtaliits

TABLES

1 Concentration distribution data for Vg = 0.035 foot per
seconds tampilttude= MOOS 5) LOO tea sc) sue) ell elle) el a pele

2 Concentration distribution data for Vg = 0.035 foot per
Second wampilekeudem<am0 09 Sao Olt cious eueviieli tel) je touts ie ve

3 Concentration distribution data for
Ven = 00626"and 0c 0498s footaper se cond 3) 7) 3 el oi) oie

Page

CONTENTS--Continued

FIGURES
SWplsit Cantal Mreteeie Smee neue o otnrsitc airetll cle eMac cite Tem mi circus
OpElcCalMmConcent ration Metetynan) owe Pele! holm) loan ema chou
Yokessuppor.t oruconcenitratvom) meters ey si tei) ot le

Calibration curve for sediment diameter:
OR4y/ mailsimeters So DE< 0) 49/5) madelmeters ss ee es

Examples of measured concentration distribution curves.

M versus Up (eq. 4) for amplitudes equal to or greater
than 0.693 foot and sediment-settling velocity,
Ve = W505) oo jer SOCOM 6 6 6B a Sls SoG 6o 68

M versus Up for optical equipment moving with the flume
and stationary in space, uSing a 0.925-foot amplitude
stOIe AULIL MSCS WHRSNENES 6 Sg GG) 6 6 OO Ge on dud 6.0 6c

M versus Uo for sediment-settling velocity,
Vg. = O5085 SOE joe! SSCGOMG G6. 65 Bio 066d O10 oe

M versus location of optical equipment for identical
PLOW CONGE TONS Veli= OL O55 oot PeRySeCOnd. js 1s 6 ie

Concentration) dasitaibutrony form muny Slay sit vey el
Concentration adi sitaalbucaong tors ouia 02) vere eaimiey tons
Concentration adastab talon fourm ould OSarse surements
Concentration dastributdony fom) run Oia OG a) se ces ve
Concentration distribution for Gun ol4 S05) s.) <tc oh

M versus U, for Vg = 0.035, 0.498, and 0.0626 foot
STH SIS COM Cipree pen antennae, wien Oa tance uatilraanen eel nisl Mawel aie

Functional schematic of hot-wire bridge circuit... .
Hoe ticlimssiens omvandwpcobenenieiienien te timrelnet elton onion or taille
HOt tlmmanemome ter calla braltaonitamkaiijey io) en etiet ust ere) ie

Hots tiamyproverextensTonuassSemb liygisy cis wells! lepiley leuisiune

CONTENTS
FIGURES--Continued

Output versus velocity calibration curve for hot-film
ANEMONE Cer MeaSUreMeCMESI momen emilee! lel ven Kerrey elite! ell te

Velocity. protidleracrossmcalaibmatalonnozizilen ecnn en tents
Distribution of turbulent velocity fluctuations...

Velocity scale versus elevation for flume velocity,
U5 S WS E58 shoe jo SSCOMG 5 6:5 6.66.6 0 06 6 6.6 6

Velocity scale versus elevation for flume velocity,
Way Wo SiO stow jes SOCOM 5 5 6 6 6 6 oO 6 6 5 4 oS

Velocity scale versus elevation for flume velocity,
WAS Wo JAS stooe. joer Seeemed 4 66 616 6 6 624 oa 608

Velocity scale versus elevation for flume velocity,
WES UI SHOE ew SOCOM 4 GG Se abs 6 6 S08 6

Base vertical turbulent velocity scale versus flume
velocity for a constant amplitude = 0.925 foot...

- par .
Comparison of the theoretical and measured exponent
of concentration distribution in unidirectional flow

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (ST)
UNITS OF MEASUREMENT

U.S. customary units of measurement used in this report can be converted
to metric (SI) units as follows:

Multiply

To obtain

SS SS ee

inches

square inches
cubic inches

feet

square feet
cubic feet

yards
Square yards
cubic yards

miles
square miles

knots

acres
foot-pounds
millibars
ounces

pounds

ton, long
ton, short

degrees (angle)

Fahrenheit degrees

25.4
2.54
6.452

16. 39

30. 39
0.3048
0.0929
0.0283
0.9144
0.836
0.7646

1.6093
259.0

1.8532
0.4047
1.3558
1.0197
28.35

453.6
0.4536

1.0160
0.9072
0.1745

5/9

x 1073

millimeters
centimeters
Square centimeters
cubic centimeters
centimeters
meters

square meters
cubic meters
meters

square meters
cubic meters

kilometers
hectares

kilometers per hour

hectares

newton meters

kilograms per square centimeter
grams

grams
kilograms

metric tons
metric tons
radians

Celsius degrees or Kelvins!

SS eee ee
lTo obtain Celsius (C) temperature readings from Farenheit (F) readings,

use formula:

Cr 705/952)
To obtain Kelvin (K) readings, use formula:

K = (5/9) (F -32) + 273.15.

SYMBOLS AND DEFINITIONS
exponential decay rate of the velocity scale
sediment concentration
calibration nozzle coefficient
sediment concentration at the base elevation
representative roughness diameter
water depth
sediment exchange coefficient
output voltage of hot-film bridge
output voltage of hot-film bridge with sensor in still water
acceleration due to gravity
crest-to-trough wave height
output voltage of photoelectric cell
output voltage of photoelectric cell for ambient light

output voltage of photoelectric cell with light beam passing
through clear water

constant of proportionality between directional components of
turbulent velocity fluctuations

wave number

amplitude of flume oscillation

length of surface wave

length scale for oscillating and unidirectional flow

exponential decay rate of sediment concentration of oscillating
flow

Manning's roughness coefficient
hydraulic radius

horizontal oscillating velocity

SYMBOLS AND DEFINITIONS--Continued
slope of the energy gradeline
velocity scale for oscillating flow

velocity scale at base elevation for oscillating flow

period of flume oscillation
time
effective heat transfer velocity for anemometer sensor

oscillating flow velocity

horizontal flow velocity

longitudinal component of turbulent velocity fluctuations
shear velocity

peak velocity of oscillating sensor

effective heat transfer velocity

mean velocity across calibration jet

centerline velocity of calibration jet as determined from voltage
measurements

sediment-settling velocity

velocity scale for unidirectional flow theory

vertical component of turbulent velocity fluctuations

angular frequency

horizontal. displacement of fluid particle in oscillating flow
horizontal distance, positive in direction of wave travel

elevation above base elevation
vertical distance, positive up from mean water surface

theoretical exponent of unidirectional flow concentration
distribution

SYMBOLS AND DEFINITIONS--Continued

measured exponent of unidirectional flow concentration

distribution

vertical displacement of fluid particle in oscillating flow

thickness of the boundary layer

water density

shear stress at elevation Y

in unidirectional flow

shear stress at bed in unidirectional flow

phase angle

SEDIMENT SUSPENSION AND TURBULENCE IN AN OSCILLATING FLUME

by
Thomas C. MacDonald

I. INTRODUCTION

Sediment transport by waves approaching the shore has been analyzed
in two ways. Inshore of the breaker zone, the extremely complex flow
patterns and turbulence resulting from the breaking waves have necessi-
tated only a qualitative approach to sediment transport with quantita-
tive estimates based on field measurements. Offshore of the breaker
zone in relatively deep water, the problem of sediment transport can be
approached in a more theoretical manner. In this zone, sediment trans-
port studies are simplified because there is no turbulence in the flow
field from breaking waves and the flow condition near the ocean bottom
can be better estimated from linear wave theory. This report concerns
sediment transport offshore of the breaker zone.

Laboratory and field observations indicate that, as in unidirection-
al flow, sediment transport at the ocean bottom offshore of the breaker
zone is of two different types--bedload and suspended load. The dis-
tinguishing feature between these two types of transport is that in
suspended transport the entire weight of the sediment is continuously
supported by the fluid; whereas, in bedload transport the sediment rolls,
skips, and jumps along the bed and therefore its weight is partially
supported by the stationary bed. For moving sediment to be supported
by the bed means that the regime of bedload transport is contained in a
thin layer adjacent to the stationary bed, two-grain diameters thick as
proposed by Einstein (1950). The majority of the sediment in motion in
this area is bedload and thus most research has concentrated on the
turbulent boundary layer and the oscillatory bedload rate due to wave
action (Li, 1954; Manohar, 1955; Kalkanis, 1957, 1964; Abou-Seida,
1965). Sufficient advances in the theory of bedload movement in an
oscillating flow have warranted studying the suspended load to deter-
mine: (a) Approximately, what percentage of offshore movement is due
to suspended load, i.e., a second-order approximation to total trans-
port; and (b) if any of the now-predicted bedload is partially suspended
load.

This investigation develops, from an empirical approach, a method
for predicting the distribution of suspended-sediment concentration
based on the hydraulic flow conditions; i.e., surface wave amplitude
and period, depth, sediment characteristics, and bottom roughness con-
ditions. Although only one bottom roughness was studied, the resulting
method is general enough to be extended to other roughness conditions
by additional experimentation. The suspended distributions, when used
in conjunction with the bedload function of Kalkanis (1964), should
give a better approximation of the total sediment transport.

As in Kalkanis' bedload function, the approach to the suspended
load is based on many of the same principles proposed by Einstein (1950)
in his theory of bedload and suspended-load transport in unidirectional
flow. Analysis of suspended load in oscillating flow is more complicated
than that of unidirectional flow because of two factors. First, in uni-
directional open channel flow the entire depth of flow is turbulent and
the relatively high turbulent velocity fluctuations allow the sediment
exchange coefficient to be approximated by the momentum exchange coeffi-
cient which can be obtained from the shear-stress distribution. In
oscillatory flow this is not possible. Both laboratory and field obser-
vations indicate that suspension of sediment occurs to depths considerably
above the boundary layer in an area where the shear stresses due to the
oscillating motion are extremely small and difficult to measure. Although
it may be possible to express a sediment exchange coefficient in the
boundary layer as a function of the mean shear stress, this would not
provide a means of estimating the sediment exchange coefficient above
the boundary layer. Therefore, a sediment exchange coefficient which is
not based on a shear-stress distribution must be found.

The second factor concerns the magnitude of the turbulent velocity
fluctuations. Offshore of the breaker zone where the flow velocities
near the bed are low, only a small part of the wave energy is dissipated
by friction at the boundary. The remaining wave energy is lost inshore
by the breaking waves. Because of the relatively low intensity of tur-
bulence in this offshore area, the vertical velocity fluctuations are of
the same order of magnitude as the settling velocity of the sediment.
Under these conditions, the sediment exchange coefficient is highly
dependent on the sediment--settling velocity. Therefore, measured dis-
tributions of turbulent velocity fluctuations and sediment concentrations
must be used in analyzing the upward turbulent flux and downward turbulent
and gravitational flux for each sediment-settling velocity.

To obtain a relationship between sediment suspension and flow hydrau-
lics in an oscillating flow, concentration distributions for various flow
conditions must be measured. The sediment exchange coefficient is deter-
mined from these measurements. Next, the turbulent velocity fluctuation
distribution with time at a constant elevation and its distribution with
elevation must be measured. This measurement will yield the information
necessary to describe the fluid exchange. The distribution with eleva-
tion will yield a velocity scale, one of the two variables composing the
sediment exchange coefficient. From the sediment exchange coefficient
and the velocity scale, the second variable (the length scale or its
associated time scale) can be calculated. Knowledge of these fundamental

variables of suspension as a function of the flow hydraulics should lead
to a practical method of estimating the suspended-load distribution, and
indicate the important variables of suspension in an oscillating flow.

The only other requirement for a solution to the suspended load is a
knowledge of a base concentration as a function of flow hydraulics. The
base concentration is determined from Kalkanis' (1964) bedload theory,

being the concentration at the top of the bedload layer.

Combination of the bedload and suspended load will predict the total
amount of sediment in motion under specified wave and boundary conditions.
By SuperimpoSing a constant unidirectional flow, such as the mass trans-
port or a coastal current, the amount of sediment transport can be
estimated.

In this investigation, as in many research projects, the experimental
research preceded the development of a suitable method of describing sedi-
ment Suspension. For this reason a description of the experiments and
their results will be given first, followed by a discussion of how the
results can be used to predict the sediment suspension load.

