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NAVAL S'HP RESEARUN AND DEVELOPMENT CENTERWbnton.DC. 20007.
CHARACTERIZATION OF TRE SHALLOW WATER WAVE ENVIRONMENT
PREDICTION TECHNIQUES AND MODELING FACILITIES
by
Robert J. Johnson
This document has been approved for. public release and sale; its
distri-bution is unlimited.
DEPARTMENT OF HYDROMECHANICS RESEARCH AND DEVELOPMENT REPORT
September 1970 . . .. Report 3401
,
's-.
r
V
DEPARTMENT OF THE NAVY
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER Wathington, D.C. 34
CHARACTERIZATION OF THE SHALLOW WATER WAVE ENVIRONMENT:
-. PREDICTION TECHNIQUES AND MODELING FACILITIES
by
Robert J. Johnson
This document has been approved for public release and sale; its distri-bution is unlimited.
DEPARTMENT OF HYDROMECUANICS RESEARCH AND DEVELOPMENT REPORT
TABLE OF CONTENTS Page ABSTRACT 1 ADMINISTRATIVE INFORMATION INTRODUCTION i
STATE ÒFTHE ART 2
ENVIRONMENT io
Beach il
Surf 13
FACILITIES EVALUATION 16
PROPOSED SURF ZONE AND NEARSHORE MODELING FACILITY
FOR THE MANEUVERING AND SEAKEEPING BASIN OF NSRDC. . 20
CONCLUSION 24
ACKNOWLEDGMENT 25
REFERENCES 38
Figure Figure Figure 3 Figure Figure 11 -a LIST OF FIGURES Page
i - Changes in Form of a Shoaling Wave 26
2 - Comparison of Maximum Wave Slope for the Linear and
Non-linear Wave Profile 27
- A Time History of Solitonic Interaction Showing the Decrease in the Amplitude of the Composite Wave With
Subsequent Increase in Amplitude of the Primary
Solution when the Interaction Abates 4 - A Typical Beach Profile as a Result of
Action Showing Slope Contour Elements 5 - A Cape Cod Beach of Slope 1:100 With a
Submerged Bar
6 - A Barless Beach Profile so Transformed
Horizontal to Represent a Beach of Any
Initial Slope
7 - Global Areas Where One Might Observe Heavy Surf as a Consequence of Strong, Steady Winds and Long Fetch
8 - Frequency of Wind Speed Occurrence in the North Atlantic
9 - Wave Breaking Characteristics
Heavy Surf
in the
Schematic Dìagram of Variable Beach Proposed for NSRDC MASK Facility 33 111 Figure Figure Figure Figure Figure 27 28 29 29 30 31 31
Figure 10 - Computed Surf Height Statistics for Three
e.'
LIST OF TABLES
Page Table i - Comparison of Sea State Characteristics for Deep and
Shallow Water as aResuit of Applying Linear
Wave Shoaling .. 34
Table 2 - U.S. West Coast Beach Statistics 34
Table 3 - Wave Height and Wavelength in Model Scale Required to Simulate Surf on Three Uniform Slopes Resulting from a
Shoaling Swell of 7.6-Second Period 35
Table 4 - Ten U.S. Wave Tanks Most Readily Adaptable to Surf Zone and Shallow Water Studies in Relation to
Investigations of Amphibious Craft Motions in a Nearshore
Seaway 35
Table 5 - Minimum Scale,Ratio (À) Required by Test Facilities to Simulate a Speçific Surf Height Condition on a Numbêr of
Uniform Beach Slopes 36
Table 6 Preliminary Cost Estimate for the Variable Beach
Proposed for the NSRDC MASK Facility 37
SYMBOLS AND ABBREVIATLONS Maximum wave slope
ACV Air-cushion
vehicle
CERC Coastal Engineering Research Center
H Wave height
H Deep water
o
H Model wave height
orn
H/2 Wave amplitude
Eb Surf height
H Model surf height
bui
h Water depth
hb Wave breaking water depth
i Initial' beach slope at the shoreline
L Wave length
L0 Deep. water wave length
L Model wave length
0m
'b Length of surf zone
'bui Model surf zone length
X Linear scale ratio
MASK Maneuvering and Seakeeping Basin at NSRDC
MLLW Mean low low water
NAVOCEANO Naval Oceanographic Office
SR.N5 Peripherial skirted ACV
SWL Still water level
T0 Deep water wave period
X Distance from shoreline
Y Bar crest depth
ABSTRACT
This. is a brief presentation of the state of the
art regarding the theory an4 modeling techniques of
shallow water wave phenomena. A disc-uss.ion is
incor-porated pointiñg up a substantial need for the modi-fication of an existing f acuity or the development of a new facility capable of characterizing a
realis-tic, shallow water wave environment by including
uneven bottom topography. Beach and surf statistics
are presented to serve as guides in setting the re-quirements for stich a facility. Existing U.. S.
tow-ing tanks and seakeeptow-ing basins that possess a surf zone testing capability of amphibious assault, craft
are evalúat.ed and a beach: design is proposed for the
Maneuvering and Seakeeping Basin (MASK) at the Naval Ship Research and Development Center (NSRDC).
ADMINISTRATIVE INFORMATION
This study was funded under the NAVSHIPSYSCOM Amphibious
Assault Landing Craft Program, Sub Project. Sl4-l7 Task 14174.
INTRODUCTION
Interest in high speed amphibious operations points up the
V
continuing need for methods of predicting the character of in-shore wave and surf conditions and the response of amphibious
èh'±c-ies to Although shallow water research
programs were init:iated4uring World. War II,. technology still
does not provide reliable definition of:
the transformation which a deep-ocean-seaway undergoes as it propagates inshore over ag.ven bottom topography.
the inception, extent and character of breaking waves:.
which are produced by this seaway energy propagating inshore..
(c). the changes in for.m.which indivi:thia,l non-breaking waves
undergo during these transfornations.
(d) the response of landing craft to this environment, both
in terms of gross effects such as broaching, swamping, pitch-poling, capsizing and also in terms of specific vehicle motions
and accelerations in pitch., heave, surge, etc.
Over the years a great deal of experimental and analytical effort has been expended on specific phases of the overall
problem, much of it in connection with related problems such as
beach erosion, but a satisfactory unification, of all the parts
has yet to be achieved.
In addition there are at present no facilities in this
country which have the capacity of testing suitably sized
am-phibious models in realistic inshore wave conditions.
STATE OF THE ART
This section'describes the various shallow water phenom-a thphenom-at phenom-affect the operphenom-ation of nphenom-avphenom-al crphenom-aft together with phenom-an
w
* References are listed
on page 38.
3
assessment of the current technological ability to
represent these phenomena analytically.
Wind imparts energy to the sea surface in
a random fashion
generating a general confusion of waves traveling in a
multi-tude of directions.
The height of the waves is a function of
,the strength of the wind, the duration for which It blows and the size of the surface area over which it acts.
