Vol, g, No. /

DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS

WOODS HOLE
OCEANOGRAPHIC INSTITUTION

GSAS ROPES
WOODS HOLE, Mass,

as DOCUMEN’
OLE TION
BULLETIN
OF THE

BEACH EROSION BOARD

OFFICE, CHIEF OF ENGINEERS
WASHINGTON, D.C.

VOL. 9 JANUARY 1, 1955 NO. 1

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TABLE OF CONTENTS

Page Noo
A Simplified Method of Determining Durations and
Frequencies of Waves Greater or Less Than A
Specified Height COCTCEEOHCOOCLCOEOO OHO OORT EHO OCOOOOOOCOE 1

A Comparison of Deep Water Wave Forecasts By the Pierson-
Neumann, the Darbyshire, and the Sverdrup-Munk-
Bretschneider Methods with Recorded Waves for Point
Arguello, California for 26-29 October '50 secccceccces 5

Status of Sang By=Passing Plant at Salina Cruz Harbor
Isthmus of Teherantepec, IMPS) GonDoG0D00000000000000 14

Progress Reports on Research Sponsored by the Beach
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A SIMPLIFIED METHOD OF DETERMINING DURATIONS AND FREQUENCIES OF
WAVES GREATER OR LESS THAN A SPECIFIED HEIGHT

by
Thorndike Saville, Jr.
Beach Erosion Board, Corps of Engineers

In planning for many types of marine operations it becomes important
to know the length of time over which, and frequency with which, waves
greater or less than a specified height may be expected to occur. For
example, a condition of 3-foot waves is about the maximum under which
accurate hydrographic survey data may be obtained by small boats or
DUKWS in the nearshore area, higher waves serving to mask out small
depth changes indicated on an echo sounder record due to the resultant
(up-and-down) motion of the vessel. A 3-foot wave height is also
regarded as being roughly the upper limit for some types of geophysical
survey operations, and it is the critical height for operation of one
type of barge used for transporting crude oil ashore from offshore wells.
Accurate knowledge of the frequency of occurrence of waves above or
below these limiting heights is then of considerable importance in
determining the economic feasibility of operating in an area, in choosing
between operation in one area or another, in selecting the most suitable
time for carrying out such operations, and in overall planning of the
operation (particularly as regards probable amount of lost time).

Frequency diagrams of occurrence of various wave heights are needed
for design of structures subject to wave action, and are frequently
obtained by hindcasting from weather maps. However, it is generally
only the higher waves that are of interest, those above, say, 8 or 10
feet. The lower waves, however, account for a much greater percentage
of the time involved, and methods of forecasting which would automatically
eliminate thorough consideration of these waves would result in much
more rapid and economical determination of design criteria.

In such cases as these the wave height is of interest only as it
is of greater or less magnitude than a particular value; i.e. the actual
wave height is not of importance. There would seem to be, therefore,
nothing particular to be gained in forecasting the actual height rather
than just whether or not the wave is over the limiting value.

This can be done much more simply than by making a complete forecast
of the actual height, as curves showing the values of wind velocity and
duration, and fetch length and decay necessary to produce waves of a
particular specified height may be drawn rather easily from the revised
Sverdrup-Munk curves presented by Bretschneider*. lf the particular

#Bretschneider, C. L. - Revised Wave Forecasting Relationships, Proc. of
the Second Conf. on Coastal Eng'g., Council on Wave Research, Eng'g.
Foundation, 1952.

meteorological conditions considered result in a point lying below
the appropriate curve, then the wave height will not be expected to
reach the limiting value (or height of interest); similarly if the
weather conditions result in a point on or above the appropriate curve,
waves greater than the specified values may be expected to occur (and
the unanswered question, as to whether the waves exceed the limiting
value by 1 foot or by 50, is not important to the determination).