II. CONCENTRATION DISTRIBUTIONS

1. Experimental Apparatus.

Experiments and observations indicate that near the ocean bottom off-
shore of the breaker zone in relatively deep water, sediment is held in
suspension. This is due to the turbulence resulting from the dissipation
of wave energy on the rough ocean bed. For waves with a small surface
slope, where 0/dx << d/dy, the fluid motion can be approximated from
linear wave theory. The equations describing the horizontal and vertical
displacement of a fluid particle are given by the expressions from Lamb
(1932):

ee (3) {cosh [k (y+d) ]/sinh(k d)} cos(k x - w t) (1)
A = (3: {sinh [k (ytd) ]/sinh(k d)} sin(k x - w t) (2)

where
d = the water depth

y = the distance from the mean water surface measured negatively
downward

H = the crest-to-trough wave height
KS Baia
1 = the length of the surface wave
Wei=we2h/ile

T = the period of the surface wave

The corresponding velocity components are obtained by differentiation
with respect to time of the above equations to give:

u= (3) w {cosh [k (y+d) ]/sinh(k d)} sin(k x - w t) (3)
= (3) w {sinh [k(y+d) ]/sinh(k d)} cos(k x - wt) (4)

From these equations it is evident that the vertical component of the
displacement and velocity becomes smaller as the distance from the sur-
face increases. At the bottom, where y = -d, the motion degenerates into
a simple harmonic oscillation in the x-direction. It is this horizontal
harmonic oscillation which is of first-order importance in producing tur-
bulence and suspension of sediment. The equations also indicate that the
magnitudes of the horizontal displacement and velocity change slightly
with depth near the ocean bottom and can therefore be considered constant
in the region of sediment suspension. For example, consider a 5-foot-high
wave with a wavelength of 150 feet and a period of 10 seconds in a water
depth of 50 feet. Equation (3) indicates the horizontal velocity at
y = -d is u = 0.393 sin(kx-wt) feet per second and that for y = -d+ 5
(S feet above the bed), the horizontal velocity is u = 0.401 sin(kx-wt).
The sediment suspension measurements which will be discussed later indi-
cate that the regime of measurable sediment concentrations is well with-
in the bottom 5 feet of water depth for this typical wave condition.
(Measurable sediment concentrations were actually found within 1 foot
of ‘the bed.) The change in horizontal velocity in the bottom 5 feet of
water depth is only 2 percent. Therefore, to design an experimental
apparatus to simulate the flow conditions near the ocean floor, the hori-
zontal flow velocity above the boundary layer can be considered constant
and equal to the value given by equation (3) for y = -d. Equation (4)
indicates that for the wave condition discussed above the vertical flow
velocity at y = -d is zero, and at an elevation of 5 feet above the bed
is 0.082 cos (kx-wt). The fact that the vertical velocity only increases
slightly in the 5 feet above the bed and that its motion is symmetrical
Suggests that the vertical velocity has no effect on the suspension of
sediment.

With the above assumptions of a constant horizontal oscillating
velocity and zero vertical oscillating velocity above the boundary layer,
the turbulent flow conditions which exist near the ocean floor are easily
approximated. By superimposing a constant velocity equal to that given
by equation (3) for y = -d but opposite in sign, there would be no motion
in the fluid above the boundary layer, the distribution of velocities in
the boundary layer would be inverted, and the bed would be oscillating at

the simple harmonic given by equation (3) for y = -d.

It is now only necessary that the physical apparatus which duplicates
these flow conditions contains a water depth greater than the thickness
of the boundary layer. Kalkanis (1957) made velocity distribution measure-
ments in a flume containing a still body of water with an oscillating

rough bed. Kalkanis (1964) showed that the velocity distribution in an
oscillating flow with the same assumptions as described above can be
approximated by:

u/uy = [1 + £2(Y) - 2£, (1) cos f,(Y)]# sin(wt + 6) (5)

where
£,(Y) = exp(Y-103/agD), (6)
a OO) = OaS(hQl 982 (7)

and sin(wt + 6) describes the variance of the velocity with time and
phase angle. In equations (6) and (7), Y is the elevation above the
bed measured positively upwards; a is the amplitude of bed oscillation;
B = (w/2v)?; v is the kinematic viscosity; and D is the representa-
tive roughness diameter. For the flume roughness conditions used in this
investigation (D = 0.05 foot), and the flow velocities studied (0.67 foot
<a < 2.0 feet and 2.0 seconds < T < 15.0 seconds), equation (5) indicates
the boundary layer thickness is no more than a few millimeters thick.

To approximate the shear stresses and therefore the turbulence condi-
tions near the ocean bed for a given water depth, wave period, and ampli-
tude, a flume having a moving bed under a still body of water was used.
The frame of reference, which describes the prototype fluid motion under
the above assumed conditions, is then moving with the bed. It is only
necessary to oscillate the bed in the harmonic motion described by the
linear wave theory for y = -d. The swing flume used in this investiga-
tion duplicates, on a one-to-one scale, these conditions.

The swing flume is shown in Figure 1(a). The flume bed is shaped to
an arc segment of a circle with an 8.92-foot radius, a 13.33-foot chord
length, and a 12-inch width. The flume, suspended from the ceiling of
the laboratory, is free to rotate about its center of curvature. The
flume is oscillated about its center position by a 1.5-horsepower
variable-speed motor connected to a drive wheel with an eccentric arm.
The eccentric arm is connected by a 10-foot connecting rod to a linkage
fixed to the flume bottom. The linkage at the flume is adjustable to

allow correction of the asymmetry of motion which would result from a
change in eccentricity. Variations in eccentricity and motor speed allow
the amplitude and frequency of oscillation to be varied over a wide range
of prototype wave conditions.

Within the flume is a stationary horizontal board, slightly less than
12 inches wide, 8 feet long, and at an elevation of 12 inches above the
lowest point of the curved bottom. The board, which is separately sup-
ported from the ceiling of the building and is not connected to the flume,
Suppresses any standing surface waves in the flume caused by the flume
motion. The fluid at this elevation must remain stationary to conform
to the flow conditions described above.

Asymmetric End Roughness

Two-Dimensional Roughness Elements

So Suspension

b. Cross Section
of Roughness
Elements

c. Cross Section of
Asymmetric End
Roughness

a. Elevation View of Entire Flume Horizontal Board 10
Suppress Standing
Surface Waves

Figure 1. Swing flume.

The shape of the artificial bed roughness (Fig. 1,b) was determined
by experiments. A large quantity of the artificial plastic sediment used
in concentration measurements was put into the smooth-bottomed flume.

The flume was oscillated at various amplitudes and periods covering the
range of flow conditions to be studied. After the flume was oscillated
at a constant rate for a period long enough to establish a natural bed
shape, the flume was stopped and the bed dunes were measured. The bed
shape was found to be approximately sinusoidal in the cross section under
all flow conditions. The mean wavelength of the bed shape was 5.5 inches
with a range of 4.5 to 8.0 inches; the mean wavelength-to-depth ratio was
8.0 with a range of 5.5 to 12. The fixed artificial roughness used approx-
imates this shape. The artificial dunes were constructed of wood and
fastened to a flexible sheet of plastic. Natural sediment with a mean
diameter of 0.3 millimeter was glued to both the dunes and plastic. The
plastic sheet was fixed to the flume bottom, covering the central 6.33
Hee OLe ther anc.

The asymmetric end roughnesses shown in Figure 1(c) were used to
eliminate secondary currents in the central measuring section of the
flume. Proper placement of the asymmetric roughness elements depends on
the flow conditions of the flume. The optimum placement of the roughness
elements for a given flow condition was determined by dropping potassium
dichromate crystals through holes in the horizontal wave suppressent board
and observing the movement of the dye streaks. When no transverse move-
ment of the dye streaks in the central part of the flume were observed,
the roughness elements were considered to be in the optimum location.

A lightweight, black plastic material with specific gravity of 1.25,
which had been crushed and sieved, was used as artificial sediment in the
experiments. The grain diameter of the sediments was uniform, bracketed
by two consecutive sieve sizes of approximately the same diameter as the
natural sediment glued to the flume bed. Only a small quantity of the
sediment was used in the flume during an experiment in order to limit
the deposition of sediment which would alter the flume bottom geometry.

When the sediment was first put into the flume it was found that air
bubbles adhered to the sediment particles, thereby changing its settling
velocity. To eliminate this buoyancy effect, deaerated water was used.
The water was deaerated in a 60-cubic foot-capacity tank located on the
wall of the laboratory at an elevation above the swing flume, heated by
a 5-kilowatt immersion heater to a temperature of 90° Fahrenheit, and
then cooled to room temperature. The deaerated water was transported to
the swing flume by gravity through a hose to reduce air entrainment.

The optical concentration meter used in the experiments was developed
by Das (1971) for measuring tm sttu concentrations in laboratory flumes.
The equipment consists of a light source, a beam collimator, a receiving
unit, and necessary recording units. A collimated beam of light, 8.5-
millimeter average diameter, is projected through the glass walls of the
flume to a duo-photodiode mounted on the opposite side of the flume.

The photoelectric cell produces a signal which is proportional to the
amount of light received which, in turn, is proportional to the amount
of light blocked out by suspended sediment. The signal from the photo-
electric cell is transmitted, amplified, and recorded on an analog paper
chart recorder and an analog-to-digital data acquisition system set to
sample at the rate of 58 samples per second. The light source and
receiver are shown in Figure 2.

The light source and receiver are mounted on a rigid, aluminum yoke
support (Fig. 3) held by friction brackets; by loosening four thumbscrews
the elevation of the support can be varied from below the flume bottom to
above the flume top while maintaining precise alinement of the optical
equipment. This flexibility allows calibration of the optical equipment
and flume concentration measurements to be made without removing: the
equipment from the supports. The yoke support and brackets are pinned
to the laboratory ceiling on the same axis as the flume so that the
optical equipment can swing with the flume or be held stationary in
space.

2. Experimental Procedure.
a. Settling Velocity of the Sediment. The sediment used in the. filxsit

series of experiments was the material which passed the 0.495-millimeter
sieve and was retained on the 0.417-millimeter sieve. The fall velocity
of this sediment was measured in a 2-inch-diameter glass cylinder filled
with deaerated water at a temperature of 72° Fahrenheit. The time re-
quired for 220 particles chosen at random to fall 8.59 inches was measured
with a stopwatch. The average settling velocity (V,), the range of
velocities, and the standard deviation were then calculated to be 0.035,
0.0213 to 0.0532, and 0.0059 foot per second, respectively.

b. Calibration of Optical Concentration Meter. Calibration of the
optical equipment was done in a 0.5- by 0.5- by 1.0-foot clear, plastic

calibration tank placed on the top of the swing flume. The 1.0-foot
dimension of the tank was positioned parallel to the axis of the light
source and receiver; i.e., the same width as the swing flume. The tank
was then filled with a measured quantity of deaerated water. A small,
measured amount of cleaned sediment was added to the tank and the
sediment-water mixture was stirred mechanically to give a uniform sus-
pended concentration. The collimated light beam and receiver were posi-
tioned and a 5-second record of the voltage from the receiver was recorded
on the analog chart recorder and magnetic tape. Uniformity of concentra-
tion in the tank was checked by measuring the fraction of light blocked
by the sediment at various locations in the cross section of the tank.
The mechanical stirrer was stopped and the sediment allowed to settle.
Records were then made of the voltage from the light beam passing through
clear water and the voltage of the ambient light. The fraction of light
passed was then calculated as the ratio of the voltage with sediment in
suspension to the difference between the voltages of the beam through
clear water and the ambient light. Measured amounts of sediment were

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added to the calibration tank and the procedure repeated until the range
of the optical equipment was covered. Measurable concentrations ranged
from 0).1 to 2.5 grams per liter. The logarithm of the fraction of light
passed versus the concentration in grams per liter was plotted to give
the calibration curve shown in Figure 4. The least squares, best fit
equation for this curve is:

GS (COsSeS), tan /G, =I) 5 (8)
where
C = concentration (in grams per liter)
I = mean voltage from the receiver when the light beam is passed

through the sediment-water mixture

I, = mean voltage from the receiver when the light beam is passed
through clear water

I' = mean voltage from the receiver when the light beam is turned off

The calibration curve, which was checked periodically during the experi-
ments, did not change.