The waves
travel out of the generating area in the direction of the pre-dominant wind and gradually assume a regular profile
and long-crested appearance. This indicates the high
frequency
compo-nents of the wave system are quickly damped out by vàrious mechanisms of energy dissipation,
leaving the low frequency
waves, known as swell, to propagate considerable distances from
the point of origin. Eventually swell will
encounter a
shal-low water regime where the wave will
transform and finally
dis-sipate the remainder of its energy by
mechanisms of breaking
and run-up on a beach. It is this long,
regular wave form with its subsequent transformations that characterizes
the nearshore oceanic area. Superimposed on this
gross system of waves will be the wave system produced by the local meteorological
condi-tions.
The form that a deep water wave assumes
as it propagates
inshore becomes increasingly non-linear as a result of
the
decreasing water depth. A number of non-linear
wave theories
have evolved since the initial developments
4
Korteweg and de Vri:s2 to describe this phenomenon, but each is restricted in its specific application by virtue of the bound-ary conditions imposed for the solution of the wave equation. In particular, in the last half decade there has been much
ac-tivity in the field of non-linear ocean wave research which has
help-ed to clarify many of the observed phenomena. However a
mathematical model predicting the continuous non-linear
trans-formation that a deep water wave undergoes as it propagates inshore has not been achieved. The ability to model
analyti-cally the non-linear wave environment as a function of distance
from the shoreline is at most a possibility of the future and depends on the successful matching of the existing, piecewise wave solutions together with the incorporation of improved
dis-sipation terms. Thus, the only way to gain a priori knowledge of amphibious craft response to inshore wave and surf condi-tions at this time is to employ a realistic, physical model of
the nearshore seaway.
In deep water, waves are dispersive and can be represented as sinusoidal undulations of the water surface as in the
classic linear approach. This representation is satisfactory
when the water depth h is at least twice the length of the wave L, and the amplitude H/2 can be considered infinitesimal
in comparison to the length. As the wave propagates shoreward over decreasing water depth it will shorten in length,
result-in in a greater wave steepness. The curvature of the wave
wave equation as higher order (non-linear) terms. For depths
falling in the range of one-half to one-tenth the wavelength,
StokesTi theory of finite amplitude gravity waves characterizes
the non-linearity of the wave profile adequately. As the wave
continues to shoal it becomes progressiveIy asymmetrical about the horizontal plane of the still water level (SWL) with the crest height becoming much greater than the trough depth. For
extremely shallow water depths the wave becomes non-dispersive and assumes an appearance of sharp, nàrrow crests and long,
flat troughs. The cnoidal wave theory initiated by Korteweg
and de Vries2 sufficiently characterizes this wave in water depths less than one-tenth wavelength up to depths where the wave becomes asymmetical about a vertical plane through its
crestline. With continued shoaling the wave profile becomes increasingly skewed in relation to the two planes of symmetry with extreme steepening of the forward face of the wave. When
the face or a portion thereof becomes vertical, the wave
be-comes unstable and breaks. The theory of Biesel3 sufficiently
predicts this apparent wave-slope asymmetry prior to breaking as supported by Adeymo4 and also characterizes a breaking phase
of the wave. To assist the reader, Figure 1 is presented to show the continuous change a deep water wave assumes as it propagates to a depth of twelve feet.
The point is made that the foregoing segmentation of the various wave theories into regions of applicability is somewhat arbitrary as there is sufficient overlap in these regions to
6
allow more than one of them to be used at a specific finite
water depth. It will b the ability to concurrently represent the form and characteristics of the wave in two analytical models at the transition zone that could eventually lead to a
unified wave theory.
In a recent analytical examination of the shallow water environment it was established that wave slope is the seaway characteristic that most seriously influences the roll and pitch motions of naval craft. Linear theory can be utilized to predict the change in maximum wave slope cL as a wave
propa-gates into shallow water, but as the wave begins to assume a horizontal plane asymmetry, linear theory under predicts that
slope obtained from a non-linear wave profile. This is
dramatized in the twenty-four foot depth case shown in Figure 2 where the dashed profile is a sinusoidal wave having the same
length and height as the non-linear wave. As the wave
pro-gresses into very shallow water there is still the effect of vertical plane asymmetry one should consider when establishing
change in maximum wave slope. The theory of Biesel3 might be used in future analyses for this purpose, but to date the wave slope asymmetry displayed by a wave in water with a depth less than one-fourth the wavelength has not been investigated ex-plicitly to discern its effect on the response of naval craft.
Four secondary wave properties that influence the response
f'
f
shallow water craft to varying degrees will now be discussedh.
llarmonicdéep water waves propagating over shallow,
hoti-zontal bottoms teñd tò decompose. into solitons (solitary waves)
.5 6
as pointedout by Calvin and Madsen. The phenomenon occurs
for a water.depth region define4 as i/h greater than .ten
and/or h/H less.than twenty. On a shallow bottom characterized
by an initial slope of .1:60 one then might expect a wive of
length 100 feet to decompose at a distance of 1000 feet from
the shoreline., or a 200-foot wave could start decomposition as
far as two-thirds of a mile from the shore. This indicates
that an amphibious craft may experience this phenomenon over a considerable distance in a beaching maneuver. .
An interesting feature of solitary wave interaction is the noticeable decrease in composite wave amplitudes which is
shown in Figure 3. This implies the invalidity of applying linear superposition techniques to this System of waves ánd
the resultant craft motions.
As a wave propagates toward shore part of its energy is
reflected seaward as a consequence of bottom gradients o The
arnoûnt of energy reflected is enhanced as the bottom slope
increases beyond an angle of 40 (1:14) as presented by Wiégel.7 Gradients of this order are characteristic of beacheS riot
exposed to heavy surf and are also established by thé seaward
face of longshore bars. Wave energy thus réflected back
through an approaching wave system can originate Standing wave patterns in shallow water areas with amplitUdes possibly being. hazérdous to amphibious craft operation.
A äve crest is eerally refracted as it passes over a
bottom geometry exhibiting contours otier than parallel
straight lines. This may result in focusing. wave energy at
caustics where the phase of the wave is altered by 90° and the amplitude is possibly increased thus affecting naval craft
motions. Also, in the general case, the wave crest approaches the shorel-ine at an oblique angle as a consequence of
refrac-tion thereby inducng a lonshore. currnt with speeds anging to four knots as reported in Reférence 8.. Currents of this
magnitude greatly enhance the probability of an assault craft of the displacement type to broach at the shoreline while landing on or leaving from the beach.
To conclude, i has recently beeñ shown that regular waves mechanically generated in a tank completely lose their physical identity as they propagate considerable distances from the wave generator (Benjamin and Fier9). The phenomenon is attributed
to an energy leakage f:rom the .predominant frequency into
side-bands as a consequence of the wavemaker placing a slight per-turbation on the carrier wave In that this disintegration
results from the lack of pure frequency in a harmonic wave,
this phenomenon should, be prevalent in the oceanic environment.
Knowledge of its manifestation may shed. some insight into the
:spectral energy shifts observed in deep water wave systems as
they shoal.