A set of curves showing limiting values for generation of 3-foot
waves is shown in Figure 1, The curves show values of wind velocity
and duration, and fetch and decay lengths necessary to produce the
limiting waves of 3 feet. They are used in exactly the same manner
as the usual generation curves used in wave forecasting, only instead
of reading off the height of the generated waves, the decay distance
resulting in the specified limiting wave height (3 feet) is obtained.
If the actual decay is less than this value, then the waves will be
greater than the (3-foot) limiting value; and if it is more, then the
wave height will be less than the (3-foot) limiting value. For example,
from Figure 1, with a wind speed of 20 knots, a duration of 12 hours,

a fetch of 175 miles, and a decay of 350 miles it is seen that the
wave growth is limited by duration, and that the waves will be reduced
to 3 feet after a decay of about 200 miles; since the actual decay
distance is 350 miles, the waves there will be expected to be less than
3 feet. If now the duration in this example had been 2) hours rather
than 12, the wave generation would be limited by the 175-mile fetch
length, and (from the figure) the waves would reduce to 3 feet- after

a decay of 500 miles; since the actual decay was only 350 miles, the
waves there would be expected to be esreater than 3 feet.

Although curves are shown for a 3-foot wave height only, it is a
relatively simple matter to obtain them for any desired height. The
method is shown below for the case of the 3-foot height, and a 100-mile
fetch and 500=-mile decay. Using the Bretschneider decay curves it may
be seen that for a 500-mile decay with a minimum fetch of 100 miles,
the relative decrease in wave height over the decay distance (Hp/Hp)
may range between 0.26 and 0.333; this means that the wave height at the
end of the fetch (Hp) which will produce 3-foot waves after the 500-mile
decay must be between 9.1 and 11.5 feet (these values being obtained
by dividing the Hp of 3 feet by the ratio Hp/Hp). Going again to the
decay curves and using these values for Hp, it may be seen that Hp/Hp
must be between about 0.285 and 0.295. Repeating the above process
with these new values of Hp/Hp would again reduce the range, though
this is probably not warranted as it may be seen that the desired value
of Hp/Hp will be very close to 0.29. Hence the wave height at the end
of a 100-mile fetch which will produce a 3-foot wave after a 500-mile
decay is 3/0.29 or 10.3 feet. This point may then be plotted on the
Bretschneider generation figure at the intersection of the 100-mile

WIND VELOCITY, U (Knots)

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Minimum duration, tm (Hours)

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FETCH LENGTH, F (Nautical Miles)

FIGURE [{ - FORCASTING CURVES FOR WAVE GENERATION
(3FT. WAVES)

(anoy sed say aynjoiS) MN‘ ALIDOISA GNIM

fetch line with the 10.3-foot wave height line. Other points on the
500-mile decay curve may be obtained similarly and the line drawn in.
The curves for other decay distances may then be derived in a like
manner, ‘and the entire family of curves plotted.

It is thought that curves such as those shown may be used to
considerable advantage in determining hindcast frequencies of waves
greater than a particular limiting value, representing a large time
saving over previous (but more complete) methods.

A COMPARISON OF DEEP WATER WAVE FORECASTS BY THE PIERSON-NEUMANN,
THE DARBYSHIRE, AND THE SVERDRUP-MUNK=BRETSCHNEIDER METHODS WITH
RECORDED WAVES FOR POINT ARGUELLO, CALIFORNIA FOR 26-29 OCTOBER ‘50

by
Robert F. Dearduff, Hydraulic Engineer
Research Division, Beach Erosion Board

A brief comparison of deep water wave forecasts made by the
Darbyshire and the Sverdrup-Munk-Bretschneider methods with recorded
waves at Point Arguello, California for October 26-29, 1950 has pre-
viously been made (1,2)*. A further comparison for this same period
with the method recently developed at New York University(3) is believed
to be of further interest; this method is referred to herein as the
Pierson-Neumann or Wave Spectra method.