In setting up the calibration experiments, it was found that a change
in the focus of the optical equipment would change the resulting calibra-
tion curve. To eliminate this problem a brace was made to hold the equip-
ment in focus. A check of the focus was made during each concentration
measurement by a wire-screen filter which, when placed in the light beam,
blocked out a known and constant amount of light. If a change in focus
was detected by the filter measurements, the concentration measurements
were not used.

c. Concentration Distribution Measurements. For concentration dis-
tribution measurements in the flume, a datum elevation of the optical
equipment had to be established. The mean elevation of the crest of the
artificial dunes was used as the base elevation and was determined by a
scale fixed to the flume and a pointer fixed to the optical equipment
brace.

The desired period and eccentricity were selected and the flume link-
age adjusted to give a symmetric oscillation. The flume was filled with
deaerated water to the elevation of the wave suppressent board (12 inches
above the lowest point of the bed), and the asymmetric end roughnesses
were positioned. Depending on the flow conditions chosen, 100 to 500
grams of sediment was cleaned and deposited in the flume. The flume was
then oscillated until the distribution of sediment in the flume was at
equilibrium. The equilibrium condition was determined by periodically
measuring the concentration of sediment at a fixed point in space until
the concentration did not change with time.

2 |

T’)] , FRACTION OF LIGHT PASSED

Te/ (eli

C=-0.585 In [I/(Ip-1)]

OF2

0.02

0 0.4 0.8 lee 1.6 220 24
C, CONCENTRATION (gf™')
Figure 4. Calibration curve for sediment diameter:

0.417 millimeter < D < 0.495 millimeter,

Vg = 0.035 foot per second.

The concentration distribution in the vertical was then measured for
the flow condition selected. Again, for each elevation, voltage records
were made for the sediment-laden water, clear water, ambient light, and
clear water plus the filter. If the optical equipment was held stationary
in space, the records for clear water and clear water plus filter were
made while the flume was oscillated at such a long period that no sediment
was in suspension. The time interval of the record for sediment-laden
water, clear water, and clear water plus filter was always an integer
multiple of the flume oscillation period. This procedure automatically
allowed any irregularities in the transmissibility of the flume windows
to be compensated for when calculating the fraction of light passed.

The output signal of the photoelectric cell, which was recorded on
Magnetic tape at the rate of 58 samples per second, was not constant
With time, due to instantaneous concentration fluctuations. Because the
concentration is related to the logarithm of the output voltage, it was
necessary to calculate the concentration for each sample and then average

the concentrations over the period of record to determine the true mean
concentration.

The concentration measurements were usually started as near the bound-
ary as possible, about 0.5 centimeter above the crest of the roughness
elements. The flume was stopped, the elevation of the optical equipment
was raised and recorded, and new measurements were taken. This procedure
was followed until an elevation was reached at which the concentration
was too low for the optical equipment to measure. The optical equipment
was then lowered in a stepwise fashion until near the boundary to obtain
concentration measurements at intermediate elevations. In this manner,

7 to 15 concentration measurements were obtained to describe the concen-
tration distribution for one flow condition.

3. Results.

Sixty-five concentration distribution curves were obtained of the
form,

C=C, exp(MyY) , (9)
where
M = slope of the curve (in feet 1)
C, = concentration at the base elevation (in grams per liter)

C = concentration of sediment (in grams per liter); average of
the concentrations calculated from equation (8) for each
sample of record during the period

Y = elevation above the crest of the artificial roughness (in feet)

The variable used to describe the flow condition is the flow
velocity; U,, defined as:
U,= @L/T , (10)

where L is the amplitude (in feet) and is equal to one-half the arc
length which passes a fixed point during one-half cycle, and T is the
period of oscillation (in seconds). The flow conditions studied ranged
from a minimum of U, = 0.235 foot per second (minimum to allow suspension
of sediment) to a maximum of U, = 1.18 feet per second (maximum allowed
by flume construction). The amplitudes and periods used in these experi-
ments ranged from 0.235 to 1.60 feet and 1.65 to 15.16 seconds, respec-
tively. Figure 5 shows some typical concentration distribution curves
that were obtained.

For the 65 different flow conditions studied, the base concentration,
C, (eq. 9), could not be correlated to any of the hydraulic parameters
but depended on the amount of sediment in the flume. For different flow
conditions the sediment in the flume would be distributed differently
along the bottom of the flume, thereby giving a different and uncontrol-
lable base concentration.

The 65 experiments also showed that two different laws exist in two
ranges of conditions governing sediment suspension. For amplitudes of
0.693 foot and larger, the concentration distribution is determined by
the flow velocity alone. For amplitudes less than 0.693 foot, the con-
centration distribution is a function of the amplitude relative to the
wavelength of the artificial roughness.

Thirty-six of the 65 concentration distribution curves were deter-
mined using amplitudes of 0.693, 0.770, 0.925, 1.25, and 1.60 feet. For
these five amplitudes, it was found that the slope of the distribution
curve is a function of the flow velocity, independent of amplitude.
Figure 6 graphically illustrates the relationship between M, the slope
of the concentration distribution curve of equation (9), and U,, the
variable of equation (10) used to describe the flow conditions of the
flume. These data are also tabulated in Table 1 which gives the periods,
amplitudes, and use of the optical equipment. The least squares, best
fit equation for this relationship is:

Ye atIS ee GSS) Uy. (11)

where U, is in feet per second, and M is the slope of the concentration
distribution curve (in feet™!). There is no statistical evidence to indi-

cate that this relationship is significantly different from a higher order

polynomial.

Results of experiments by Shinohara, et al. (1958) confirm the above
results. They found the same linear relationship between the logarithm of
concentration and elevation and qualitatively determined that as the inten-
sity of the flow increased the slope of the concentration distribution
curve, M, became flatter.

518.01
518.02
518.03
713.03
612.01

CONCENTRATION RATIO

Cie

0 0.1 ©:2 0:3 0.4 O'S 0.6 ONG
Y, ELEVATION ABOVE CREST OF ROUGHNESS ELEMENTS (ft)

Figure 5. Examples of measured concentration distribution curves;

sediment-settling velocity, V, = 0.035 foot per second.

(29)

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Table 1. Concentration distribution data for Vs = 0.035 foot per second,
amplitude > 0.693 foot.

Slope, Variance in
d(1nC)/d|least squares Remarks
(Eta) curve

-5.60 0.0182 optics

-7.99 0.0184 stationary

-11.28 0.0196

-13.91 0.0236

-15.39 0.0136

optics
stationary

optics
moving
optics
moving
optics
moving
optics
moving

optics
moving

Not calculated.

The same results were obtained more recently by Kennedy .and Lacher
(1972). Their investigation examined the behavior of the mean sediment
concentration and the periodic sediment concentration fluctuations. The
experiments were conducted in a stationary flume with a fixed bed on which
a limited amount of loose sediment was distributed. Turbulence for sedi-
ment suspension was caused by surface waves generated by a wave generator.
The sediment concentrations were measured with optical equipment which
incorporates the same theoretical principles as the equipment used in the
swing-flume experiments but of a much smaller size. The smaller size and
configuration of the equipment allowed measurements very near the bed and
sampled a much smaller volume of flow.

Kennedy and Locher's (1972) experiments in mean sediment concentra-
tion distribution were limited to a wave height of 0.24 foot, a wave
period of 1.0 second, and a mean water depth of 0.82 foot. The mean
sediment concentration was measured at various elevations along five
evenly spaced verticals in the flow. The spacing of the verticals was
selected to cover one wavelength of the bed dune shape. A total of 78
data points was measured, and when the logarithm of the mean concentra-
tion was plotted against elevation above the bed a well-defined linear
relationship of C = C, exp(-36.5 Y) was obtained. This relationship is
identical to that obtained in the swing-flume experiments, with the ex-
ception of the high rate of decay of sediment concentration, (-36.5).
Kennedy and Locher used a quartz sediment of 0.14-millimeter mean dia-
meter in their experiments. The settling velocity of this sediment was
not reported; it was probably about 0.050 foot per second, which is 43
percent greater than that of the principal plastic sediment (settling
velocity of 0.035 foot per second) used in the swing-flume experiments.
Swing-flume measurements, using sediments of different settling velocities,
are discussed later in this section. For a given flow velocity a higher
rate of decay of concentration is expected, as settling velocity increases.

Much of the analysis of data by Kennedy and Locher dealt with the
periodic sediment concentration fluctuations. Although no specific con-
clusions were obtained regarding these fluctuations, the data did indi-
cate the fluctuations were only apparent near the bed (within about 0.05
foot of the bed). This explains the lack of periodicity in concentration
fluctuations for the swing-flume measurements, in that 0.05 foot is near
the lower limit where the much larger optical equipment of the swing
flume could be used.

Similar exponential concentration curves were obtained for the two
different methods used in simulating sediment suspension in an oscillat-
ing flow; i.e., an oscillating flow over a fixed bed as used by Shinohara,
et al. (1958) and Kennedy and Locher (1972), and an oscillating bed under
a ''stationary" body of water as used in the swing-flume experiments.

Figure 7 shows the relationship between M and Uj, _ for two condi-

tions. One set of data represents the condition that the optical equip-
ment is stationary in space; the other data points are for the optical

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equipment moving with the flume. All other variables in these experiments
were the same. The amplitude of oscillation was 0.925 foot. There is no
statistically significant difference in the results, indicating uniform
suspension along the flume. None of the measurements for large amplitudes
(greater than 0.925 foot) (Table 1) were made with the optical equipment
moving with the flume. The reason for this is at large amplitudes the
optical equipment would move into an area of the fluid where secondary
circulations due to the asymmetric roughness elements may exist and there-
fore not give a representative concentration.

The remaining 29 of the 65 experiments were made using amplitudes of
05255), 08465) and On6i7) foots | Mabile) 2 as) a\stabullation o£ the data jvand
Figure 8 shows the results of the 65 experiments. As shown in Figure 8,
there is a great deal of scatter in the data for small amplitudes; there-
fore, only qualitative conclusions have been made. In general, the
smaller the amplitude the smaller the slope of the concentration distri-
bution curve.

Experiments, movies, and photos were used to determine why the small
amplitudes do not obey the flow velocity relationship of the larger ampli-
tudes given in equation (11). Based primarily on visual observation, the
following explanation is hypothesized. For small amplitudes, the distance
of travel of the flume bottom during a half cycle is not great enough for
the boundary layer to fully develop during each stroke and to become tur-
bulent. Only at the end of the half cycle when the acceleration forces
cause separation is sediment thrown into suspension. Separation only
occurs at the downstream face of the artificial dunes. The observed sus-
pension pattern when a 0.235-foot amplitude of oscillation was used con-
sisted of plumes of suspension separated by areas of zero concentration.
These plumes were accentuated because, on the return, the half-cycle
separation at the downstream face occurred such that the succeeding burst
of sediment was thrown into approximately the same region of fluid as in
the first half cycle; i.e., the amplitude of motion was about equal to a
multiple of the wavelength of the dune shape. When the amplitude was
increased to 0.465 foot, a more fully developed boundary layer was
attained. In this case, separation occurred over a somewhat longer
distance of travel but still less than the wavelength of the dune shape
because less deceleration force was required. The suspension pattern
was the same as with the 0.235-foot amplitude but much less distinct;
the plumes were wider and overlapping. Finally, with the 0.693-foot
amplitude, separation occurred over a distance equal to or greater than
the wavelength of the dunes, and a uniform longitudinal concentration
was attained.

Special experiments were conducted to verify the above hypothesis.
The vertical distribution of concentration at various horizontal loca-
tions in the fluid was measured to determine if the concentration distri-
bution varied. If the above hypothesis is correct, the concentration
distribution should vary along the horizontal and in a regular manner
determined by the shape of the bed dunes. In addition, if suspension

Table 2. Concentration distribution data for V, = 0.035 foot per second,
amplitude < 0.693 foot.