These changes in form that deep water wave systems assume
i
inshoaling should be reflected in a simulated environment
I
'used in the test of amphibious craftmodels. Ideally this testing should be. psfor.med in a basin capable of
cháracter-izing realistic periods and.heights of waves and surf. over
representative bottom configurations and at adequate scale
ratios. The requirement fôr such a facility will be discussed
in a subsequent section; no such testing capability exists within the United States today.
If amphibious testing must be carried out in a current
facility where 'the waves generated are essentially in deep
water, then an effort should be made to alter wave making programs to introduce as much realism as possible into thé.
generated seaway for shallow wate.r testing. A simple pproach
involves characterising statistics Of the shallow water sea,
e.g. significant wave length, in the' generated deep water wave
system. The shallow water statistics are judiciously chosen as those most influential on the modes of craft motion to be
investigated for a 'particula.r design. 'Clarification of the,
procedure can best bè accomplished by presenting the' following
examples. Experience dictates that the rolling.mo:tion of
round 'bilge hull forms subjected to beata seas is influenced
mostlyby change's in maximum wave slope, and wave period.
Therefore, these two characteristics should be modeled in the deep water wave system as representative of the expêcted
shàl-low water conditions. In the case of an amphibious vehicle.
approaching the beach at surf speed, shallow water wave heights and phase velocities should be realistically reflected in the
lo
model environment. Asa final ex.ample consider au ar-.cushion vehicle proceeding over ashailow bottom at high speed ii
astern seas Here the significant height and length of the
waves affect the response of the craft to the greatest:extent, thereby making them the prime wave characteristics in the
sea-way simulation. Table 1 is presented to illustrate the change required. in modeling for the last example ata particular
depth of 50. feet. As the depth decreases the change required
becomes more dramatic.
This discussion indicates that the present policy o.f
specifying the seakeeping performance requirements of shallow water craft in terms of fully-developed, Pierson-Moskowitz seas
is erroneous. This practice could possibly lead to drawing faulty conclusions when comparing the performance of various amphibious çraft designs. . .
A complete development of the. theory of water waves prior
10
to the mid-1960s may be found in Neumann and Pierson,
11 7.
Kinsman, and Wiegel.
ENVIRONMENT
In the previous section the influence of bottom topography
on dynamic. wave behaviour in the nearshore area was discussed,
and it is indicàted that realism in a model environment can . best be achieved by incorporating some basic bthymetry in a
required for amphibious model testing is established by con-sidering the physical properties of beaches and surf on a
global scale.
BEACH
The limited amount of field data available indicates the general appearance of a beach is unchanged when viewed over considerable periods of time, e.g. in the order of a year, but the short duration beach processes continually erode or build
up the beach face. Such processes initiate the development and migration of offshore bars, features characteristic of most
beach profiles. Longshore bars are most pronounced when the beach is being attacked by storm änd hurricane waves of the fall and winter months as depicted in Figure 4. The depth and seaward steepness of the bars regulate the amount of shoreward propagating energy reflected back toward the sea resulting at times in the establishment of a standing wave pattern in the
nearshore area. It was pointed out in the preceding section that such a system of waves may have a pronounced effect on the
response of naval vehicles operating in this environment should the period of the system be critical in comparison to the
natural response frequencies of the crafts. Also, a bar can trigger wave instability manifesting itself as a wave breaking or the formation of multiple crests behind the bar as pointed
out by Byrne,12 whose field observation is presented as
Figure 5. These wave transformations can significantly
12
influence the behaviour of assault landing craft in. the
imme-diate beach line area.
This discussion points up the important hydrographic func-tions of longshore bars and indicates the necessity of this beach eÏement in an effective simulation of the shallow water
envirOnment.
The most significant feature of the profile is the
con-tinuous decrease in the beach slope with increasing distance
from the shoreline. Keulegan13 was able to characterize this feature of barless beach profiles by an empirical relationship
establishing the bottom depth as a fimnction of the product of
distance from the shoreline X and initial beach slope i. This is reproduced graphically as Figure 6.. With some simplifica-tion though, beach profiles can be partisimplifica-tioned into two slopes
as done in Figure 4, the foreshore and the offshore slopes. Both play important roles in wave modification as the gradual
slope can create asymmetry in a wave and initiate wave decom-' position while the steeper slope with associated bars
deter-mines breaking of 'the wave and the extent of the reflected
energy. This signifies an inadequacy of modeling beach
ter-rain in the vicinity of the shoreline by a uniform slope.
Table 2 presents sorne beach statistics extracted from the.
profile data of Johnson and Bascom14 for U. S. West Coast. beaches. It is observed that the foreshore slope of exposed
'aches (which are the predominant case) in the proximity of thé mean low low water (MLLW) line, ranges from: 1:50. to 1:80
13
with an average of 1:65 while the fo'reshore slopes of less
exposed beaches range from 1:33 to 1:40. Wiegel7 presents a number of sheltered beaches with foreshore slopes of 1:5 to
1:10. Typical:ly', the offshore slope of aIl U. S. West Coast
beaches is steeper than 1:200 with an average of 1:160 while
the East Coast offshore slopes are much more gradual with marty
falling between 1:250 to 1:500.
The data presented above will be. considered typical of
the world oceanic beaches and will be used to'set the design requirementsof the f cility presented 'in a following section.
SURF
The most recent Navy performance specifications set for
amphibious logistic and trpop landing cr'afts Indicate they need
-only to negotiate an eight foot surf for compliance with
con-tract requirements. As it is estáblished that landing mission's
might have to be accomplished in a number of world beach areas' where a surf of ten feet ór more can be expected over a
sig-nificant portion of the year, the inadequacy of this surf,
requirement is now addressed.
The wind wave generation mechanism has been pursued since
'the initial undertakings of Sverdrúp and
Munk)5
It has beenconfirmed that the initial wind energy arises 'the high
fre-i quency end of the 'seaway spectrum .in a short period of time
and with continued wind, excitation of the lower frequency
14
reversed with high frequency energy. being viscously. damped ut
or absorbed 1eavin the low frequency content to propagate away fromthe generation area. It is this long period wave as
indi-cated earlier that one finds pre4ominantly in the surf zone
area near the shoreline. As the long wave approaches the surf zone its profile transforms characteristically shortening in
length and steepening its forward face, i.e. Figure 1. By
invoking the empirical shoaling characteristics obtained by
16
Nakaniura et al., the inc±ease in breaking height can be
predicted to be as much as a factor of two over t:he deep water
wave height should the initïal wavelength be long enough and
the bottom slope be sufficiently steep.
The amount of field data available for verifying surf heights and surf periods is quite limited but the compilation of surf data of Helle17 indicates that a seven to nine, second
surf period is about the average observed oh the northwestern
U. S. coast. This surf period is a consequence of the shoaling storm waves generated in the North Pacific. Similar deep ocean
seaways are arisen in the North Atlantic and the other geogra-phical locals designated in Figure 7 where there exists a long
fetch in conjunction with strong, steady wind systems.