This latter method differs from the Sverdrup-Munk-Bretschneider
method in that:

(1) Greater cognizance is taken of the entire wave spectrum
which is treated as the sum of numerous simple sine waves. In the use
of the method, each simple component is treated individually, and the
resultant characteristics obtained by summing up the components per-
tinent to the particular place and time. (The Darbyshire method also
does essentially the same.)

(2) Wave decay is considered as being due entirely to dis-
persion (the stretching out of a wave train as the longer period,
higher velocity waves pass through and beyond the shorter period waves)
and to angular spreading (the spreading out of the area of wave
activity due to the difference in direction of the various wave com-
ponents). This latter means that fetch width is considered as an
important factor in the determination of wave height after decay. For
example, given two fetches, one being twice as wide as the other, the
waves created by the wider fetch will be 2 higher than those of the
narrower fetch. Important consideration is thus given to the angular
spread of the waves as they are propagated from the fetch front to a
coastal point. That is, the greater the angle between a line drawn
from the same point of observation to the extreme end of the fetch front
and a line extended from the fetch side, the relatively higher the waves
will be at the point of observation (see Figure 1).

% Numbers in parentheses refer to References at the end of the article.

Application of the Pierson-Neumann method, as developed at New
York University ,to the October 1950 storm showed that the first. wayes
generated by this storm would arrive at Point Arguello at about
1800 October 26, more or less at the same time as predicted by
Bretschneider(2), and by the Darbyshire method. (See Figure 2). For
the following 18 hours, the waves predicted by the "Wave Spectra
Method" were considerably lower than those predicted by Bretschneider
and those shown by the recorder; but were almost identical with those
predicted by the Darbyshire method. During the following 48 hours,
the waves predicted by the Pierson-Neumann method were considerably
higher than either the recorded or those predicted by Bretschneider,
averaging about twice as high as those predicted by Bretschneider; this
average was taken over 6-hour intervals (see Figure 2). The peak
storm waves occurred at 1200 October 27 according to both Bretschneider
and the recorder and were about 1 feet in height; however, the peak
waves obtained by the Pierson-Neumann method averaged about 21 feet
in height and arrived 6 hours later at 1800 October 27.

An hourly average taken over the 66-hour period from 1800 October
26 to 1200 October 29, showed that the wave height determined by the
Pierson-Neumann method was 10.4, feet as contrasted with 7.8 feet for
Bretschneider (for a more exact comparison see Figure 2). Due to the
variance in wave height between Bretschneider, Darbyshire and the
recorder as against the Pierson-Neumann results, it was believed
possible that errors had been made in the application of this method,
and a second independent hindcast analysis was made by another Beach
Erosion Board staff member. The results were about the same; the
wave heights obtained by the Pierson-‘eumann method again being about
twice the others for the period from 1200 October 27 to 1200 October 29,
and the storm peak height being about 23 feet.

There would appear to be several possible explanations for the
difference between the two results. One is, of course,error in applica-
tion of the newer method. Another is possible error in analysis of the
observed waves -- these were obtained from a pressure recorder, and
analysed by the significant wave concept, which generally gives some-
what (5 to 15 percent) lower values than actual. Still another is
difficulty in using the Co-Cumulative Spectra Curves of the Pierson-
Neumann method. In this connection it was often almost impossible to
determine with any accuracy the frequencies, hourly durations and the
corresponding energy (E) values located near the curve extremes (and
frequently values determined for these regions from one set of curves
would not agree with those from another). A portion of the differences
in height may certainly be ascribed to this reason (i.e. difficulty
in accurately reading the curves for high velocities and low durations).
It is understood that these curves have now been redrawn and are in the
process of publication by the Navy Hydrographic Office, so that this
difficulty will no longer exist in the future.