Curve Period | Amplitude Uo Slope Variance in
d(1nC)/d | least squares Remarks
No. (s) (ft) (ft/s) (ft-!) curve
621.01 Zeelell 0.617 Mg 70 -11.15 0.0511 optics
OZ 02 Dolls ORG, OaTT, = 6.5 0.0459 stationary
621.03 4.60 0.617 ORS 37 -13.10 0.0134
621.04 6.58 0.617 ORS75 -15.12 0.00268
621.05 9.38 0.617 0.263 -10.95 OF0233

628.01} 9.40 ORION 0.263 optics
628.02 |] 6.57 0.617 0.376 moving
628.03} 4.59 0.617 0.538

629. optics
629. moving
629.

629,

Te optics
plays moving
“ae

lols:

plea:

ples

Wakako

802.
802.
802.
802.
802.

optics
moving

0. 0. 0 optics
0.465 0.585 -14.10 0.0239 stationary
0.465 0.585 -12.82 0.0208

0.465 0.585 Sol Se 0.0152

0.465 0.585 -14.00 0.0447

M,SLOPE OF CONCENTRATION DISTRIBUTION CURVE (ft7')

|
oO

nm
fo)

I
De)
on

ds
fo)

Figure 8.

M versus U, for sediment-settling velocity,

AMPLITUDE = 0.693 ft
AMPLITUDE = 0.617 ft
AMPLITUDE = 0.465 ft
AMPLITUDE = 0.235 ft

04 0.6 0.8 1.0 ine
, FLUME VELOCITY (ft/s)

= 0.035 foot per second.

B72

for small amplitudes is a function of location, the shape of the concen-
tration distribution curve for a particular vertical may not be the same
flume velocity, U,, but with a large amplitude. The following is a
description of the experiments.

The flume was adjusted to a 0.465-foot amplitude and a 3.18-second
period was selected. A special brace with attached scale was construc-
ted to hold the optical equipment stationary in space, and therefore
stationary relative to the fluid. This brace allowed relocation of the
optical equipment to any desired new location along its arc while main-
taining the freedom to change the elevation of the optical equipment
relative to the bed of the flume. An initial location of the optical
equipment was chosen and a vertical concentration distribution measured.
The optical equipment was then relocated to a new position and another
concentration distribution was measured. This procedure was repeated
until five concentration distribution curves were obtained. Each was at
a different horizontal location relative to the position, at a fixed
phase, of the flume bed, but with identical flow conditions of the flume.
The horizontal range of the five distribution curves was about equal to
one wavelength of the bottom roughness shape. The results of these ex-
periments (Fig. 9) indicate that the distribution of concentration is not
uniform along the flume bed for the 0.465-foot amplitude studied. Figure
9 also indicates that the rate of sediment concentration decay is less in
the areas between the dunes and greatest at the crest of the dunes. This
implies that the plumes of suspension are above the trough of the bed
shape, where it would be expected if the sediment is thrown upward and
downstream from the downstream face of the dunes.

Figures 10 to 14 are the concentration distribution curves measured
for the locations indicated in Figure 9. Although not conclusive, these
data indicate that the vertical distribution of sediment in the plumes
does not conform to the exponential distribution of equation (9). The
relationships shown in Figures 11 to 14 display a slight, but statisti-
cally significant curvature and were obtained at locations in the plume;
whereas, Figure 10 shows no curvature and was obtained at a location
between plumes. This could be explained by the existence of periodic
stationary eddies, one located on each side of the plume axis. The eddies
would sweep sediment into the base of the plume axis giving a relatively
high concentration and carry sediment out of the top of the plume, causing
the concentration to be lower than would be predicted in a randomly tur-
bulent flow field.

The small amplitudes studied represented rare prototype conditions ;

therefore, all subsequent experiments were limited to amplitudes greater
than 0.617 foot.

4. Experiments Using Sediments of Different Settling Velocities.

Two different sediments of the same black plastic were selected
and investigated to determine the effect of settling velocity on the

M, SLOPE OF CONCENTRATION DISTRIBUTION CURVE (ft7')

al
1)

ale
iS

als
D

814.03

Numbers opposite
the points indicate
curve numbers

flume is reversing its direction of motion

Faigumey O)

M versus location of optical equipment for identical

flow conditions, V, = 0.035 foot per second.

C/Cy , CONCENTRATION RATIO

0.4

0.04

002

Jn Cll o=(-17.20) ¥

0.05 0.1 OziS 0.2
Y, ELEVATION ABOVE CREST OF ROUGHNESS ELEMENTS (ft)

Figure 10. Concentration distribution for run 814.01.

C/C,, CONCENTRATION RATIO

0.4

O.2

0.04

0.02
O

In C/Cy =(-14.08) Y

0.05 0.1 0.15 0.2
Y, ELEVATION ABOVE CREST OF ROUGHNESS ELEMENTS (ft)

Figure 11. Concentration distribution for run 814.02.

C/Cy , CONCENTRATION RATIO

In. C/C,=(-12.83) ¥
oO

0 0.05 OE 0.15 0.2
Y, ELEVATION ABOVE CREST OF ROUGHNESS ELEMENTS (ft)

Figure 12. Concentration distribution for run 814.03.

Sih

Cee, CONCENTRATION RATIO

0.2}

0.02

O 0.05
Y, ELEVATION ABOVE

bn. C/Cg=(-15.70) Y

O.| Oxl5 0.2
CREST OF ROUGHNESS ELEMENTS (ft )

Figure 13. Concentration distribution for run 814.04.

CONCENTRATION RATIO

Ln C/C, =(-14.00) ¥
{e)

0.05 0.1 0.15 Ore
Y, ELEVATION ABOVE CREST OF ROUGHNESS ELEMENTS (ft)

Figure 14. Concentration distribution for run 814.05.

SHS)

concentration distribution. The first of these sediments was the material
which passed the 0.701-millimeter sieve and was retained on the 0.589-
millimeter sieve. Settling-velocity measurements of 225 randomly chosen
particles determined the mean settling velocity, the velocity range, and
the standard deviation as 0.0626, 0.0387 to 0.113, and 0.0131 foot per
second, respectively. The second sediment was the material which passed
the 0.589-millimeter sieve and was retained on the 0.495-millimeter sieve.
Settling-velocity measurements of 240 particles of this material deter-
mined the mean settling velocity, the velocity range, and the standard
deviation to be 0.0498, 0.0285 to 0.0754, and 0.00885 foot per second,
respectively.

Table 3 gives the experimental results obtained for the two sediment
types and Figure 15 shows how these results compare with the results for
sediment with a settling velocity of 0.035 foot per second. As expected,
for sediment with a higher V,, the concentration of sediment decreases
with elevation above the bed at a higher rate. Only this qualitative
conclusion was obtained. Not enough data were obtained to define quanti-
tatively the relationship between Vg and M.

Table 3. So eaeae eae distribution data for
Vs = 0.0626 and 0.0498 foot per second.

Curve Period Amplitude
No.
[eS CGB se Re Na ORES (&t/s)

0.0626 a olneeee ey ee

Variance in
least squares
curve

Slope,
d(inc)/@

Ge")

0.0327
0.0154
0.00497
0.000966

= 0.0498 ft/s

0.00095
0.00698
0.00378
0.00177

The interesting indication of these measurements is that the increase
in the rate of decay with elevation of the concentration for a sediment
of higher settling velocity is not as great as predicted from the O'Brien
(1933) equation for concentration equilibrium conditions. Consider the
concentration equilibrium equation used in unidirectional flow for sus-
pended sediment:

Glvs) E(de/dy)) = 0.) (12)

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where

C = concentration
V, = settling velocity of the sediment particle
E = sediment exchange coefficient (which here is assumed equal to

the momentum exchange coefficient in unidirectional flow)
Y = elevation above the bed

Inserting the expressions for C and (dC/dY) obtained from equation
(9) into equation (12) and solving for E yield:

E = Wait 0 (13)

In unidirectional flow and for relatively low sediment concentrations,

it is assumed that the sediment exchange coefficient is equal to the
momentum exchange coefficient, is a function of the fluid motion only,
and is independent of the particle-settling velocity. For this assump-
tion to be valid in oscillating flow, the slope of the concentration dis-
tribution curve must be directly proportional to the settling velocity.
Although Figure 15 indicates M is proportional to V,, it does not
indicate direct proportionality. This discrepancy is discussed in
Section IV.

5. Summary of Experimental Results.

The following is a summary of the results of the concentration meas-
urements and a brief discussion of their limitations.

a. The vertical distribution of sediment concentration can be ex-
pressed by equation (9). Sediment is held in suspension by the random
motion of turbulence which is generated in the boundary layer and is
transported by diffusion upward while decaying continuously because of
viscosity. As shown later in Section III, the turbulence intensity
decays rapidly with elevation above the bed. The upper elevation to
which the turbulence can diffuse (the water surface in the prototype
and the wave suppressent board in the flume) is larger than the eleva-
tion at which the turbulence intensity decays to extremely small values;
therefore, this upper boundary can be approximated as being at infinity.
Under these conditions it is reasonable that the empirical results given
by equation (9) indicate an exponential decay (as is commonly found in a
diffusion process), and only become zero at Y = infinity. As expected,
the concentration distribution in oscillating flow is different than in
unidirectional flow. In unidirectional flow the turbulence is distrib-
uted between the bed and the water surface, the turbulence intensity is
Significant at the water surface. Because the water surface is not effec-
tively at infinity, the distribution of both the turbulence and the sedi-
ment concentration would be different than in oscillating flow.

b. The base concentration, C, (eq. 9), for flume measurements
is a function of the sediment charge in the flume and therefore could
not be correlated to flow hydraulics. As shown by Einstein (1950), a
flow is only capable of transporting a limited amount of sediment of a
given size. This limiting capacity is determined by the flow velocity,
sediment characteristics, and roughness of the boundary. In addition,
the flow will only transport this capacity rate if there is a sufficient
supply of sediment available. Otherwise, the transport rate will be
reduced by the ratio of the supply rate to the capacity rate. Because
the capacity transport rate for a given flow is determined by the proba-
bility of a particular sediment particle being subjected to sufficient
hydraulic forces to move it, there must be some particles in the bed that
are not in motion at any instant of time. Had there been enough sediment
in the flume to satisfy the flow's sediment transport capacity, the
measured Co, could have been correlated to flow velocity. Unfortunately,
under those conditions some sediment must be loosely deposited on the
flume bed, thereby changing the fixed-bed geometry and roughness. There-
fore, only the flow's capacity to transport sediment of a specific size
can be estimated. This estimate must use the capacity base concentration
calculated from Kalkanis' (1964) bedload equation and not the base concen-
trations measured in this investigation.

canines thesrangerotetiliow velocities W0.2foot per second i<sU-¥< il
feet per second, for amplitudes of oscillation equal to or greater than
0.693 foot, and for V, = 0.035 foot per second, the slope of the exponen-
tial distribution of sediment concentration is a function of flow veloc-
ity only. The slope, M, can be approximated from the flow velocity,
U>, by equation (11). This equation is only a best fit empirical rela-
tionship and cannot give reasonable approximations of M for Ug values
very far outside the stated range. This becomes apparent when substitut-
ing iniarlarge-valuevof WU, 330 exe, 2.0lneet per second, andjicaleulating
M. The result would be a positive value for M; i.e., the concentration
of sediment increases with elevation which is not reasonable. The limit-
ing value of M for extremely large values of U, should be zero, or
uniform concentration of sediment throughout the depth. At the other
extreme, equation (11) gives a value of M = -18.45 feet! for Uz = 0 foot
per second which is also not reasonable. But, for low values of U,, any
continuous function is not expected to give a correct relationship since
at some point the flow changes from turbulent to laminar. In laminar
flow there is no turbulence and therefore no sediment suspension. As Up
is increased, the flow, at some velocity, suddenly changes from laminar
to turbulent and just as suddenly the suspended-sediment concentration
changes from zero to some positive value. Therefore, the relationship
expressed by equation (11) becomes invalid at some small value of U)-

d. For the flow velocities studied, the sediment-settling velocity
has a significant effect on the slope of the concentration distribution
curve. Not enough data were obtained to define the relationship between
V, and M, but the data did yield the qualitative relationship that for
constant U,, M decreases (or becomes a larger negative value) with in-
creasing Vs. As discussed earlier, if the sediment exchange coefficient

is equal to the momentum exchange coefficient, as is assumed for unidirec-
tional flow, the slope, M, should be directly proportional to V,. The
experimental results for oscillating flow did not indicate direct propor-
tionality. Therefore, the sediment exchange coefficient for oscillating
flow given by equation (13) is, as yet, an undetermined function of Vz.
and U,. A discussion in Section IV indicates why this result is expected.