To establish a reasonable surf height as.spciated. with this
seven to nine second period range the following discussion . presented. The wind wave generation theory of
moue18
in4i-'te.s that .a constant thirty knot wind c'an produce that part
sEconds within ten hoúrs. A25 knot wind generates this sea in about 17 hoúrs while a 40 knot wind accomplishes the same
in approximately 6 hours. This rangeof wind speeds is a sig-nificänt portión of the wind speed distribution observed i
the North Atlañtic as presented by Roll19 añd shown in Fig-ure 8, thus making the occurrence of wave perlcds of seven to
nine seconds quite probable. In fact, Roll indicates that the above wave period range with an associatEd waveheightrange 6.7 to 11.5 feet constituted 21 percent of the total two year
wave observation taken in the North Atl.aùtic -though no clear
indication is made to the concurrent meteorological conditions. If waves of a 7.6 second, period (T0) and heights (H)of
6.7 and 9.0 feet are shoaled acco.rding to the empirical;
rela-tionships of Nakamura et
al)6
and presented in Figure 9, one will obtain the surf heights (Hb) displayed in Table 3 for the three uniform beach slopes of 1:10, 1:30 and 1:50. Thegreat-est surf is found to be 11.5 feet as aresult of shoaling the 9.0 foot high wave on a 1:10 slope. This same wave shoaled on a 1:30 slope provides a surf height of 10.1 feet. This
greater than 10-foot surf, height is readily supported by field
observations of Helle17 and Johnson and Bascom14 for the
U. S. North Pacific coast.
The, Naval Oceanographic Office (NAVOCEANO) uses the
Sverdrup-Munk forecasting procedure to produce the statistics
displayed in Figure 10. These valu-es further indicate that as
a rEsult of long fetch length along with strong excitation
16
winds, the beaches of. Ireland (III, Figure 7), w.. Pakistan
(II, Figure 7), and Iror Coast (IV,.Figure 7 expect a'suf
condition in excess of 9 or 10 feet ovér a significant portion
of the'year. In. particular, a greater than 10-foot suri shows
an occurrence, frequency of 26 percent on the west and southwest
coasts of Ireland during the fall and winter months, and during the southwest monsoon season the West Pakistani coat is
sub-jected to a 'greater than 9-foot breaking wave at a rate of one
out of every four.
Other geographical areas possessing high surf potential
as a result' of shoaling storm waves are:
Western Australia (VI, Figure 7)
Tasmania and S. New Zealand (V, Figure:7) and Southern. Chile (VII, Figure 7).
In view of the surf values presented in the foregoing
discussion, it appears reasonáble, that: the performance
speci-fications of amphibious craft should include the negotiation
of a 10-foot high surf. Thus, the capability o.! testing
am-phibious craft' models in simulated' 10-12-foot surf heights
with periods ranging as high as 14 seconds should be available
to, the design. contra&or. .
FACILITIES EVALUATION
A number of U.' S. seakeeping facilities including those
».0 .
of NSRDC were evaluated for théi.r modeling' capacity of a
facility is to model the nearshore seaway as realistically as possible by incorporating basic bottom topography. The study is now presented.
The dimensions of the facility and necessary wave making capability are established by requiring a scale ratio A of five or six, thereby allowing for the test of a five-foot model of a 30-40-foot amphibious craft in this environment. By imposing
this requirement viscous scale effects can be kept to a mini-mum while promoting adequate response resolution. Table 2
implies that a scale ratio of nearly six necessïtates the beach to be in the order of two hundred feet to incorporate the area
of submerged bars. This two hundred feet of beach length is further required to allow for sufficient water depth at the toe of the slope to permit deep water waves generated at the wavemaker to propagate onto the slope without appreciable height attenuation or breaking at this point. It is granted
that the wave will be transformed at the foot of the slope into a non-linear wave form, the degree of transformation de-pendent on the initial height and length of the wave.
As established in the last section, a surf height of at least ten feet should be included as a moderate upper limit in a test designed to effectively evaluate the capability and survivability of an assault landing craft. This implies that
the craft be tested in a seaway severity (surf height to craft ,,. length) of 1:4 instead of the established requirement of 1:7
or greater.
Based on these requirements the .number of facilities
cap-able of modeling the nearshore seaway was reduced to the .ten
presented in Table .4 along with their size, maximum regular
wave capability and.necessary modification. The facilities are
listed in order of their preference, this order' being based on
their physical size and the scàle ratio required to simulate the nearshore conditiòns as presented in Table 5. These scale
ratios were obtained by limited information consisting mainly of thé facility's highest deep water wave and associated
period. Empirical energy and power relationships for a water wave presented inWiegel7 were used to establish the character-istic curve of maximum wave height vs. period for each facility where such a curve was not available.. Cross-curves of L vs.
o
H with beach slope a parameter were established for four
's'pe-cific breaking heights. The shoaling is according to .Nakamura
16 . . .
et al.. as presented in Figure 9. The wave making capability
of each facility, was compare.d to the cross-curves to define the
'miflimum scale ratio required for each facility to attain the
four wave breaking conditions. .
The scale ratios presented in Table 5.should be a modést over-estimate for the facility. Generally, the facility will require a slightly larger scale factor to accomplish thé
spé-cific wave condition as a result of over-estimating the. wave
height capability at a specific period. Also, a requirement .wá°s imposed that the deep water wave to be simulated be at
least 150 feet long, this establishing a 'lower limit of
V
approximately 5.4 seconds for the wave pe-riòd T. This is not
unrealistic when cônsidering that a test is being designed to
estab-lish an upper limit n the craft cápability bearing in mind realistic surf observations, It is acknowledged that the majority of the scale ratios in Table 5 epresent a wave period below the seven seconds indicated earlier as a desired moderate teit limit with an associated 10 foot surfheight.
By virtue of the above discussion the proposed MASK
facil-ity is found to be the best suited to accomplish a realistic surf zone and nearshore wave environment suitable for testing amphibious craft models f adequate size while operating in a
variety of wave conditions. The facility will be discüssed in
detail in the next section.
It should be noted before concluding this section that experimental investigations which attempt to define thé extent of the surf zone are often handicapped by viscous scale effects as exemplified by the recent work of Horikawa et al.2° who
attempted to define the ràte of energy dissipation in the surf
zone. The viscous effect is significant as the wave becomes
less than one inch in height and/or less than two feet in length as shown by Plakida and Perepetch.21 This indicates
that, as in all modeling processes, the larger the model, the
better the representation. Surface tension effects aré
negli-gible as they become noticeable for w ves possessing leng,ths
less than four inches.
PROPOSED SURF ZONE AND NEARSRORE NODELING
FLCILITY FOR THE MANEUVERING AND SEAKEEPING BASIN OF ÑSRDC The shallow water facility discussed below is proposed as an integral part of the Maneuvering and Seakeeping Basin (MASK)
of 'NSRDC. This basin is 360 feet long by 240 feet wIde and
20 feet .deep with two adjacent sides of, the tank equipped with
segmented banks of pneumatic typewave generators capable of producing regular, irregular long-crested4 and
multi-directional short-crested seaways. As, shown in Tablé 4 the
wave makers are designed to generatè up to a two foot high deep water regular wave with a length of forty feet, but it is
known that' a wave with a height of 1.75 feet and length of
50 feet can readily be attained.
