NARRAGANSETT MARINE LABORATORY
University of Rhode Island
Kingston, Rhode Island

Reference No. 53-21
SEDIMENTATION PROJECT
AVERAGE MONTHLY SURFACE WAVE BOTTOM
OSCILLATIONS OFF SOUTH BEACH, MARTHA'S VINEYARD

by
STEACY D. HICKS

Technical Report No. 2
May 1954

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NARRAGANSETT MARINE LABORATORY
University of Rhode Island
Kingston, Rhode Island

Reference Noe 53-21
SEDIMENTATION PROJECT

AVERAGE MONTHLY SURFACE WAVE BOTTOM
OSCILLATIONS OFF SOUTH BEACH, MARTHA'S VINEYARD

by
STEACY D. HICKS

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TECHNICAL REPORT NO. 2

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ABSTRACT

Graphs are presented showing the maximum speeds >
~and lengths of bottom oscillations due to surface waves as
_a function of depth for each month jexcept June} off South
Beach, Martha's Vineyard, The salcwiatione are bas

the thecry of waves of small amp’ itude. “he data r
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Wavese

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INTRODUCTION

The most important water movements off exposed
coasts ere due to waves, and long shore and rip currents.
The purpose of this study was to determine the movements
due to wave motion acting along the bottom in a specific
area off an exposed coast; namely, South Beach, Martha's
Vineyard. Since waves cause oscillatory motion along the
bottom, this report is concerned with calculations of the
lengths of these oscillations and the maximum speeds which
particles attain in such an oscillation. This information
is important, not only in its effects on objects resting
on the bottom, but also in its effects on erosion, trans-~
portation and deposition of sediments.

DISCUSS ION

; Wave height and period observations from July 196
to May 1917 (Seiwell 1948) and from January to April 19h)
(Bigelow 19147) were used as representing average monthly
conditions of waves in the vicinity of South Beach, Martha's
Vineyard. Seiwell's observations were made with an under-
water pressure recorder located about one and one-quarter
‘miles south of Cuttyhunk Island in 75 feet of water; Bigelow's
-were surf observations at South Beach.

Deep water is defined as water of depth greater
than 1/2 of the wave length, shallow water as water of depth
less than 1/20 of the deep water wave length and intermediate
water as water between 1/20 and 1/2 of the deep water wave
length.

Both sets of observations were first reduced to
their equivalent values in deep water using the plates in H.0.
No. 234 and the Supplement to HeOe 234- The areas are in
such close proximity that the same deep water waves approach
both areas even though they have different values at the two
observing places due to differences in depth and topography.
Refraction was not considered, due to lack of sufficient ob-
servations and reliability (within the accuracy of the work)
for calculations in such a complex topography as that exist-
ing from No Mans Land out to deep water.

The deep water heights and periods for March and
April from the two sets were then averaged.

Using the plates from HeO. 234 (and Supplement), the
heights and lengths for each month (except June) were deter~
ree ee
Goa Sa ee

mined for depths of 20, 40, 60 and 80 feet. No refraction
was considered, due to lack of observations. However, the
waves approach from the south, generally, and the contours
are approximately straight and parallel. No significant
error should result from failure to apply corrections for
refraction in this area for average monthly conditions.

In deep water the individual particles of water
associated with progressive waves describe circles, the
diameter of their orbits being equal to the wave height
at the surface and decreasing exponentially with depth.
For intermediate and shallow water waves, these orbits are
flattened rather than being perfect circles. At any lo-
cation in intermediate and shallow water, these orbits
become more and more flattened with depth such that at
the bottom the motion has no vertical component and merely
oscillates back and forth.

The horizontal velocity component of particle
motion, u, for intermediate water is given by the expression
(Arthur 1951):

u = Ag~cosh k(z+h) cos(kx -o-t)
sinh kh os

Where A is the amplitude (Height ,H)
( 2
k, the wave number ( TF
(Length,L

)
)
° a, the frequency ( 240 )

(Period,T)
h, the depth of water

and Z, the depth of the particle.
(positive upwards)

In shallow water:

u = Agcos(kx -ct)
kh -
For the maximum horizontal particle velocity at the
bottom, these equations are:

v= HT for intermediate water and
T sinh 27d
L

i eels for shallow water.
etd
ey
oe RR tee, rr en eee

fie

Figure 1 presents the results. The maximum speed
of oscillation is given as a function of depth for each month.

The equations for the orbital diameter of particle
motion are;

D =-2A cosh k(2zth) sin(kx -ct) for inter-
Sinh kh
mediate water and

D=- 2A sin(kx -7t) for shallow.
kh

These in turn reduce to:

D= H (Intermediate) and
Sinh 2d
L

D= HL (Shallow) for the length of the hori-
end

{ : It
zontal oscillation at the bottom. Figure 2 shows these lengths
as a function of depth of water for each month.

Table I gives the data from which the graphs (Fig. 1
and 2) were drawn. It should be pointed out that the calcula~
tions express the upper limits of conditions since Seiwell's

~wave meter was located in 75 feet of water and, therefore, did

.not record waves of less than 150 ft. in length. Bigelow's
observations were of surf and were probably "significant waves"
(Munk 194). It is therefore logical to assume that these
graphs (Fige 1 and 2) present the results of the average month’ y
Significant wavese

SUMMARY

Figures 1 and 2 show the maximum speeds and lengths
of bottom oscillations due to surface waves as a function of
the depth of water for each month (except June) off South
Beach, Martha's Vineyard.

The calculations for December show large values of
speed and length due to the very high wave height average
reported by Seiwell. The average wave length for December
was the lowest for the entire year, however, which leads to
the conclusion that the condition was caused by one or more
local storms during the months The curves for December,
therefore, probably give abnormally large values.

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REFERENCES

Seiwell, He Re
1948 Results of Research on Surface Waves of the
Western North Atlantic, Vole X, Noe 4, PPOM,
MIT and Woods Hole Oceanographic Institution.

Bigelow, He Bes and We To. Edmundson
1947 Wind Waves at Sea, Breakers and Surf, Us Se
Navy Hydrographic Office Noe 602.

Hydrographic Office
19h Breakers and Surf, Principles in Forecasting,
Us. Se Navy Hydrographic Office Noe 23 and

Supplement.
Arthur, Re Se
1951 Class Notes for a Course in Ocean Waves,
Scripps Institution of Oceanography.
(Mimeographed)
Munk, We He ‘ :
1944 Proposed Uniform Procedure for Observing

Waves and Interpreting Instrument Records.
Scripps Institution of Oceanography Wave
Report Noe 26

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