III. DISTRIBUTIONS OF TURBULENT VELOCITY FLUCTUATIONS

ils Experimental Apparatus.

Successful measurements of turbulent velocity fluctuations in fluids
have been made using either constant current or constant temperature
hot-film anemometers. A constant temperature, quartz-coated hot-film
sensor, model number 6010 made by Thermo-Systems Incorporated, Minneapolis,
Minnesota, was used in this investigation. The sensor was connected to a
1050 series anemometer also made by Thermo-Systems Incorporated. The
anemometer uses a bridge and feedback system to maintain a constant resis-
tance and therefore a constant temperature of the sensor. Any change that
affects the heat transfer between the sensor and the environment is reflec-
ted in the voltage output of the bridge. This output voltage is amplified
and recorded on magnetic tape. The record of voltage fluctuations is then
converted by use of a calibration curve to a record of velocity fluctua-
tions. A schematic of the hot-film bridge is shown in Figure 16. The
hot-film sensor and probe are shown in Figure 17.

Calibration of the hot-film anemometer was done in the calibration
tank (Fig. 18) which was divided into two chambers, a fore chamber and a
calibration chamber. The fore chamber contained two wire screens to
ensure a uniform velocity distribution. The two chambers were connected
by a 1-inch-diameter nozzle located at the midpoint of the partition
Separating the two chambers, 5.25 inches above the bottom of the tank.

An overflow was located at the downstream end of the calibration chamber,
4.75 inches above the nozzle. Water was supplied from the deaeration
tank, the rate controlled by a 0.25-inch needle valve. The flow into
the calibration chamber was a submerged jet. The probe with sensor was
held at the downstream face of the nozzle by clamps connected to a point-
gage assembly. The point-gage assembly was used to raise and lower the
sensor known amounts to obtain velocity measurements across the diameter
of the nozzle. The water collected at the overflow in a measured time
was weighed to determine the flow rate and mean nozzle jet velocity.

Measurements of the turbulent velocity distributions were conducted
in the swing flume. Only minor modifications to the flume apparatus
were necessary to accommodate the anemometer equipment.

As shown in Figure 17, the sensor is extremely delicate and there-

fore cannot be used in flows containing solid particles. For this reason
the flume had to be cleaned of all the black plastic sediment used in

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Figure 18. Hot-film anemometer calibration tank.

concentration measurements. To ensure that the natural sediment glued
to the artificial dunes did not.break loose and damage the sensor, the
surface of the dunes was sprayed with a thin film of plastic. The plas-
tic was thin enough to not alter the surface roughness and strong enough
to hold the sediment in place.

To accommodate the anemometer equipment, the yoke support used in
concentration measurements had to be removed from the support frame
(Fig. 3). The hot-film probe assembly (Fig. 19) was attached to the
support frame at a position midway across the flume. The elevation of
the sensor could be changed by loosening two friction clamps and reposi-
tioning the probe holder in relation to a scale fixed to the assembly.

A 6-inch-square opening was cut into the wave suppressent board to allow
the sensor to be lowered to the flume bottom.

2. Experimental Procedure.

The hot-film sensor is extremely sensitive to both water temperature
and water quality. Therefore, it was necessary to determine a new cali-
bration curve each day that velocity measurements were made in the flume.
Water temperature readings made during calibration measurements were com-
pared to readings made during flume measurements and did not vary. It
was necessary to use deaerated water in both the calibration and flume
measurements to prevent air bubbles from adhering to the hot-film sensor,
thereby either burning out the sensor or altering its heat transfer char-
acteristics. Periodically, during both calibration and flume measurements
a record was made of the base voltage; i.e., the voltage for the sensor in
Still water. These voltage readings were then averaged to obtain a mean
base voltage which is needed in calculating the calibration curve.

Both days that velocity measurements were made with the anemometer,
a 5-percent overheat of the sensor was used. This ensured uniform sensi-
tivity of the sensor and base voltage of the measurements. The conditions
for measurements on both days were so similar that the’two calibration
curves could not be distinguished. This allowed all the calibration data
to be used for one curve and only one equation used to convert voltage
into velocity.

a. Calibration of the Hot-Film Sensor. The hot-film sensor was
positioned at the center and as close to the downstream face of the cali-
bration nozzle as possible (approximately one-eighth inch). A high flow
rate through the flume was obtained by fully opening the needle valve.
This flow rate was allowed to continue until a steady flow through the
calibration tank was established (about 5 minutes). The flow through the
nozzle was monitored by the continuous voltage output of the hot-film
bridge displayed on the anemometer equipment. When the voltage readings
became constant with time the flow rate was steady. A 24-second magnetic
tape record was then made at the rate of 117 samples per second. Simul-
taneous with the voltage record, a flow rate measurement was made. The
flow rate was determined by timing the period required to collect 10 to

\
FRICTION CLAMPS TO
ALLOW ASSEMBLY
TO BE MOVED
VERTICALLY

CLAMP

ELECTRICAL LEADS
TO ANEMOMETER

BOA SEE DETAIL "A"

LeOety
PROBE HOLDER

A. DETAILS OF CLAMPS

PROBE HOLDER

TIP SUPPORT 12"

PROBE HOLDER
13" (approx.)

SENSOR HOLDER

Figure 19. Hot-film probe extension assembly.

15 pounds of water at the overflow of the calibration tank. The water
was weighed on a scale to the nearest 0.05 pound. The flow through the
flume was then reduced by partially closing the needle valve and a second
set of measurements made. The procedure was repeated until five voltage-
velocity points were measured for a calibration curve.

The results of the two calibration curves are shown in Figure 20.
The velocity range measured was from 0.0374 to 0.580 foot per second.
The relationship between velocity and voltage was:

Ine(E' - E,) = (0.422) ing(Uz) + 7.147 , (14)

where E' is proportional to the output voltage of the hot-film bridge,
and E9 is proportional to the mean output voltage for the sensor in
still water. U,, the actual velocity of the fluid, was calculated by
dividing the mean velocity determined from flow rate measurements by the
nozzle coefficient, C,. The log-log relationship shown in Figure 20 is
consistent with the theoretical results from the manufacturer and the
results by Das (1968). Because magnitudes of the voltage readings for a
given flow velocity are dependent on the water temperature, water quality,
overheat percentage, and amplification of the sensor output signal, no
attempt was made to compare quantitatively the measured calibration curve
‘with other published curves.

b. Determination of the Nozzle Coefficient. The sensor was posi-
tioned close to the downstream face and at the lower edge of the nozzle.
After establishing a high, constant flow rate through the nozzle, the
voltage from the hot-film bridge was recorded. Without interrupting the
flow, the sensor was then raised a small measured amount and a second
voltage record made. This procedure was repeated until the sensor was
at the upper edge of the nozzle. The velocity of flow was estimated for
each location from a calibration curve similar to Figure 20 but not cor-
rected by a nozzle coefficient. The velocity profile across the diameter
of the nozzle for the high flow rate is shown in Figure 21(a). Because
of the high flow rate, the water surface elevation in the deaeration tank
was lowering a Significant amount, thereby decreasing the flow rate
through the calibration tank. This is the reason for the lower measured
velocity at the top of the nozzle. The mean velocity was determined by
integrating the velocity profile across the jet. The nozzle coefficient
was then calculated from:

ay sg! F 2
C= Ore) Chee CR. Ohes (15)
where
Cy = nozzle coefficient
Vaan = mean velocity across the jet

(dia.) jo4 = diameter of the jet

(dia.). = diameter of the nozzle (1 inch)
Ue ) = velocity determined from voltage measurements

O |2 Jan. 1973 data
@ 19 Jan. 1973 data

dn (E-Eq) = (0.422) dn Us + 7.147

Ue, FLUID VELOCITY (ft/s)

SO) (Ou aclom cla Cou acley "Merere
(E-E,), HOT-FILM BRIDGE OUTPUT MINUS
BASE OUTPUT

Figure 20. Output versus velocity calibration curve for hot-film
anemometer measurements.

(ft/s)

U,, VELOCITY OF FLUID

(ft/s)

FLUID

Ue, VELOCITY OF

(a) Flow rate velocity = 0.567 ft/s

Measured velocity
= OOO atts

Mean velocity
= 0.487 ft/s

C,= 0.99

Measured velocity
=OLOW Se fits NS Mean velocity

= 0.0668 ft/s \

\
\
\
i)
\
\
\

Calibration nozzle

0 0.4 0.8

DISTANCE ALONG THE DIAMETER OF CALIBRATION
NOZZEE)> Cin)

Figure 21.. Velocity profile across calibration nozzle.

The nozzle coefficient for the high velocity (0.569 foot per second) was
then calculated to be 0.99. This set of measurements was repeated for

a low flow rate. The results of these measurements are shown in Figure
21(b). The nozzle coefficient for the low velocity (0.072 foot per sec-
ond) was calculated'to be 0.98. The nozzle coefficient for intermediate
velocities was assumed to be a linear interpolation between the two above
values.

c. Flume Measurements of Turbulent Velocity Distributions. The

velocity, which is of significance in attempting to describe the sus-
pension of sediment in an oscillating flow, is the vertical component of
velocity fluctuations due to turbulence, v'. When the swing flume is
operating, the only velocities which exist in the fluid are: (a) the
three directional components of velocity fluctuations caused by turbu-
lence, and (b) the oscillating flow contained in the boundary layer.

The boundary layer extends only a few millimeters above the bed of the
flume. Sediment is in suspension at an elevation considerably above
the upper limit of the boundary layer. Therefore, the flow regime of
interest has no measurable mean or periodic velocities, only the random
motions caused by the turbulence diffusing upward from the bed. The
problem, then, is to determine only the vertical component of the veloc-
ity fluctuations.

Das (1968) developed a method of measuring v' in a still body of
water with an oscillating rough bed. This method involved imparting an
oscillating motion to the sensor in the vertical direction. If only
measurements made during the peak velocity of the sensor are considered,
then the total velocity affecting heat transfer from the sensor is:

v2 = (V + vt)? + ut? + wi2 - (16)
where
Ve = total velocity affecting heat transfer
Vv = peak velocity of the sensor; known from the period and
amplitude of oscillation
Vie = vertical component of the turbulent velocity fluctuations
u' and w' = turbulent velocity fluctuations in the remaining two

directions
Dividing this equation by v2 yields:
CES We GNM ee ICON Ca De. (a7)

If the sensor oscillation is such that V >> v', u', and w', then the
above equation can be approximated by:

CENA Osean” (18)

This equation is sensitive to only v'. Experiments by Das were conduc-
ted in a stationary flume in which only a horizontal bottom plate was
oscillated to produce turbulence. The results showed some promise for

the method.

When Das' method of measuring v' was tried in the swing flume, it
was not successful because of excessive vibrations of the sensor. These
vibrations were mainly due to: (a) the long holder required to extend
the sensor to the flume bottom, and (b) attaching this holder to the
support frame which was indirectly subjected to the vibrations from the
flume motion. The velocities of the sensor due to vibrations were
greater than the velocities of the turbulent flow; therefore, no com-
ponent of turbulent velocity could be distinguished.

An approximation to v!' had to be obtained based on the following
assumptions. It was assumed that at a given elevation the root-mean-
square value of the three components of turbulent velocity fluctuations
is proportional to each other. It was also assumed that the heat con-
vected from the sensor due to velocities in the direction parallel to
the sensor axis was insignificant compared to the heat convected by
velocities perpendicular to the axis. This assumption is justified in
that the hot-film has directional properties making the maximum sensi-
tivity at right angles to the flow. Also, the aspect ratio (length-
diameter) of the sensor is such that its properties approach those of
an infinite wire where there is no effect of a longitudinal velocity.
Based on these assumptions, the effective velocity causing heat convec-
tion is, as an average:

Uss=eiivic Ke yas) (19)

where Ug is the velocity corresponding to the output voltage of the
hot-film bridge, K' is the constant of proportionality between the
vertical component and one of the horizontal components of turbulent

velocity fluctuation, and v' is the vertical component of the turbulent
velocity causing heat convection from the sensor. It is apparent then
that the sensor must be placed in the flume with its axis horizontal.