The' variable beach 'is presented schematically as Figure 11
'and consists of 28 modules each having a plane dimension of
'20 feet by 20 feet and a six-inch thickness. The modules are
constructed of ¼-inch aluminüm sheeting weldedbetween a rec-tangular grid of six-inch I-beam such thateach section con-tains four symmetrically located, floodable compartments. When hinged together the sections forma contourable surface 200 feet long by 40 feet wide with a 40-föot ramp at the deep water end and a 40-foot shoreline slope at the other. The
surface 'is supported by a system òf 39 hydraulic jacks capable
of raising and lowering the false bottom through a total
V' ' '
'vertical distance of five feet. The jacks are set atop posts attached to'a concrete stabilizing bed on the basin floor.
The posts are so jointed, braced and hinged t allow them'.to
coIlapse horizontally beneath the false bottom 'when the
.facil-ity is not in use and lying flat against the concrete base. When the beach is needed the modules are made buoyant simulta-neously by forcing air into the floodable compartments causing
- the sections to float to the surface as a unit. The system
then lócks itself into position by design of the braces and hinges at the bottom of the posts. The assembled beach is ¡nade
secure by pinning it to the permanent concrete wave absorber along the short side of the basin. A preliminary cost estimate
for the facility, is presented as Table 6 with the total cost
being approximately $300,000.
The variable beach is of practical design to allow it to be set into position and adjusted in the minimum time of one to two work shifts without the aid of divers. The hydraulic jacks
can be actuated individually or concurrently to allow for
inul-tiple. slopes and canting of the surface relative to approaching
wave systems. This unique feature allows for the refraction bf
the wave crests as they approach the shoreline and the
induce-ment of littoral currents. It was pointed out earlier that this current enhances the broaching probability of a displace-ment type landing craft as it beaches or retracts through the
srf.
Inclusion of this current in a shallow water facility allows one to evaluate the ability of'the craft to reach orleave the beach in an acceptable orientation.
The multiple slope capability allows for testing an
as-sault craft in realistic surf condïtions in that the bottom
contour controls the extent of breaking (length o,f surf
zone see Table 3), the height of. breaking and the breaker
type. The difficulty that an amphibian experiences while
pass-ing through and retractpass-ing through surf is dependent on all
three coñditions. There is indication that the problem of
re-trat1ng can be alleviated in the case of an ACV by passing
back through the surf at an angle much less than 900 relative
to the crest line.. An SR.N5 found the least resistance and
sevérity of craft motions at a retraction angle of 450 in
ten-foot breaking wave.s (Ha.rmen22) . The proposed shallow water
facility is suitable for conducting model studies of the above
maneuver at a number of retraction angles and surf conditions, thereby allowing a more complete evaluation of the craft's performance. in inshore wave conditions.
The facility is large enough to allow for the test of a
five-foot model representing a forty-fopt craft in a simulated twelve-foot surf with 7.6-second period. The surf óapability of the facility for a number
of
beach slopes is partially indi-cated in Table 3. Also, the facility is designed to acceptmolded forms to represent submerged bars and other typical
bathymetry, thus allowing for induced non-linear, wave forms,
multiple crests and reflected wave patterns. These shallow
water properties have been shown to influence the. operation of
an amphibian in this seaway.
I
The facility has twò inherent problems. .The beach is.notlong enough to prevent the introduction of some transformation
to. the wave profile of. the very long waves as they propagate
23
over the 40-foot ramp onto the toe of the slope. With,
subse-quent shoaling on a very gradual slope the. waves may decompose
into shorter, non-linear, solitary wave forms rather than prop-.
agate as a single wave. As long as the water depth at this point over the slope is kept greater than six feet for the long wave cases, the problem can be minimized at some expense of
realisth in therepresentation.
Seco'nd, the proposed facility design necessitates removing
two feet of the twenty-foot water depth of the basin over the
collapsed beach. The reduction in wate'r depth will have two
effects on the wave systems employed, in the seakeeping tests
conducted in this basin. There. will be a slight height and
length attenuation for waves with lengths greater than 36 feet,
plus a refraction effect at the. edges of the collapsed beach.
Neither effect appears to, alter the deep water seaway
substan-tially. It was established that a fifty-foot wave (L) of
two-foot height (H) sustained oniy a 0.2-inch reduction in height and
0.4-foot
reduction in length as a consequence ofreducing t.he water depth from twenty feet to eighteen feet.
The Arthur et al'.23 ray equation indicates for the same wave
only a refraction of 1.6 .degrees at a distance óf 50 feet 'from
the' forward' edge of the collapsed beach. An interaction of the two effects has not been investigated. .
Both .of the problems can be moderated if the concrete
stabilizing bed can be dispenséd with by attaching the support-Ing posts directly to the basin floor. "This would .then
beach. Also, it is mentioned, other beach designs are being considered for the MASK-which would circumvent the storage problem discussed here.
CONCLUSION
- The need for a nearshore and inshore environmental test
facility has become pronounced in the past few years, since, for one to gain more fruitful design and character assessment of amphibious vehicles operating in a wave system in the
prox-imity of the shoreline, realistic test conditions will have to be employed. It has been shown in the foregoing discussion that a facility incorporating the major features of the near-shore wave environment including bathy-metry can be developed.
There Is indication that the resultant hydrography may have a significant Influence on response characteristics of small
naval craft. The versatile facility proposed for the MASK of NSRDC could serve as a general purpose laboratory for the study
of- many aspects of the total oceanographic problem such as the
identification of the principles controlling the transforma-tions exhibited in a shoaling deep water seaway.
Investiga-tions of this phenomenon will allow the naval architect to more realistically define the shallow water energy spectrum of this seaway, it being necessary for meaningful prediction of ship
response to this wave system. The facility will also allow for .ácurate modeling of multi-body problems incurred in salvage,
launch and recovery operations; man-in-the-sea experiments, and
V
investigations of shallow water wave forces on off-shore drill-Ing and observationplatforxns.
ACKNOWLEDGMENT
The author wishes to thank Professor P. R. Van Mater,
Jr.-and.Mr. R. Wermter for their suggestions and technic-al
assist-ance in this project. The preliminary cost estimate for the beach designed for the MASK was performed by the Systems
Engi-neering Branch of NSRDC.
«f
WATER DEPTH 30' 24' 13' 12'. WAVE NEAR BREAXU t- .25L -si )- 22L-4 L 160'-k2: 9993 H 7.3' : 73'L 2W-1
I2= .912 26 H = 7.6' 1:238'1
- 1.61 k2= 740 LSIHU.SOÍDALá =53 WAVE SLOPE = .82 ASYMMETRY DEVELOPI1iGFigure 1 - Changes in Form of a Shoaling Wave
LSU4USOIÛALJ h1 H h1 (CH O1DAL) L DEEP L.x 33ß' '4
c
60't
3fl5' 'If
4-t
27
Sinusoidal max. wave slope (ci) = 0.113 Cnoidal max. wave slope () 0.149
For both waves
L 216 ft.