We e-
Point of
observation

Yh We gle

FIGURE |.CONSTRUCTION OF ¢ ANGLES FOR ANGULAR SPREADING FACTOR

Recorded
—__»—— Darbyshire

Bretschneider
_____ Pierson —Neumann

Ho (feet)

1200 Oct.26 1200 Oct.27 1200 Oct.28 1200 Oct.29

FIGURE 2. WAVE HEIGHTS PT. ARGUELLO, CALIFORNIA OCT. 26 - 29,

1200

1950

Another major source of difference is, of course, the analysis
of the meteorological situation from the data shown on the weather
maps. In this case the fetch lengths, decay distanceg, wind velocities
and durations were chosen essentially identical with those used by
Bretschneider; these values have been ¢hecked and used by other authors
(1,4,5) and would appear to be the best available data. However, the
selection of these values is largely subjective, and other analysts
might well select different values. The use of different values (as
say, lower wind velocities and positioning of the front edge of the
fetch closer to the indicated front - see Figure 1) while not necessarily
reducing the differences between the results obtained by the two methods,
would result in values obtained by the Pierson-Neumann method being
much closer to the observed.

In the use of the Pierson-Neumann method an additional subjective
factor enters in the determination of the fetch width. Fetch width
in relation to decay distance has important significance in the
Pierson-Neumann theory; that is, the greater the fetch width, the
greater the wave height, all other things being equal. There is
possibility of error here, in that exact determination of the fetch
width is dependent on the accuracy of judgment of the user, which is
to be obtained only by a great deal of experience in the use of the
method and comparison with recorded values. Such experience is lacking
here, and it is quite possible that a more applicable value could have
been chosen.

The angular spread of the waves as they are propagated from the
fetch front to a point of observation is also of importance in this
method. An energy correction factor for this angular spread is a function
of the angles formed by drawing lines from the point of observation to
the two extremes of the fetch width and extending lines from the fetch
sides (see Figure 1). Assuming a true initial angle of 7°,a difference
of 15° in fetch direction, in a negative (upward) direction, would result
in an increase of 45 percent in wave height. Conversely, a difference
of 15°, in a positive (downward) direction, would result in a decrease
of 68 percent in wave height (see Figure 3). A graph depicting per-
centage increases and decreases in wave height for true initial angles
of 7°, 12°, 22° and 32° and angular differences of 1° through 15° is
shown on Figure h.

A combination of differences in fetch width and angular spreading
values may give rise to possible wave height increases of large magnitude.
For example, assuming an angular negative difference (upward) of 15°
in combination with a fetch width difference of 2 (twice the fetch
width being used) the resultant wave height would be 1.7 times that
otherwise obtained. This is based on an initial angle of 7°; for
initial angles of greater degree, the wave height increase would be
relatively smaller. Figure 5 illustrates the relative height increases
due to an angular negative difference of 15° for initial angles of
7°, 129,220 and 32°, For a positive (downward) angular difference of
15°, the resultant effect upon the wave height is negligible, ranging
from 0.93 to 1.12 for the same angular range as above.

8

¢,= true initial angle = 7°
bo = —15°— 7° = — 22° (erroneous initial angle due to hypothetical
angular error in fetch front )

$, = true initial angle = 7°

$o = — 7° + 15° = + 8° (erroneous initial angle due to hypothetical
angular error in fetch front )

FIGURE 3. POSSIBLE ERRORS IN CONSTRUCTION OF ¢ ANGLES

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The weather situation resulting in the peak waves is shown in
Figure 6; the fetch used by the author is also shown (as a solid line),
delineating the fetch width and decay angles. This was also essentia]ly
the fetch determined by the second (independent) Board forecaster.
Although from the weather maps, this would appear to the author (and
his co-workers) to be the most accurate determination of the fetch (in
view of the pictured weather situation), certainly otherScould be
chosen. Such a fetch as shown by the dotted line, although not appearing
to the author to represent as closely the weather siutation pictured,
on the map, might well still be possible of selection (particularly by
a forecaster more experienced in the use of this method) and would
give results much closer to those observed.