The magnitude of the vertical component of velocity fluctuation can then
be calculated and is, as an average:

ECs TE (20)

Although equation (20) is only an approximation, the assumptions used
do not. affect the basic relationships (a) between the root-mean-square

value of v' and elevation above the bed, and (b) between the root-
mean-square value of v' at a fixed elevation and the flow velocity, Up.
The assumptions also allow an approximation of the absolute magnitude of
the root-mean-square value of v'. The horizontal component of turbulent
velocity fluctuation is probably on the same order of magnitude as the
vertical component and therefore, for qualitative analysis, the value

of K"' in equation (20) can be approximated as equal to unity.

The procedures used in measuring velocity distributions in the flume
were as follows. A period and an amplitude of flume oscillation were
selected and the flume linkage adjusted to give a symmetric motion.

After the flume was filled with deaerated water to the elevation of the
wave suppressent board, the asymmetric roughness elements were adjusted
to eliminate secondary currents in the central part of the flume. The
sensor was then placed in the flume as near the bottom as possible and
its elevation recorded. The flume was started and the motion allowed to
continue until equilibrium flow conditions were established. A record

of the hot-film bridge output voltage was made on magnetic tape, the
length of which was an integer multiple of the flume oscillation period.
The flume was stopped and the sensor elevation raised for a new measure-
ment. The procedure was repeated until an elevation was reached at which
the velocity fluctuations were too small to be accurately measured with
the anemometer. The sensor was then lowered in a stepwise manner to
obtain velocity measurements at intermediate elevations. In this manner,
10 to 13 velocity-elevation measurements were obtained to give a velocity
distribution for the flow condition used. The period of the flume was
changed and the measurements repeated to give a second velocity distribu-
tion. In all, four velocity distributions were obtained for four differ-
ent flow conditions.

3. Results.

The purpose of the velocity measurements was to obtain the following
three relationships needed for an analysis of the suspended-load equation:
(a) An approximation of the magnitude of the root-mean-square value of v'
versus flow velocity, Up; (b) the distribution of the root-mean-square
value of v' versus elevation above the bed; and (c) the distribution
with time of v' at a constant location in space. Results pertaining
to the third unknown listed above will be discussed first.

Two sets of data were analyzed to determine the distribution with
time of v'. The period and amplitude of flume oscillation for both sets
of data were 10.48 seconds and 0.925 foot, respectively. In both cases,
the length of record analyzed was 10.48 seconds (1,224-voltage samples).
One set of data was taken at an elevation of 0.168 foot above the crest
of the artificial dunes, the other 0.209 foot above.

The data were analyzed in the following manner. For each voltage
sample recorded, the effective heat transfer velocity, U,, was calcu-
lated from equation (14). The velocities were ordered and percentages

595

equal to or less than various selected velocities calculated. These
percentages were divided by two and plotted against velocity on normal
probability paper. The percentages were divided by two in order to
adjust for the fact that the anemometer measured the absolute effective
velocity without regard to its direction; i.e., the velocities in each
range were composed of an equal number of negative and positive veloci-
ties, thereby giving twice the percentage of actual positive velocities.
As shown in Figure 22(a, b), these plots approximate straight lines and
the 50-percent velocity is zero, thereby indicating that the distribu-
tion of the turbulent velocity fluctuations is approximately normal with
a mean of zero. Similar data by Das (1968) give the same results.

The above result suggests that the standard deviation, s, of the
normal distribution (which equals the root-mean-square velocity) be used
as the velocity scale describing turbulence intensity for a given eleva-
tion.

The data were then analyzed to determine the distribution of s with
respect to elevation. For each sample of a voltage record, the effective
heat transfer velocity was calculated from equation (14). From the velo-
city record, the root-mean-square effective velocity was calculated.
Knowing this velocity the velocity scale for the elevation at which the
record was made was calculated from:

s = U,/v2 , (21)

where s is the velocity scale and is equal to the standard deviation of
v' for the elevation of the record and flow conditions of the flume, Us
is the root-mean-square effective heat transfer velocity of the record,
and v2 comes from equation (20) when K' is assumed equal to unity.

The velocity scale was plotted against elevation on semilogarithmic
paper to give the relationships shown in Figures 23 to 26. In general,
these relationships can be expressed by:

Si =a Sn exp CA NY) (22)

where s, is the value of the velocity scale (in feet per second) at the

elevation of the crest of the artificial bed dunes, A is the slope of
the exponential curve (in feet-!), and Y is the elevation (in feet)
above the crest of the bed dunes. The flume flow conditions for which
a velocity scale-elevation distribution was measured were Up = 0.353,
0.510, 0.748, and 0.930 foot per second.

Comparison of the four velocity-elevation distributions revealed that,
for the range of flow conditions studied and bed roughness used, the slope
of the exponential relationship was constant. This implies that the in-
tensity of the turbulence decreases in a manner which is independent of
the flow velocity generating the turbulence. The constant rate of velo-
city decay appears to apply to elevations near the bed, within 1.5 centi-
meters as measured with the hot-film sensor.

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O 0.05 0.10 0.15 0.20 0.25
Y, ELEVATION ABOVE CREST OF BED DUNES (ft)

Figure 23. Velocity scale versus elevation for flume velocity,
U5 = 0.353 foot per second.

s, VELOCITY SCALE (ft/s)

Oo
~ o@ 02

O 0.05 0.10 0.15 0.20 OXZS
Y, ELEVATION ABOVE CREST OF BED DUNES (ft)

Figure 24. Velocity scale versus elevation for flume velocity,
U, = 0.510 foot per second.

s= 0.1160 exp (-10.86: Y)

S| VELOCITY SCALE (ft/s)

Oo
~ o o2

O 0.05 0.10 OAS 0.20 0725
Y,, (ELEVATION: ABOVE: CREST OF BED DUNES 4( ft,

Figure 25. Velocity scale versus elevation for flume velocity,
U, = 0.748 foot per second.

i
9
8
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5

s, VELOCITY SCALE

o
~ wo oD

O 0.05 0.10 Ors 0.20 O3Z5
Y, ELEVATION ABOVE CREST OF BED DUNES (ft)

Figure 26. Velocity scale versus elevation for flume velocity,
Up = 0.930 foot per second.

The base velocity, So (eq. 22), was found to be a function of the

flume flow conditions. The relationship between s, and U, is shown
in Figure 27. From the limited data it was only possible to determine
an approximate mathematical relationship between s, and U,. This
relationship is:

See (0.0885) UR OOS57., (23)

which, from boundary considerations, only gives approximate s, values
in the range of experimental values of Up).

4. Summary of Experimental Results.

The following is a summary of the results of the turbulent velocity
fluctuation measurements and a brief discussion of their limitations.

a. The velocity fluctuations caused by turbulence are, for a con-
stant elevation above the bed and a constant flow velocity, approximately
normally distributed with a mean of zero. The standard deviation of the
distribution, s, is used as the velocity scale to measure turbulence
intensity at any elevation. Most turbulent velocity fluctuation measure-
ments give approximately Gaussian results, although it is known that
except for isotropic turbulence, the distribution cannot be Gaussian.

b. For the range of flow conditions studied and the bed roughness
used, the velocity scale can be expressed by equation (22). The exponen-
tial nature of this relationship was discussed in Section II, paragraph
4(a). The relationship also conforms to the boundary conditions of the
flow. As expected, the turbulence intensity assumes a limiting value,
Sp, at the ocean bottom (Y = 0). This limiting value of turbulence in-
tensity is determined, in some manner, by the flow velocity, UL: As

the turbulence diffuses upward its intensity decays because of viscosity.
The body of fluid into which the turbulence diffuses is, by comparison,
extremely large; therefore, the empirical relationship is expected to
indicate that the turbulence intensity decays to zero at an infinite
distance from the bed.

c. The slope, A, of the exponential distribution of the velocity
scale is constant with respect to elevation and constant throughout the
range of flow conditions studied. It was found to be -10.57 feet !.
This result is not surprising since the rate of turbulence intensity
decay for the oscillating flow conditions measured is determined by vis-
cosity. Therefore, for fluids of the same viscosity and density, the
rate of decay should be constant and independent of flow velocity.

d. The base velocity scale, s, (eq. 22), is a function of the
flow velocity and can be approximated by equation (23). This equation
is a best fit relationship of the empirical data and does not apply for
flow velocities outside the measured range. This becomes obvious by

letting Up = 0 foot per second and finding sy = 0.0557 foot per second.

(ft/s)

Uy, FLUME VELOCITY

OLS)

0.8

0.6

Sq = 0.0885 U,+ 0.0557

0:5

0.4

OS
©1877 = .O109 0. | O.) | 0.12 OAS 0.14
Sy — VERTICAL COMPONENT OF TURBULENT VELOCITY
FLUCTUATIONS AT THE CREST OF THE BED ROUGHNESS
ELEMENTS (ft/s)

Figure 27. Base vertical turbulent velocity scale versus flume
velocity for a constant amplitude = 0.925 foot.

In the range of flow velocities where equation (23) is valid, the calcu-
lated so is an approximation of a base velocity at an arbitrary eleva-
tion, the crest of the bed dunes. To apply the experimental results to

a real situation, the constants in equation (23) must be adjusted to give
So values at the elevation of the top of the bedload layer. This eleva-
tion depends on the grain diameter of the sediment being considered and
on the bed geometry; therefore, no attempt was made to express Ss, at
the bedload elevation.

IV. THE SUSPENDED LOAD IN OSCILLATING FLOW
1. Suspended-Load Theory in Unidirectional Flow.

The suspended-load theory for unidirectional flow and the available
field data to test the theory supply valuable insight to some problems
which exist in determining the suspended load in oscillating flow. For
this reason, Einstein's (1950) suspended-load theory and field data from
the Missouri and Atchafalaya Rivers are presented.

The suspension theory in unidirectional flow is based on an equilib-
rium equation for mass flux across a unit horizontal area in the flow.
Assume the unit horizontal area is at elevation Y. Across this area
fluid is being exchanged by the vertical component of the random motion
of fluid particles caused by turbulence. From continuity, the picture of
fluid exchange can be simplified by assuming that through one-half of the
unit area, fluid is moving upward with an average velocity of v; through
the other half area the fluid is moving down with an average velocity -v.
If the exchange occurs over an average distance of 1, it can be assumed
that the downward-moving fluid originates, as an average, from an eleva-
tion Y + 1/2 le while the upward-moving fluid originates from Y - 1/2 le.
The important assumption is made that the fluid preserves, during its
exchange), the propertiesvot ithe) fluid iat ats pointiof or1vein. | bi. the
concentration of sediment at elevation Y is C and the sediment has
a settling velocity of V,, the equilibrium equation for sediment flux
is given by:

[c - Fle (ac/ay)| (3) (ava) +
[c ce (ac/ay)| (3) (-v-Vz) = 0. (24)
This equation reduces to:
CV, + sl, v (dc/d¥) = 0. (25)

To solve this equation the term, 1/2 fv omust ibevevaluated? eathuaisi as
normally done by equating this term to the corresponding term in a similar
equation of momentum exchange; i.e., the sediment exchange coefficient is

assumed equal to the momentum exchange coefficient. Assuming that shear
due to viscosity may be neglected, compared with that due to momentum
transport, the depth, d, may be introduced:

t= t) [(d-Y)/d] = Sv 0 {[u - $16 (au/av)| i lu tole (au/ayy|} , (26)
where

To = shear stress at the bed; equal to goRS

t = shear stress at elevation, Y
R = hydraulic radius (in feet)

S = energy slope

g = acceleration due to gravity
o = density of the water

u = horizontal flow velocity

Using the logarithmic formula based on von Karman's (1934) similarity law
for the distribution of flow velocity, du/dY may be calculated:

du/dY = (1.0/0.4) (u,/Y) , (27)

where u, is the shear velocity and equal to Gone. Substituting this

value into equation (26) and solving for 1/2 1, v yield:

Fle v = (-0.4) Yu, (d-Y)/d . (28)

Using this value in equation (25), separating variables and introducing
the abbreviation:

Zia VE CORA uy) (29)

the result can be integrated from a to Y. The solution is:
(C/o Ned Wi nayy duane! 2 (30)

It has been found that equation (30) gives the correct form of the
distribution function, but the value of the exponent Z _ given by equa-
tion (29) does not always agree with the exponent that fits the measured
data. Let Z' be the exponent which best fits the data. It was found
that torshagh) values o£ Z)/CZ>10)),) 2" was) stenifacantliy, less. Asi iZ) jas

reduced, the difference between Z and Z' decreased and finally when
Z assumed values less than unity, which is normally the case, the dif-
ference between Z and Z'! was small enough such that use of equation
(29) allows accurate results. The relationship between Z andi Ze ass
shown in Figure 28 (Einstein and Chien, 1954).