H 7.8 ft.
h =24 ft. = 360 ft. = 8.0 ft.
Figure 2 - Comparison of Maximum Wave Slope for the Linear and Non-linear Wave Profile
,iiiiIIIIIIIUIUHhIUIIIIIIII1I! I!!II1!
I!!!!! !I1I!IU
iijjjÍI IiiflhIIIHUhUIIiIIII
11111111 11111 111111
iiiiUhIIiPIIlIIIiIIIIIiIIIIII IlIllilill
111111 111111
ititiiIiIIlIIIiIIlIIIIIIIIIIIIlIiIIII 11111111
Iii IllIllilIl 11111111
111111111 11111111 iIiIIIIiIIII
IIIIIIIIItIIII1IIIIII1i IllIllUIllIll 11111111
11111 liii liii 11111 IIIIIlIIlIflulIIIII
iiiiiPiIIIIIII LIIIIIIIIIIIIII1IIIIIIIIIIIUI1 I
iiiiiriravirii
II!ÏIIII1IíIILItIIM1Mt'
iiiiiiii;iiiiIifliUIiU11iiJiJ1IJUl
Figure 3 - A Time History of Solitonic Interaction Showing the Decrease in the Amplitude of the Composite Wave with Subsequent Increase in Amplitude of the
Primary Soliton when the Interaction Abates
(The measurement is of waves propagating in approximately one-half foot of water and was made at a distance of many wavelengths away from the wave generator in
the 96-foot wave tank at the Coastal Engineering Research Center. The scales are
not defined, but the solitofts are of about one-second period and the height of the primary soliton is about three inches. Time -increases toward the right).
MLLW
-NEAR SHORE OR OFFSHORE SUBMERGED BARS FORESHORE STEP FO RES HO RE SLOPE BERN -SCARPOFF SHORE OR NEARSHORE
SLOPE
BACH
28
Figure 4 - A Typical Beach Profile as a Result of Heavy Surf Action Showing SlOpe Contour Elements
(Continuous change in the beach gradient which is charaçterized here by two uniform slopes)
-
WAVE CRESTS o 4 16 20 p S UBME RG E BAR 29 DIRECTION OF WAVE PROPOGAT IONFigure 5 - A Cape Cod Beach of Slope 1:100 With a Submerged Bar
(The bar increases the number of wave crests ob-served in Area B by a factor of two in comparison to that in Area A. In this case the relative bar
depth (Y/L) was approximately 0.045; the ratio of wave height to bardepth, 0.45; the wavelength L
was near 25Q feet.
O 4 8 12 16 20 24 28 32 36 40
X.i IN FEET
Figure 6 - A Barless Beach Profile so Transformed in the Horizontal to Represent a Beach of Any Initial Slope
13
f
30
Figure 7 - Global Areas Where One Might Observe Heavy Surf as a Consequence of Strong, Steady Winds and
Long Fetch I - U.S. Pacific Coast II - W. Pakistani Coast III - S. W. Irish Coast
IV - Ivory Coast
V - Tasmanian and N. Zealand Coasts VI - W. Australian Coast
VII - S. Chilean Coast
T T - I I
çd
IUPUIIIIL.&UI,
1UJUIIIlIVVAIIIY4iE
VIIliii
_uu.
1:
i....4 i ... L... L :0.28 0.00 o 4 Figure 8 -10 20 30 40 60 80 100 Le/Ho
Figure 9 - Wave Breaking Characteristics
F s s I ..ss s .--. I i I I I I I
-I
IId
1 .1 1.0 0.9 12 16 20 24 28 32 36 ¿0 1.2Wind Speed, knots
.0.8
Frequency of Wind Speed Occurrence in the
0.7
North Atlantic
(as indicated by Roll'9)
0.6 0.5
t
2.0 1.9 1.8 1.7 1.6 1.5i.'
1.3 1.2 , F/
/ / I F F,/
/
/
%\ s s 0.24 0.20 0.16 g o 4, o, o o o 0.12 0.08 4, gj 0.04
IR 1V
Beach Area number is that defined-by the
Sea
and Swell
Section of NAVOCEANO. All waves are shoaled on n 1:50 bottomsiope.
Figure 10 - Computed Surf Height Statistics for
Three Geographical Locations AND BEACH AREA (S.W. 3 BEACH AREA S.W. 4 BEACH AREA 5 (W. BEACH AREA 6 W. BEACH AREA N.W. 7 - BEACH AREA 8A N.W SURF HT. ft. > (Z) 10 (Z) >1. (Z) >8 (Z) >10 (Z) >16 (Z) >8 (Z) >10 (Z) >16 (Z) >8 (Z) >10 (Z) >16 (X) >8 (Z) >10 (Z) >16 (X) >8' (Z) >10' (X) >16' (Z) SEASON Wintei 42 29 14 30 23 lo 30 23 10 40 31 13 25 14 4 11 8 2 Spring 25 15 5 16 11 3 15 10 3 24 17 5 11 6 1 2 1 0 Sumner 23 14 4 16 11 3 15 10 3 23 16 4 9 6 2 2 0 0 Fall 40 29 13 30 23 10 28 21 9 39 30 13 19 13 5 7 5 0 FAK5TAN BEACH AREA 3 -BEACH AREA 4 BEACH AREA 5 BEACH AREA 6 -BEACH AREA 7 SURF HT.(ft.) 6' 9' 6' 9' 6' 9' 6' 9' 6' 9' SEASON Nov.-Mar. 4 1 3 1 6 1 3 1 6 3 Apr. 16 6 12 5 14 4 15 5 18 10 May-Sept. 58 34 53 27 51 28 1 22 56 36 Oct. 7 2 5 2 7 2 7 2 13 7
)RY COAST SURF HT.(f
8'
lo'
&,6
SEASON Winter 7 3 2 Spring 17 9 6 Summer 17 10 6 Tall lO 5 2g
F
BEACH 322'-6" $ORTh tLAvOkEft Figure 11- Schematic Diagram of Variable Beach
Proposed for
TABLE 1
Comparison of Sea-State Characteristics for Deep and Shallöw Water as a Resu1t of App1ying Linear Wave Shoaling
TABLE 2
US. WestCoast Beach Statistics
15
(Johnson and Bascom )
34 WATER sEAzTATE* CHARACTERISTICS . -deep water. Significant Wave Height 1.0 2.0 ¿.0 6.6 10.2 16.2
- deep Vater Ayerage Period 2.0 3.3 ¿.3 5.3 6.3 7.6
50 ft.
Significant
Wave Height 1.0 1.? 3.7 6.0 9.4 15.0
50 ft. Average Period 2.0 3.3 4.2 4.9 5.5 6.2
* The sea-state definition is in accord with that developed by Wilbut Marks. The deep water wave data is obtained from faired.çurves of statistics from the Wilbur Marks sea-state chart.
