ORIGIN AND DEVELOPMENT OF BEACH CUSPS AT
MONTEREY BAY, CALIFORNIA

Dan Howard Smith

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ORIGIN

AND DEVELOPMENT
MONTEREY BAY,

OF BEACH CUSPS
CALIFORNIA

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Dan Howard

Smith

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ORIGIN AND DEVELOPMENT OF BEACH CUSPS

AT

MONTEREY BAY, CALIFORNIA

by

Dan Howard Smith

Lieutenant Commander, United States Navy

B.S., State University of New York, Maritime College, 1962

Submitted in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the
NAVAL POSTGRADUATE SCHOOL
September 1973

/ M

Library

Naval Postgraduate Scnool

Monterey, California 93940

ABSTRACT

Beach cusps were observed daily on Del Monte Beach and measurements
obtained so that a quantitative description of the parameters which affect
formation and size of cusps could be determined. In addition a theory of
cusp formation was formulated and an insight obtained into the factors
which influence the shape and size of cusps throughout their lifetime.
Finally, the events leading to cusp destruction were examined.

It was determined that beach cusps are depositional in nature, form-
ing most easily in coarse, loose sediment. Cusp development commences
at a rise or area of accretion on the beach. A series of beach cusps
forms sequentially rather than simultaneously.

The width of beach cusps are a function of wave height; the larger
waves producing wider cusp spacing. Uniform spacing of cusps in a series
can be attributed to the same size waves striking the beach during the
formation period of the cusps.

Once formed, cusps are stable and tend to maintain their dimensions
unless a large change in wave or beach condition occurs.

TABLE OF CONTENTS

I . INTRODUCTION— - 7

A. DESCRIPTION OF PROBLEM 7

B. OBJECTIVES 9

C. REVIEW OF THE LITERATURE 9

II. DATA COLLECTION 23

A. COLLECTION PERIOD AND LOCATION 23

B. PARAMETERS MEASURED 26

III. DATA ANALYSIS AND PRESENTATION 31

A. CUSP WIDTH AS A FUNCTION OF MEASURED PARAMETERS 31

B. SEDIMENT ANALYSIS - - 35

C. RELATIVE PERMEABILITIES— 35

D. BEACH PROFILE 35

IV. DISCUSSION AND INTERPRETATION 38

A. CUSP FORMATION - 38

B. MEASUREMENTS DURING THE FORMATION OF A CUSP SERIES 47

C. CHANGES OCCURRING DURING THE LIFETIME OF CUSPS 55

D. DESTRUCTION OF CUSPS—- 57

V. SUMMARY AND CONCLUSIONS 58

VI. RECOMMENDATIONS 60

REFERENCES CITED 62

INITIAL DISTRIBUTION LIST 64.

FORM DD 1473 66

LIST OF TABLES

I. Tabulation of the Regression Analysis Results 34

II. Sediment Size Distribution Statistics for Sand Samples

Taken along Del Monte Beach 36

III. Tabulation of Relative Permeability Measurements of

Beach Cusp Horns and Bays along Del Monte Beach 37

LIST OF FIGURES
Figure Page

1. Ideal Beach Cusps Which Frequently Form Along

Monterey Bay Beaches 8

2. Diagram Showing The Diffraction Of The Swash

As Proposed By Ph. H. Kuenen 16

3. Typical Swash Pattern Observed In Beach Cusps 19

4. Locations Of The Observation Sites Along Del

Monte Beach On Monterey Bay 25

5. Description Of The Parameters Associated With

Beach Cusps 27

6. Characteristic Water Motion Near A Cusp Horn

On Del Monte Beach - 41

7. Movement Of Swash In Arc Within The Embayment

Of A Beach Cusp - 44

8. Destruction Of A Cusp Horn At Del Monte Beach — 48

9. Collection Of Seaweed At A Horn Apex On

Del Monte Beach - 49

10. Arc Of Swash Removing Loose Material From

The Bay And Rebuilding Of The Horn 50

11. Row Of Measurement Stakes Embedded In Del

Monte Beach 51

12. Relative Beach Plot For Days One Through

Five Of Beach Sediment Depth Measurements 52

13. Relative Beach Profile Plot For Days Six

Through Ten Of Beach Sediment Depth Measurements 53

ACKNOWLEDGMENTS

The author is genuinely indebted to Dr. Robert Bourke of the Depart-
ment of Oceanography, Naval Postgraduate School, Monterey, California, for
his assistance and inspiration. Assistance in the processing of sediment
samples is gratefully acknowledged from Dr. Robert S. Andrews. Technical
advice was freely given by Dr. Warren C. Thompson, Dr. Thomas D. Burnett,
and Lcdr. Charles K. Roberts, USN. Logistic support was provided by Mr.
Jack C. Mellor and Mr. Jerrold G. Norton.

Special acknowledgment is extended to Barbara Smith for her help in
editing and preparing this thesis.