2. Similarities Between Oscillating and Unidirectional Flow.

The similarities between oscillating flow and unidirectional flow
with low shear velocities are pronounced. It was found that the concen-
tration distribution in oscillating flow (from equation 9) could be ex-
pressed by:

€/€, = exp(MY) , (31)
where M was found in Section II to be (from equation 13):
M= -V,/E , (32)

E is the sediment exchange coefficient. The coefficient, M, which
defines the rate at which the concentration decays with elevation, behaves
in a manner similar to Z of the unidirectional flow theory. In oscillat-
ing flow, as in unidirectional flow, the value of M fitting the experi-
mental results was different than the value which would be predicted from
equation (32), assuming E independent of V,. Figure 15 and Table 3
show that for the four concentration distribution curves obtained when

V, was increased from 0.035 to 0.0626 foot per second, the absolute value
of M increased, as an average, by the factor 1.19. When V, was in-
creased from 0.035 to 0.0498 foot per second, the absolute value of M
increased, as an average, by 1.13. If the exchange coefficient, E, of
equation (32) were a function of the flow hydraulics only and independent
of the sediment-settling velocity, then the average increase in the abso-
lute value of M would have been 0.0626/0.035 (= 1.8) and 0.0498/0.035
(= 1.42), respectively. Therefore, it can be concluded that the sediment
exchange coefficient, E, is a function of both Ve) sand) Up; vandathac
M, for a constant flow velocity, is not directly proportional to Vg.
This conclusion agrees with Einstein and Chien (1954) that in unidirec-
tional flow for high values of settling velocity relative to the flow
shear velocity the sediment exchange coefficient cannot be accurately
approximated by the momentum exchange coefficient.

The difference between the sediment and momentum exchange coefficients
depends on the relative magnitudes of the sediment-settling velocity and
the turbulence intensity. If the sediment-settling velocity is small
compared to the turbulence intensity, the two coefficients are approxi-
mately equal; when Vz = 0, the two coefficients are identical. As V,
becomes relatively larger, the difference between the two coefficients
increases. In unidirectional flow the turbulence intensity is usually
very large compared to V, and the theory is accurate under most situa-

tions. Unfortunately, this is usually not the case in oscillating flow.

“(vS6T ‘USTYD pue UTOJSUTY WOLF) MOTF TBUOTZOOLTPTUN UT UOTINqTI3STp
uoT}eIjUSDUOD Fo YUsUOdXS poInseou puke [eOTJEeTO9YI oY FO uostaedwoyj *gz oAN3TY

*ay SA =Z GalvindqWw2

Ov Ge Oe Ge Ove G‘l 0'| SO 0

YSAIY VAVIWVHOL
SINZWAUNSV3aN 256
SINJW3YNSV3W ISEI

YSAIY INNOSSIN

Ove

iZ Q3YNSVAW

Examining results b, c, and d of Section III, the range of the root-mean-
Square valluenofmuy CS) y's Os O00V25< 1S <1 0)10/5) footy pers second amine
settling velocities of the sediments used in the experiments were

Vg = 0.035, 0.0498, and 0.0626 foot per second. V, is then, the same
order of magnitude as the velocity scale. As discussed earlier, the
sediment used in the experiments had a specific gravity of 1.25. There-
fore, the settling velocity of natural sediment would be even larger
compared to turbulence intensity in the approximate prototype flow con-
ditions of the experiments.

For illustration, a typical oscillatory flow condition of this in-
vestigation will be approximated as a quasi-steady unidirectional flow
and compared to the field data of Figure 28. This is possible because
the time scale for oscillation is much greater than the time scale of
the turbulence. For example, the average flow had a period of 6 seconds
and an amplitude of about 1 foot, Up = 0.667 foot per second. A time
scale of turbulence can be defined as S/S where 6 is the thick-
ness of the boundary layer and s, is the base vertical velocity fluc-
tuation. If 6 is defined as the distance above the bed at which the
boundary layer oscillation velocity is equal to 99 percent of the free-
stream velocity (velocity given by linear wave theory for y = -d),

6 can be calculated from equation (5). This calculation indicates that

6 is equal to or less than 0.05 foot and from Figure 27, So is 0.11 foot
per second. Therefore, the time scale for the turbulence is 0.45 second

as compared to a 6-second time scale for the oscillation. To calculate
the theoretical Z value for the quasi-steady unidirectional flow it is
necessary to determine a mean flow shear velocity. The flow shear veloc-
ity 1s given by:

De GES) (33)
where R is the hydraulic radius (in feet), g is the acceleration due
to gravity (in feet per second squared), and S is the energy slope of
the quasi-steady flow. The energy slope is obtained from Manning's
equation by using the root-mean-square flow velocity (= 0.707 2 Il L/T),

and estimating values of the roughness coefficient, n, and the hydrau-
lic radius, R. The expression for the energy slope is:

a
See= 1 (n/ RO Pei (Sal Alin. (34)
Substituting equation (34) into equation (33) yields:
Big eS (GY i Ge RO OME) 5 (35)

Using the above expression for u, in equation (29), the Z value for
the quasi-steady flow becomes:

A (Me) TF ROOMS GLB. an ih) < (36)

For the average flow conditions, Vg is 0.035 foot per second, T is
6 seconds, and L is 1.0 foot. Based on the bottom roughness shape and

the hydraulic radius, n is approximately 0.015 foot2:167. The hydrau-
lic radius is estimated from the flow geometry as about equal to unity.

Since Z is proportional to R_ to the 0.167 power, and therefore tends
to unity, there is probably not much error in using this estimate. Using
these values in equation (36) yields Z = 2.1. In Figure 28, this value
of Z is well into the range where the sediment exchange coefficient is
Significantly different from the momentum exchange coefficient.

Because not enough data were obtained to define a relationship be-
tween M and V, and because the sediment exchange coefficient could
not be expressed as a function of the shear-stress distribution, no
attempt was made to derive a theoretical relationship for the concentra-
tion distribution as was done in Einstein and Chien (1954) for unidirec-
tional flow.

3. Sediment Suspension in an Oscillating Flow.

This investigation was done to determine the behavior of sediment
suspension in an oscillating flow and present a method by which the sus-
pended load could be approximated from flow hydraulics. It is apparent
from the field measurements of unidirectional flow (Fig. 28), and the
results of this investigation for oscillating flow that the mechanism by
which sediment is held in suspension is complex and not fully understood.
For this reason, the following method for estimating the suspended load
in oscillating flow as a function of the flow hydraulics is based on the
general turbulent mixing length theory first proposed by O'Brien (1933).
His derivation is as follows:

There is a continuous up and down motion of fluid across any horizon-
tal plane caused by the turbulent vertical velocity fluctuations. This
exchange motion is capable of transporting suspended matter. Consider a
horizontal reference section of unit area at a distance Y from the bed.
The transfer of sediment in the vertical direction from the region of
high concentration to a region of low concentration through this unit
section will be -1/2 1, v dC/dY, where 1, is the mixing length for the
sediment exchange, v denotes the exchange discharge through the unit
area due to vertical velocity fluctuations, and C is the concentration
of suspended sediment with settling velocity, V,, at elevation Y. How-
ever, a continuous settling of particles through the unit area at a rate
of C Vg exists. A statistical equilibrium condition is given by equa-
tion (25). This equation is identical to the equation derived by Einstein
(1950), but without the assumption that the origin of the sediment is the
same as the origin of the fluid and without assuming any distribution of
fluid exchange.

The mixing length theory incorporates all of the factors which affect

sediment suspension in two artificial variables, the velocity scale and
the length scale. The velocity scale for oscillating flow was measured

directly in this investigation and is given by equation (22). The sedi-
ment exchange coefficient which is the product of the length and velocity
scales was also measured directly and is given by equation (13). From
these two equations, the corresponding length scale can be calculated as:

ale =H GV Mesyy) extn (An Yo) (37)

For the limited flow conditions investigated, all the variables of
equations (13), (22), and (37) have been found as a function of U,,
where U, is a function of the surface wavelength, period, and water
depth. The variable A was found to be a constant (= -10.57 feet-!),
and M and s, are graphically given in Figures 6 and 27, respectively.
These expressions for the velocity and length scales are physically
reasonable. Not only is the base turbulent velocity a function of the
surface wave intensity (Fig. 27), but the exchange length tends to small
values as the ocean bed is approached, indicating that no sediment should
be exchanged across the bed surface.

4. The Base Concentration, C,.

With the exception of the base concentration, C,, all the variables
needed to describe the suspended load as a function of flow hydraulics
have been discussed. The following is only a brief discussion of the
base concentration. Kalkanis (1964) provides a complete mathematical
derivation.

In oscillating flow, as in unidirectional flow, sediment transport

is by two different types: (a) Bedload transport, and (b) suspended-load
transport. As discussed in Section I, the thickness of the bedload layer
is about two-grain diameters. Therefore, for both prototype and experi-
mental sediments, the bedload is contained in the boundary layer described
in Section II. The theory proposed by Kalkanis to predict the amount of
bedload transport and the concentration of sediment is general and only
requires knowledge of the surface wave characteristics, the water depth,
the bed sediment characteristics, and statistical parameters which have

been found experimentally. Because the thickness of the bedload layer

is small, the concentration of sediment in this layer is assumed constant
and equal to Cy. The concentration, Co, for the bedload is the base
concentration to be used for the suspended load.

Using Co as the suspended-load concentration incorporates a small
error in the total suspended load. As indicated previously, the bedload
is contained in the boundary layer. The distribution of sediment concen-
tration in this area is unknown. Because the distance between the top of
the boundary layer and the top of the bed layer is small, extension of
the exponential suspension distribution down to the bed layer would incur
only a minor error in the total amount of sediment in motion.

5. Net Transport of Sediment in the Ocean.

The initiation of sediment movement in the ocean is by wave action.
Since the waves are approximately linear, the wave-induced fluid motion
is a symmetric oscillation causing an equally symmetric movement of the
sediment. This motion ordinarily cannot cause net transport of sediment,
but it does suspend sediment so that currents superimposed on the oscil-
lating velocity will cause a net transport of the sediment. Examples of
unidirectional currents in the ocean are the longshore current caused by
waves attacking the coastline at an acute angle and the secondary currents
caused by the coastline geometry. These two examples indicate that deter-
mination of the transporting current shouid be by field measurement.

6. Additional Investigations Needed to Complete the Suspension Theory.

The suspended-load theory is by no means complete. The relationship
between the rate of decay of sediment concentration, M, and sediment-
settling velocity, Vs, is needed. Figure 15 indicates that settling
velocity has a significant affect on the distribution of sediment con-
centration, but there are not enough data to indicate the relationship.
Additional measurements are required to quantitatively determine the
relationship between M and V, for a constant Up.

Another variable affecting the suspended-load theory and not studied
in this investigation is the bed roughness. It is probable that a change
in bed roughness would affect the intensity of turbulence at a given
elevation. Also, as discussed in Section II, the amplitude of oscilla-
tion relative to the wavelength of the bed roughness has an affect on the
distribution of suspended sediment. Determination of how the bed rough-
ness affects sediment suspension requires a great deal of experimentation;
however, the results of this investigation will supply some guidelines
which would reduce the amount of experimental work required.