NM FORESHORE SLOPE OFFSHORE SLOPE X1, ft. ft. ft. Greenville Bay 1:55 1:200 Copalis 1:83 1:143 600 3 Ocean City 1:77 1:160 850 1200 6 Leadbetter 1:42 _1:16O 600 1600 2 Oystervifle 1:45 1:166 800 1700 6 Solando Wreck 1:28 1:93 600 1200 ¿ Co]ubj Beach 1:72 1300 Mansanita 1:71 1:89 700 1650 5 Cape Lookout 1:50 1 :84 800 1600 5 Camp Meriweather 1:55 600 1700 5 Lookout Cove 1:52 750 1200 Coos Bay 1:63 700 10 Table Bluff 1:71 1800 6 Pismo Beach 1:57 Surf Beach 1:65 Sea Bright 1 :36
Sea Cliffe 1 :36 X1, X2, Y1 and beach slopes are Moss Landing N. 1:36 aadèfined in Figure 4. Moss Landing S. 1:50
Fort Ord Sta. À 1:20
Fort C'rd Sta. B 1:22
Fort Ord Sta. C 1:24 Point Joe 1 :47
Standard Oil Pier 1:36 Hotel Cup 1:73 Miramar 1:41. Municipal . 1:40 -. Carmel River 1:15 -¿ u, Carmel Beach 1:33
s
TABLE 3
Wave Height and Wvelength in Model Scale Required to Simulate Surf on Three Uniform Slopes Resulting from a Shoaling Swell of
7.6-Second Period
TABLE 4
Ten U.S. Wave Tanks Most Readily Adaptable to Surf Zone and Shallow Water Wave Studies in Relation to Investigations of Amphibious
Craft Motions in a Nearshore Seaway
35 H0, it. H SLOPE ft. h 1b ft. ).. 1bin' ft. 11be ft. Lome ft. HP ft. 6.7 0.02 1 1O 1.35 9.0/. 0.96 8.67 0.29 87 6 14.5 1.5 50.0 1.12 19 4.6 0.1.8 15.8 0.35 9.0 0.03 1110 1.28 11.5 1.00 11.5 0.38 115 6 1'.2 1.97 5(V 1.50 19 6.0 0.60 15,8 0.47 6.7 0.02 1230 1.20 8.0/. 1.01 8.12 0.81 2/.4 6 1.0.7 1.31 5'.O 1.12 19 12.8 0.42 15.8 0.35 9.0 0.03 1 230 1.12 10.1 1.01 10.8 1.10 330 6 55.0 1 .8 50.0 1 .5 19 17,/. 0.53 15,8 0.47 6.7 0.07 1150 0.99 6.63 1.12 7.1.2 0.56 168 6 78.0 1,10 50.0 1.12 T 8.8 0.35 5.d 0.35 9.0 0.03 1:50 0.94 8.46 1.13 9.56 0.77 231 6 38.5 1.41 50.0 1.50 19 12.2 0.1.1. 15.8 0./.7 * (16)
On slopes greater than 1:50 the surf zone extends to the shoreline (Nakamura et al).
FACILITY SIZE
(length x width x depth)
MAX. 1G. WAVE
(deep vater)
REMAllES
MSRIC MASK Facility 360' x 21.0' x 20' 24" x ¿0' (See section en proposed MASK facility)
Chicago Bridge & Iron 250' x 33' x 18' 18" x 30'
No major sdification except fnr
ex-tending the present cootcurable beach.
Bydronautics 308' x 21.' x 18' 16" x 1/.' A beach has to be installed
Univ. of Michigan 360' x 22' x 12' 12" x 15'
Iaprovesnt of irreg. wave capability.
Slight modification of existing beach.
Langley 2800' x 2/.' x 8.5' 12" x 30' A beach has to be installed
General Dynamics-Convair 300' x 12' x 6' 1/." x 12' A beach has to be installed
Stevens Tank #3 315' x 12' X 5.5 7" x 15' A beach has to be installed
Offshore Technology 120' x 1.8' x 15' 11e" x 15'
This tank is short for shallow water studies, and also recuires a beach.
CE3 635' x 15' z 20' 72" z 70'
To be destroyed In '72; bas no irreg. wave capability; carraige modification.
TABLE 5
Minimum Scale Ratio (A) Required by Test Facilities to Simulate a Specific Surf Height Condition on a Number
of Uniform Beach Slopes
* The bar () signifies a marginal case implying this surf condition could more readily be achieved at the next higher scale ratto.
36
Beach Slope 1:10 1:30 1:50 1:100
Proposed MASK Facility 4
5
T
7Chicago Bridge & Iron 5 5 6 8
Hydronautics 7 7 8 11 IJniv. of Michigan g 9 10 13 Langley 7 8 9 12 General Dynamics-Convair 8 8 10 13
Stevens Inst. Tank #3 12 13 18
Offshore Technology 7 8 10 12
CERC 4
4
.4
4U.S. Naval Academy 4
4. 4 5
Proposed MASK Facility 5 7
9
Chicago Bridge & Iron 6 6 7 9
Hydronautics 9 10 13 Univ. of Michigan 10 11 12 16 Langley
V
T 15 Genera]. Dynamics-Conva±r 10 lo IT 15Stevens Inst. Tank #3 16 23
Offshore Technology lo 10. TT 15
CEEC 4 4
4. 4
U.S. Naval Academy 4 4 5 6
Proposed MASK Facility 6 7 g ii
Chicago Bridge & Iron 7 7 8 10
Nydronautic s 10 11 12 15 Univ. of Michigan i 2 13 15 20 Langley 10 11 13 13 General bynainics-Convair 11 12 13 13 Stevens nst. ank Offshore Technology 11 12 13 13 CERO 4 4 4 4
U.S. Naval Academy 5 5 7
Proposed MASK Facility 7 8 9
Chicago Bridge & Iron 8
W
9Hydronauti cs 11 12 li
Univ. of Michigan 14 15
l'f
Lang]; e IT 13 15
General Dynamics- Convair 13 14 16
Stevens Inst. Tank #3 i 3 2 i 23
Offshore Technology 13 14 16
CERO 4 4 4
U.S. Naval Academy 5 6
t
-
TABLE6Preliminary Cost Estimate for the Variable Beach Proposed for the NSRDC MASK Facility
37
1'
ITEM NO. Q'D COST/ITEM TOTAL COST
Beach Modules 28 $ 4500 $ 126000
Outboard Positioning Jack and Post Unit
26 915 23790
Inboard Positioning Jack and Post Unit
13 1025 13325
Support Braces i0000
Concrete Base 1 36000 36000
Est. Cost for Mfg. 209115
Hydraulic System 25000
Air System 150b0
Beach. Design 25000
Subtotal 274115
Contingent Items 25000
REFERENCES
Stokes, G. G., "Onthe Theory of Oscillatory Waves,"'
Mathematical and Physical Papers., I, Cambridge University
Press (.1880)
Korteweg, D. J. and de Vries, G., "On the Ch ange of Form
of Long Wàves," Phil. Nag., No. 5, Vol. 39,p. 422 (1895). Biesel, F., "Study of Wave Propagation in Water of
Gradually Varying Depth," National Bureau of Standards
Circular 521, Nov. 1952.