In conclusion, it might be stated that the larger wave heights
forecast in this one example by the Pierson-Neumann method could result
from inaccurate or inapplicable determination of fetch width and
angular spreading, inability to accurately interpret the Co-Cumulative
Spectra Curves, difficulties inherent in the subjective choice of the
applicable meteorological parameters, and lack of experience with this
newer method. It should be emphasized that this paper is based on a
comparison of forecast methods as applied to one storm only and is per
se limited in its scope; no conclusions as to the relative accuracy of
the methods can be drawn until much wider application of the newer method
is made, so that some sort of statistical comparison over a long period
of time (as 1 year) can be made.

REFERENCES

1. Datz, M. - Comparison of Deep Water Wave Forecasts by the Darbyshire
and Bretschneider Methods and Recorded Waves for Point Arguello,
Calif., 26-29 Oct 1950, Bull. Beach Erosion Board, V.7,No. h,
1953.

2. Bretschneider, C. Le - Revised Wave Forecasting Curves and Procedure,
Univ. of Calif., Inst. of Eng'g. Research, Ser. 29, no. 155-17,
1951 (unpubl. )

3. Pierson, W. J», Jr.,G. Neumann, and R. W. James - Tech. Rpt. No. 1
(prepared for project AROWA) N.Y.U. College of Eng'g., Res.
Div. "Practical Methods for Observing and Forecasting Ocean
Waves by Means of Wave Spectra and Statistics".

4. Kaplan, K. - Analysis of Moving Fetches for Wave Forecasting, Beach
Erosion Board Tech. Memo. No.35, 1953.

5. Beach Erosion Board - Shore Protection Planning and Design, Beach
Erosion Tech. Report No. h, 195k.

STATUS OF SAND BY-PASSING PLANT AT
SALINA CRUZ HARBOR, ISTHMUS OF TEHUANTEPEC, MEXICO

Details of the Salina Cruz stationary by=-passing plant
were presented in two previous Beach Erosion Board Bulletins.
An article in the July 1951 Bulletin described the completed
installation and pointed out the difficulties in creating a
natural flow of sand into the reaches of the suction lines

of the pumps. An article in the April 1952 Bulletin reviewed
the functional aspects of the installation, including some
characteristics of the beach in the vicinity of the harbor.

The 1952 article pointed out that creating a natural flow of
sand to the pump intake had not been satisfactorily accomplish-
ed as of that date.

The report herein covers the general progress of the Salina Cruz
by-passing plant since 1952, as outlined in a September 195) letter received
from the Director, Mexican Free Ports. Figure 1 shows the Port of
Salina Cruz, which is located on the Pacific Coast of Southern Mexico,
The Port is divided into an inner and outer harbor with the by-passing
plant located adjacent to thewest breakwater of the outer harbor.

The basic intent of operation of the by-passing plant was to intercept
the eastward drifting sand and pump it through a discharge line extend-
ing over the loading docks and a swing span separating the two harbors,
thence, to the shore east of the east breakwater. The intakes for the
pumps were located landward of the high water line and attempts were
made to create a movement of sand to the suction lines by means of a
dragline and other equipment. These attempts to feed the sand to the
point of pump intake, with the intention of causing recession of the
shore line, have been discontinued since the procedure has proven to be
inefficient and very costly. Another factor which caused the temporary
discontinuation of the sand by=passing operation was the frequent
interruption of pumping necessary for opening the discharge pipe swing
span to allow all types of craft to enter or leave the inner harbor.
This resulted in a negligible quantity of sand being by-passed.

Since the discontinuation of operations, the harbor has shoaled
at a more rapid rate. At the beginning of 195) it was necessary to use
two hopper dredges, the "Presidente Aleman" and the "Coatzacoalocs" in
order to maintain the harbor.