7. Conclusions.

These experiments in an oscillating flow simulating wave motion at
the ocean floor provide results which, in some cases, substantiate pre-
vious results and provide new information on the behavior of sediment
suspension. It should be stressed that the conclusions of this investi-
gation are confined to the rather limited range of the variables studied.

The conclusions obtained from sediment concentration measurements are:

a. The relationship between the mean sediment concentration and
elevation above the bed is exponential. This conclusion is based on 65
concentration distribution relationships covering a wide range of proto-
type flow conditions and each composed of numerous point concentration
measurements. Typical examples of this relationship are shown in Figure
5 and the basic data substantiating this conclusion are given in the
appendix. Although this relationship was determined using an artificial

. sediment with a settling velocity less than found in the prototype,
results of experiments by other investigators using prototype sediments
resulted in the same exponential relationship. In addition, the bed
roughness used by other investigators varied; therefore, this conclusion
does not appear to be limited to the single-bed roughness used in this
investigation.

b. Using the above conclusion and the O'Brien's (1933) equation for
continuity of sediment exchange results in a sediment exchange coefficient
which is independent of elevation above the bed. Behavior of the rate of
sediment concentration decay with elevation, which is related to the sedi-
ment exchange coefficient by equation (13), was found to be a function of
the flow velocity causing the suspension and the settling velocity of the
sediment. A linear relationship between the flow velocity and the sedi-
ment concentration decay rate was found for the constant sediment-settling
velocity used in the majority of the experiments. This relationship is
shown in Figure 6. The relationship between flow velocity and the sedi-
ment concentration decay rate for other sediments studied in this investi-
gation is shown in Figure 15. The limited data indicate a possible linear
relationship for the different sediment-settling velocities. There is not
enough data to determine the relationship between the concentration decay
rate and settling velocity for a constant flow velocity. Only qualita-
tive conclusions can be obtained from the eight concentration distribution
Measurements shown in Figure 15. For a constant bed roughness and flow
velocity, a higher sediment-settling velocity results in a higher sedi-
ment concentration decay rate. The limited data consistently indicate
that the concentration decay rate is not proportional to the settling
velocity to the first power; i.e., they are not directly proportional.
This and equation (13) imply that the settling velocity is an important
variable influencing the sediment exchange coefficient. Therefore, in
oscillating flows the sediment exchange coefficient cannot be accurately
approximated by the momentum exchange coefficient as is commonly done
in unidirectional flow analysis. No experiments were conducted in this
investigation to determine how the above relationships would change with
a change in bed roughness.

The conclusions obtained from measurements of the turbulent velocity
fluctuations are:

a. The distribution of turbulent velocity fluctuations at a constant
elevation in an oscillating flow was found to be approximately normal with
a mean of zero. This relationship was determined from distribution analy-
ses of measurements made at two elevations above the bed, both of which
were above the boundary layer described in Section II. Results of these
analyses are shown in Figure 22.

b. The relationship between the root--mean-square turbulent velocity
fluctuation and elevation above the bed was found to be exponential. This
conclusion is based on measurements of distributions made for four differ-
ent flow velocities, all using an amplitude of oscillation of 0.925 foot
and covering approximately the same range of prototype flow velocities as

studied in the concentration measurements. Results of these measurements
are shown in Figures 23, 24, 25, and 26, and are tabulated in the appen-
dix, Table A-5. This relationship was valid for elevations of approxi-
mately 0.04 foot above the crest of the bed dunes. The relationship below
this elevation, which would be in the boundary layer, was not determined.
The turbulent velocity fluctuation distribution was only measured for the
single-bed roughness described in Section II.

c. Based on the four turbulent velocity fluctuation distributions
described above, it was concluded that the rate of turbulent velocity
decay with elevation above the bed is independent of both the elevation
and the flow velocity generating the turbulence. The exponential decay
rate, determined from a least squares curve fitting of the data, for the
four distributions ranged from -10.38 to -10.86 feet-1, with a mean of
-10.57 feet™! and a variance of 0.05 foot 2.

d. The relationship between the flow velocity and the root-mean-
Square turbulent velocity fluctuation at zero elevation (calculated from
the empirical relationships) is shown in Figure 27. A linear relation-
ship is indicated. However, this relationship, which is far from con-
clusive, is based on only four data points with a significant amount of
scatter. The qualitative conclusion that the turbulence intensity at
zero elevation becomes larger with greater flow velocities is not only
indicated by the data but is logical.

Ue)

LITERATURE CITED

ABOU-SEIDA, M.M., ''Bed Load Function Due to Wave Action," Technical
Report No. HEL-2-11, Hydraulic Engineering Laboratory, University
of California, Berkeley, Calif., 1965.

DAS SMM ce WExtended Application of a Single Hot-Film Probe for the
Measurement of Turbulence in a Flow Without Mean Velocity," Technical
Report No. HEL-2-20, Hydraulic Engineering Laboratory, University of
California, Berkeley, Calif., 1968.

DAS, M.M., ''Mechanics of Sediment Suspension Due to Oscillatory Water
Waves,"' Technical Report No. HEL-2-32, Hydraulic Engineering Laboratory,
University One Calattornilam sBenkele yen Calera, Olly

EINSTEIN, H.A., ''The Bed-Load Function for Sediment Transportation in
Open Channel Flows,'' Technical Bulletin No. 1026, U.S. Department of
Agriculture, Soil Conservation Service, Washington, D.C., 1950.

EINSTEIN, H.A., and CHIEN, N., "Second Approximation to the Solution of
the Suspended Load Theory,'' M.R.D. Sediment Series No. 3, Institute
of Engineering Research, University of California, Berkeley, Calif.,
1954.

KALKANIS, G., "Observation of Turbulent Flow Near An Oscillating Wall,"
‘M.S. Thesis, University of California, Berkeley, Calif., 1957.

KALKANIS, G., ''Transportation of Bed Material Due to Wave Action," TM-2,
U.S. Army, Corps of Engineers, Coastal Engineering Research Center,
Washington, D.C., Feb. 1964.

KENNEDY, J.F., and LOCHER, F., ''Sediment Suspension by Water Waves,"
Waves on Beaches, Academic Press, New York, 1972.

LAMB, H., Hydrodynamics, Dover Publications, New York, 1932.

LI, H., "Stability of Oscillatory Laminar Flow Along A Wall,'' TM-47, U.S.
Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Aug.
1954,

MANOHAR, M., "Mechanics of Bottom Sediment Motion Due to Wave Action,"
TM-75, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington,
DiGue Junegl9S5.

O'BRIEN, M.P., "Review of the Theory of Turbulent Flow and its Relation
to Sediment Transportation," Transacttons, Amertcan Geophysical Union,

Apr. 1933, pp. 487-491.

SHINOHARA, K., et al., "Sand Transport Along A Model Sandy Beach by Wave
Action," Coastal Engineering in Japan, Vol. 1, 1958.

VON KARMAN, T., "Turbulence and Skin Friction," Journal of the Aeronautical
DCLECHCES NOM le NO) Jans L954) ppe) l= 20)

BIBLIOGRAPHY
BIJKER, E.W., ''Littoral Drift Computations on Mutual Wave and Current
Influence, Delft University of Technology, Department of Civil Engi-
neering, Delft, The Netherlands, 1971.

EATON, R.O., "Littoral Processes on Sandy Coasts," Proceedings of the
First Conference on Coastal Engineering, 1950.

EINSTEIN, H.A., ''A Basic Description of Sediment Transport on Beaches,"
Waves on Beaches, Academic Press, New York, 1972.

EINSTEIN, H.A., and LI, H., "The Viscous Sublayer Along A Smooth Boundary,"
Transactions, American Soctety of Civil Engineers, Vol. 123, 1958,
pp. 293-317.

HENDERSON,’ F.M., Open Channel Flow, Macmillan, New York, 1971.

JOHNSON, J.W., “Sand Transport by Littoral Currents," Proceedings of the
Fifth Hydraulte Conference, 1953.

MILNE-THOMSON, L.M., Theoretical Hydrodynamics, Macmillan, New York, 1969.

SUTHERLAND, A.J., “Proposed Mechanism for Sediment Entrainment by Turbu-
lent Flows,'' Journal of Geophysical Research, Vol. 72, No. 24, 1967.

WIEGEL, R.L., Oceanographical Engineering, Prentice-Hall, Englewood Cliffs,
N.J., 1964.

ins

APPENDIX

EXPERIMENTAL DATA

Table A-1. Basic data, concentration distribution measurements, Ve = 0.035 foot per second, amplitude 2 0,693 foot.

717.01
(0.392)

602.06
(0.292)

602.07
(0.235)
612.01
(0.422)
612.02
(0.504)

612.03
(0.600)

2.64

518.01
(1.00)
518.02
(0.681)

518.03
(0.470)

717.02
(0.328)

HPuubaun
SROSGHEEOE

$18.04
(0.394)

518,05
(0.339)
- 602.01
(1.157)
602.02
(0.737)

602.03
(0.504)
602.04
(0.420)

602.05
(0.348)

717.04
(0.667)

euro

RU Sauunsd
SaFTRSES

anon

»
hy

BRB

am
Be

L, any . NeO@eSC VME
SSeS] Ree BK ES] SRE

CNA@O HUE

721.04
(0.352)

OP nur neune

SBllRs

ON ARON YUE

S
WUIwvaaan
Beaurbauan
SSSSesee

Tahle A-2. Basic data, concentration distribution measurements, Vg = 0.035 foot per second, amplitude < 0.693 foor.

Curve No. Curve No. | Concentration | Elevation Curve No. {Concentration | Elevation
(Uo, £t/s) (Uo, £t/s) (g/1) (Uo, ft/s) (g/1)

802.04 r

(0.247)

mH OSC CORN

814.01
(0.585)

NE COCO ONN

Seeneusyss

814.02

(0.585)
711.07
(0.890)

629.04
(0.448)

hBabousvonvo

BNSURAeUMO] CONAVEaUNHOS
Deo wo
Ora Seng

eeveuag
Uneee oe

BRU BaAVIYUEE
Hone RWoRo
eae Ab emer

Beooa

621.05
(0.263)
628.01
(0.263)

628.02
(0.376)

CeNUNeEH oO] NUeUAan

NooCCOnN

AWreouwe
S28

RN EUDeUHS

814.04
(0.585)

KuNnneaeno

Lavovoveawvo
BORE EGane

OREN UNE OS

aPeSeseey

RNASE O

802.03
(0.363)
814.05

(0.585)

BLES Sesse

bm aovo00

&
HUUNAaNS

BOR Rhee ee

SRSLSSRs lel Rsegss

CRN Un RRO

Subeue
Salers

PN RNA SUR'S

@BuUUnise x .W

Uaeoovoov0d
SSaseeeess

z6S0°0 z690°0

vot’o L0v0°0O 8S20°0 0980°0

9bT°O £220°0 por°o L950°0 0ss0°O 6T90°0

88T°O £9T0°O 8bT°O z1Z0°0 12) Sa!) £1£0°0 6S20°0 z590°0
o£z°0 Stt0°O 88T°O T8600°0 SbT°O 8420°0 2650°0 z6£0°0
£L7°0 O£TO°O 0£2°O £S600°0 88T°O S£T0°O Ov0T’O 0v£0°0
1Sz°0 02T0°O ££2°0 z£10°O 0£Z°0 SOTO°O OLbT "0 9ST0°0

OIz°o ££T0°O Tsz°0 s£Z00°0O 0sz°o £9200°0 o8st-oO ZST0°O
L9T°O $0z0°0 602°0O O£T0°O 802°0 80T0°O 0602 °0 $2600°0
921°0 09£0°0O 89T°O v6T0°O L9T°O 4020°0 SL9T°O 62T0°0
ss80°0 Z6¢0°O | 9zT°0 $920°0 >zT°O 0z£0°O o9zT°O £4Z0°0
8S20°0 $s60°0 0v80°0O 2L¢0°0 S£80°0 zTS0°0 0s80°0 8s£0°O
8S70°0 8POT°O 0ss0°0 Sb90°0 8SZ0°0 9Z80°0 zveo°o $290°O

(s/33) (s/33 ‘°n) (s/az *n) (s/az *°n) (s/az ‘°n)
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