Adeymo, M. D., "Effect of Beac.h Slope and Shoaling on Wave
Asymmetry," Proc. of 11th Conf. oñ Coastal Eng.. (Sep 1968).
Benjamin, T. B. and Feir, J. E., "The Disintgration öf Wave Trains.on Deep Water, Part I -- Theory," Jour. of Fi. Mech., Vol. 27, pt. 3, pp. 417-430 (1967).
Galvin, ,C. J., Jr., "Finite Amplitude, Shallow-Water Waves
of Periodically Recurring Form," Unpublished Memo of
Research Division, Coast. Eng. Res. Cent.ér (Rev Mar 19.68).
Madsen,.O., "Long
Waves Over
an Uneven BottOm," MIT Thesis (to be published in 1970).Wiegel, R.,, L. , Oceanographical Engineering, Prentice-Hall,
Inc., Englewood Cliffs,, Ñew Jersey, xi + 532 p. (1964).
Commander Amphibious Force, AtlanticFleet1 and Commander Amphibious Force, Pacific Fleet, "Joint Surf Manúal,"
Commander Amphibious Force,. Atlantic Fleet Instruction
,,"384O.lE and Commander Amphibious Force, Pacific Instruction
= 3840.3B (May 1967).
. .
10 Neumann, G. and Pierson, W. J., Jr., Principles of Physical
Oceanography, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, xii 512 p. (1966)
il. Kinsman, B., Wind Waves-Their Generation and Propagation on The Ocean Surface, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, xxiii + 676 p. (1965).
Byrne, R. J., "Field Occurrances of Induced Multiple
Gravity Waves," Jour. of Geophysical Res, Vol. 74, No. lO
(May 1969).
Keulegan, G. H., "Depths of Offshore Bars," Beach Erosion Board Technical Memorandum 8 (Jul 1945).
Johnson, J. W. and Bascom, W. N. "Beach and Surf Atlas," Univ. of California at Berkley, Dept. of Engineering, Rpt. HE - 116 - 174 (1949).
Sverdrup, H. V. and Munk, W. H., "Wind, Sea and Swell: Theory of Relations for Forecasting," U. S. Hydrographic
Office Publication 601 (1947).
Nakamura, M. Shiraishi,
J. and Sasaki,Y., "Wave Decaying
Due to Breaking," Proc. of
the10th Conf. on Coastal Eng.,
ASCE (Sep 1966).
Helle, J. R., "Surf Statistics for the Coasts of the United States," Beach Erosion Board Technical
Memorandum 108 (Nov 1958).
moue, T. , "On the Growth of the Spectrum of a Wind Generated Sea According to a Modified Miles-Phillips
Mechanism," New York University School of Engineering and
Science, Geophysical Sciences Lab. Rpt. TR 66-6 (Apr 1966)..
40
Roll, H. U., "Height, Length and Steépness of Seawaves in the North Atlantic nd Dimensions of Seawaves as Functions of Wind Force," SNAME Technical and Research Bulletin i
-19 (Dec -1958).
Horikawa, K. and chin-Tong Kuo, "A Study on Wave
rransformation Inside a Surf Zone," Proceedings of 10th
Conf.. on Coastal Eng., ASCE (Sep 1966).
Piakida, M. and Perepetch, N., "The Investigation of the Waves at the Bay on the Model of the 'ixed Bed and the
Estimation of the Scale Effect," Coastal Engineering Conf., Inst. of Civil Engineers, Paper 54 (Sep 1968). Harmen, J. M., "Cushionborne Surfboard," Air-Cushion
Vehicles, The International Hover Craft Journal, Vol. 12.,
No. 76 (Oct 1968).
23 Arthur, R.. S. et al., "The Diréct Construction of Wave
Rays," Trans. Of the Amer. Geophysical Union, Vol. 32,
DDFORM 1473- (PAGE 1)
I NOV 65 UNCLASSIFIED
-bOCUMENT CONTROL DATA.
R&D
-(Security classification of title, bodr of abstrertand indeaing ennoition musi be niered wSen the oreretl report le cIaIaIfIod) t. ORIGINA TUNG ACTIViTY (cr(e author) .
-Naval Ship Researçh and Development Center
Washthgton,. D.C. 20034 -
-Za. REPORT SECURITY CLASSIFICATION
2b.
-3. REPORT TITLE - - -
CHARACTERIZATION OF THE SHALLOW WATER WAVE ENVIRONMENT: PREDICTION TECHNIQUES AND
-. MODELING FACILITIES --
-4. DESCRIPTIVE NOTES (Type el report and IncluaSve dal..) -
-5. AUTHOR(S) (First name. niiddló miSiá!. Saat nOme)
Robert J. Johnson - - -. - - - -.
6. REPORT DATE
September 1970 - .
7C. TOTAL NO. OF PAGES
47
7b. NO. OF REFI
23
Ba. CON TRAC T OR GRANT NO.
-b. PROJECT NO.S 14.17
-- Task 14174
-- d.
-ge. ORIGINATORS REPORT NUMBERIS)
-3401
-s.
OTHER REPORT NO(S) (Any oth.t numb.,. that may be oaltod this report)
-10. DISTRIBUTION STATEMENT - - -
-This document has been approved for public release and sale; its distribution is
unlimited.
It. SUPPLEMENTARY NOTES
-12. SPONSORING MILITARY ACTIVITY
-NAVSHIPSYSCOM -
-IS. ABSTRACT - -
-This is a brief presentation of the state of the art regárding the theory and modeling techniques of shallow water wave phenomena. A
dis-cussión is incorporated pointing up a substantial need for the modifi-cation of an existing facility or the- development of a new facility
- capable of.characterizing a realistic, shallow water wave environment
- by including uneven bottom topography. Beach and surf statistics are presented to serve as guides in setting the requirements for
such-a fsuch-acility. Existing U.S. towing tanks and seakeeping basins that
-- possess a surf zone testing capability of amphibious assault craft
-- are evaluated and a beach design is proposed for the-Maneuvering and
--
-. Seakeeping Basin (MASK) at the Naval Ship Research and Development
Cénter (NSRDC).
-'54 -
-S/N 0101.807.6801 Security C1assifiction
.s,,
UNCLASS IF I ED
UNCLASSIFIED
Sccurty CIassi1icati,n
flfl FORM t473 (BACK)
i P4OVC5(PAGE 2)
.14 .
KEY WOROS . LINK A
. LINK B LINK C
-
-ROLE WT ROLE WT ROLE WT
Anphibious Assault Landing Craft
Response
..-Nonlinear Wav.é Forms
Shallow Water Wave Transformations
Beach and Surf Statistics .
Shallow Water Tèst Facility
1
UNCLASSIFIED