A program has been undertaken to reduce shoaling in the harbor and
reactivate the byrpassing plant. The program consists of building a
rubble mound groin normal to the beach (as indicated in Figure 1),
about 2,000 feet west of the dredge installation. The present length
of the groin is about 260 feet, and its final length will be approximately
560 feet. The purpose of this groin is to reduce the supply of sand

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to the beach between the groin and the stationary by-passing plant,
with the expectation that this reduction in supply will cause this
shore line to recede to the desired design alignment. The initial
behavior of the groin if as designed, even though it has not been
constructed to its final length. It was anticipated that the sand
eroded from between the groin and by-passing plant would be transport-
ed into the harbor and this condition is being resolved by having a
hopper dredge operate within the outer harbor.

It is expected that when the groin has been constructed to its
design length, and its impounding capacity has been reached, the beach
to the east of the groin will have eroded sufficiently to enable the
stationary by-passing plant to operate directly offshore as originally
designed.

To overcome the problem of pumping interruption occurring when
the pipe swing span is opened, an. impermeable pier is planned on, the
harbor side of the west breakwater. This structure is designed to
serve two purposes, first, as a sand trap to prevent any further
shoaling of the outer harbor and, second, as a mooring place for hopper
barges which will receive the sand pumped by the stationary dredge.
The hopper barges will then be towed across the harbor where they
will be emptied by means of a pumping plant located on the eastern
breakwater, and the sand will be deposited on the beach east of the
breakwater.

PROGRESS REPORTS ON RESEARCH SPONSORED BY
THE BEACH EROSION BOARD

Abstracts from progress reports on several research contracts in
force between universities or other institutions and the Beach Erosion
Board, together with brief statements as to the status of research
projects being prosecuted in the laboratory of the Beach Erosion Board
are presented as follows:

I. University of California, Contract Noe DA=9-005-eng-8, Status
Report No. SG 1 July through 30 September 195].
Good progress was made on the statistical compilation of the data

for the sand samples collected around the rocky promontories in Southern
California. This compilation is now 90 percent completed.

In September a voyage was made in cooperation with Scripps Institution
of Oceanography using the vessel E. R. SCRIPPS, to take underwater photo-
graphs of the sediments off Point Dume, and the southern side of Catalina
Island. A good selection of photographs was obtained by aqualung divers,
the divers being trained scientists who made detailed observations of the
sea bottom in conjunction with the photographs. A well defined series
of ripple marks were present upon the sea bottom in this area, their
axes being essentially parallel to the front of the waves approaching
the coast. In one place transverse sand waves with amplitudes of 6 to 7
feet and heights of nearly 1 foot were observed just outside the breaker
zone. The axis of these ripples was essentially at right angles to the
coast line.

II. University of California , Contract No. DA-l9-005-eng-17, Status
Reports L,5 and 6, 1 January to 30 September 195L.
Experimental work on the various stages of ripple formations until
their final disappearance was continued using materials of different
sizes and density. Analyses indicate that steepness of the ripples during
these stages can be described as a function of a dimensionless parameter
involving the maximum velocity, density, and size of the particles, and
the kinematic viscosity of the fluid in which the motion takes place. The
function can also be used to define the initial and general movements and
also the initiation and the final disappearance of the ripples.
III. University of California, Contract No. DA-l9-005-eng-31, Status
Report No. z

Three reports dealing with water surface roughness and shear stress,
and wind waves and set-up in shallow water were in preparation.

IV. University of California, Contract No. DA-49-055-eng-l),, Status

Report No. 1, 1 July through 30 September 195h.

Laboratory studies of wave refraction are to be made, this study
being an extension of a prior study where wave refraction on a beach of
1:40 slope with beach orientations of 15, 3h, and 50 degrees with respect
to the direction of the generated wave train, was studied in an effort
to evaluate the usefulness of Snell's Law. The present study uses the
same beach orientations, but the slope of the beach is varied; 1:20, 1:40,
and 1:60 slopes are used. The ripple tank four feet wide, twenty feet
long and five inches deep has had a glass plate 45" x 72" x 3/8" installed
in the middle of the tank bottom for these experiments.

Large scale studies of wave refraction using a 150' x 60! x 23!
model basin with a built in beach and a flapper type wave generator are
planned. Large scale comparisons with model results will be made using
a slope of 1:40 and beach orientations of 15 and 50 degrees. The beach
in the large basin will also be modified to allow waves to continue over
the beach into a constant depth of water (d/i = 0.1); hence, they will
not break on the beach. In this case slopes of 1:20, 1:40 and 1:60, and
beach orientations varying from 5 to 85 degrees, if possible, will again
be used.

Ve Scripps Institution of Oceanography, Contrac® No. DA=-l\9-055-eng-3

Quarterly Progress Report No. 21, July-September 19

Periodic measurements of sand-level changes with reference rods have
now extended over a period of 18 months. The maximum change during the
entire period now stands at 0.18, 0.21, and 0.07 ft. in areas where the
water depth is approximately 30, 52, 70 feet respectively.

Results of the quarterly survey of the valley heads of Scripps
Submarine Canyon seem to indicate a considerable shoaling of the valleys
and some shoaling of the ridges between them. Divers reported that
instruments placed on the canyon bottom are being rapidly covered by kelp
and sand.

VI. The Agricultural and Mechanical College of Texas, A & M Project 95,
Quarterly Report for period en 14 September 195.

This project consists of preparation of Statistical Wave Data on the
United States shore of the Gulf of Mexico obtained by hindcast methods.

This period was devoted to organization and to training of project
personnel, including personnel for construction of refraction diagrams
for various areasof the Gulf Shelf and computation of generation of wind
waves over a shallow bottom of variable slope. A simple and yet accurate
method of hindcasting wind waves over a shallow continental slope is being
investigated.

‘VII. Waterways Experiment Station, Vicksburg, Mississippi
Wave Run-up Study:

Testing was resumed on the 1 on 14 slope step-face wall,
and these tests were completed. Testing was initiated on a recurved
wall.

VIII. Beach Erosion Board, Research Division, Project Status Report for
Quarter ending 15 December 195].

In addition to the research projects under contract to various
institutions which are reported on above, the Research Division of the
Beach Erosion Board is carrying out certain projects with its own
facilities. The main unclassified projects have been described in pre-
vious numbers of the Bulletin, and a short description of some of the
work accomplished through the last quarter is given below.

The Study of The Reforming of Waves After Breaking - Beach bar
slopes of 1:90, 1:60, 1:30, and 1:10 with varying depths over the bar

have been tested and the data is now being analysed.

Study of Sand By-Passing Operation at Port Hueneme - Data taken
before, during and after the Fort Hueneme dredging project is being
reviewed, organized, and analysed. It is hoped that a hydrographic
survey may be obtained in the near future to serve as a 6 month comparison.

Routine progress, testing and analysis have been made on the other
projects being carried out by the Research Division. In addition,
Research Division reports on "Laboratory Study of Equilibrium Profiles
of Beaches" by R. L. Rector and "Laboratory Study of Effect of Varying
Wave Periods on Beach Profiles" by G. M. Watts, were completed and
published as Technical Memor andums No. 1 and 53. Also reports result-
ing from contract investigations made for the Beach Erosion Beard were
published as follows: "Modification of Wave Height Due to Bottom Friction,
Percolation and Refraction" by ©. L. Bretschneider and R. 0. Reid;
"Field Investigation of Wave Energy Loss in Shallow Water Ocean Waves"
by C. LE. Bretschneider; "Statistical Significance of Beach Sampling
Methods" by W. C. Krumbein; "Generation of Wind Waves over a Shallow
Bottom", by C. L. Bretschneider; and "Theory of the Ocean Wave Spectrum
and Its Uses in Wave Train Analysis", by W. J. Pierson, were published
as Technical Memorandums No. 5, 6, 50, 51 and 56 respectively.

Also a h-week work conference of representatives of various Corps
of Engineers Offices was held at the Beach Erosion Board to analyse data
on waves in inland reservoirs. A rough draft report was completed,
showing that the S.M.B (Sverdrup-Munk-Bretschneider) curves agree very
closely with observed results if proper corrections are made for fetch
width and the difference in velocity between over-water and over-land
Winds.

BEACH EROSION STUDIES

Beach erosion control studies of specific localities are usually
made by the Corps of Engineers in cooperation with appropriate agencies
of the various States by authority of Section 2 of the River and Harbor
Act approved 3 July 1930. By executive ruling the costs of these
studies are divided equally between the United States and the cooperat-
ing agencies. Information concerning the initiation of a cooperative
study may be obtained from any District or Division Engineer of the
Corps of Engineers. A list of authorized cooperative studies follows:

AUTHORIZED COOPERATIVE BEACH EROSION STUDIES
MASSACHUSETTS

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

Problem: To determine the most suitable methods of shore pro-
tection, prevention of further erosion and improvement
of beaches, and specifically to develop plans for pro-
tection of Crescent Beach, the Glades, North Scituate
Beach and Brant Rock.

CHATHAM. Cooperating Agency: Department of Public Works.

Problem: To determine the best method of preventing shoaling of
Stage Harbor and damage to shore property, and the effects
on Stage Harbor and adjacent shore property of probable
changes to Nauset Beach and Monomoy Island and any works
which may be constructed for protection of Stage Harbor.

CONNECTICUT

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

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

NEW YORK

N. Y. STATE PARKS ON LAKE ONTARIO. Cooperating Agency: Department of Con-
servation, Division of Parks.

Problem: To determine the best method of providing and maintaining
certain beaches and preventing further erosion of the
shore at the Braddock Bay area owned by the State of New
York

20

FIRE ISLAND INLET AND VICINITY: Cooperating Agency: Long Island State
Park Commission

Problem: To determine the most practicable and economic method of
providing adequate material to maintain the shore ina
suitably stable condition and an adequate navigation
channel at Fire Island Inlet.

SUFFOLK COUNTY (ATLANTIC COAST BETWEEN MONTAUK POINT AND FIRE ISLAND
INLET). Cooperating Agency: Department of Public Works, State
of New York.

Problem: To determine the most practicable and economic method of
restoring adequate recreational and protective beaches
and providing continued stability to the shores.

NEW JERSEY

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

Problem: To determine the best method of preventing further erosion
and stabilizing and restoring the beaches, to recommend
remedial measures, and to formulate a comprehensive plan
for beach preservation or coastal protection. The current
study covers the shore from Barnegat Inlet to Cape May.

DELAWARE
STATE OF DELAWARE. Cooperating Agency: State Highway Department
Problem: To formulate a comprehensive plan for restoration of
adequate protective and recreational beaches and a program
for providing continued stability of the shores from
Kits Hummock on Delaware Bay to Fenwick Island on the
Atlantic Ocean.
NORTH CAROLINA
CAROLINA BEACH. Cooperating Agency: Town of Carolina Beach.

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

2i

CALIFORNIA

STATE OF CALIFORNIA. Cooperating Agency: Department of Public Works,
Division of Water Resources, State of California

Problem: To conduct a study of the problems of beach erosion and
shore protection along the entire coast of California.
The current studies cover the Santa Cruz, Orange County
and San Diego Areas.
WISCONSIN

MANITOWOC-TWO RIVERS. Cooperating Agencies: Wisconsin State Highway
Commission, Cities of Manitowoc and Two Rivers

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

MICHIGAN
BERRIEN COUNTY. Cooperating Agency: City of St. Joseph

Problem: To determine the most effective methods of preventing
erosion of the shore by waves and currents.

TERRITORY OF HAWAIT

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

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

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