I. INTRODUCTION

A. DESCRIPTION OF PROBLEM

Throughout the past century, many papers and articles have been written
concerning beach cusps. Although cusps can form with many modifications to
the basic shape, most observers describe them as regular, crescent-shape
forms which frequently appear on the surface of the beach. Cusps have been
noted to form in many types and sizes of sediments from fine sand to large
cobblestones [Johnson, 1909] and even large boulders [Butler, 1937]. A
series of typical beach cusps which were formed along Del Monte Beach on
Monterey Bay are shown in Fig. 1. A typical cusp consists of two raised
horns inclined towards the water. The horns are roughly triangular in
shape with the points or apices directed seaward. In general, the top of
a horn is built-up to a level higher than the surrounding undisturbed
beach. The area between the horns is eroded away such that an embayment
is formed. The back or shoreward side of both the horns and bays are con-
nected to and blend into the beach berm.

The origin of cusps has baffled observers on both lake and ocean
beaches. Many theories have been presented concerning the origin and dy-
namics of beach cusps, but none have been universally accepted as a satis-
factory solution. The mechanisms which cause cusp formation as well as the
factors which influence the size and shape of beach cusps are not well known.
Similarly the factors leading to the destruction of beach cusps have not
been agreed upon.

Figure 1. Ideal Beach Cusps Which Frequently Form Along Monterey
Bay Beaches.

B. OBJECTIVES

As described by Dolan and Ferm [1968] there is a hierarchy of cusp
sizes varying in width from 2300-4900 ft (700-1500 m ) to only a few centi-
meters (inches). The cusps observed and analyzed in this study were medium
sized cusps of from 33-213 ft (10-65 m) in width. These correspond to
Evans' [1938] "ideal" cusps. All the cusps from which data were obtained
and which are documented in this thesis were formed in ocean beach sand.

It is the purpose of this thesis to present a theory of formation of
these moderate size sand cusps. The parameters which affect the formation
and size of the cusps will be qualitatively discussed. A quantitative de-
scription of some of the major parameters which determine cusp size will
be presented. The stability of the shape of the cusps and the forces which
influence the shape and size of the cusps throughout their lifetime will
be discussed. Finally, the events leading to cusp destruction will be ex-
amined.

C. REVIEW OF THE LITERATURE

Jefferson [1899] described cusps on cobble beaches having spacings of
20-30 ft (6-9 m). He ascribed their formation to seaweed piled on the beach
modifying the actions of the great waves. His definition of a great wave
was one which overtopped the average in height and extent of advance up the
beach. According to Jefferson, at intervals of approximately ten minutes,
a great wave would break evenly upon a beach on which a line of seaweed
had been deposited. The breaking wave sent tons of seawater over the cobble-
stones above the line of seaweed. Immediately after breaking, the wave
retired leaving considerable masses of water behind the seaweed. This wa-
ter could only escape through occasional breaks in the seaweed and at these

points the considerable rush of water seaward through the break area
scoured out the bay of the cusps.

The problem with Jefferson's theory of cusp development was that
cusps frequently form on beaches where there is no line of seaweed or
other barrier to uprush of the waves. In addition, his theory did not
explain the regularity of cusp spacing which is normally observed in a
series of cusps.

Another early observer of beach cusps, Branner [1900], concluded
that cusp formation was due to the interference of two sets of inter-
fering waves interacting with each other where they converge upon the
shore. According to this line of reasoning, there is a tendency for
the waves to destructively interfere with each other along the lines
of interference and to heap up the sands at these points. At points of
non-interference, the waves diverge and throw the beach sands and all
floating material alternately left and right.

Branner's theory has been refuted by Johnson [1909] who points out
that under natural conditions one could not expect the lines of inter-
ference between two sets of waves to strike the beach at the same point
twice in succession. He, in fact, states that the presence of parallel
waves is one of the physical conditions necessary for cusp formation.
One might surmise then that a set of intersecting waves at a beach actu-
ally hinders the formation of cusps.

Johnson, in addition to refuting the theories of Branner and others,
developed a comprehensive theory of origin of beach cusps and described
many of the details of the physical parameters associated with cusps.
The factors which he considered significant in determining the spacing
between cusps were wave height and possibly beach slope. As wave height

10

increased, cusp spacing was found to increase also. Johnson suggests
that doubling the height of wayes close to the shoreline results in
a doubling of cusp spacing. He found that, in general, within a series
of cusps, the spacing or distance between individual cusps was somewhat
regular. Where both fine and coarse material were present the cusps were
built of the coarser material. According to Johnson, in order for cusps
to form properly, the wave fronts of cusp forming waves must be nearly
parallel to the beach. He also believed that cusp origin was associated
with irregularly spaced depressions in the beach. Selective erosion by
the swash developed from initial depressions in the beach, shallow troughs
of approximately uniform breadth. The ultimate size of these troughs was
proportional to the size of the waves, and determined the relatively uni-
form spacing of the cusps which developed on the intertrough elevations.
Growth of the depressions or channels reached a limit whenever the tenden-
cy toward growth imposed on the more favorable channels no longer was suf-
ficient to overcome the tendency of their neighbors to enlarge. Equilib-
rium was established when adjacent channels were of approximately the same
size and at the same time of a size appropriate to accomodate the volumes
of water traversing them.

Wave tank experiments were conducted by Escher [1937] in order to
attempt to determine the origin of beach cusps. Escher obtained cusp-
like features on a laboratory beach composed of sand. He postulated that
a standing wave situated along a wave crest which was parallel to the
beach would produce areas where greater or less erosion would occur. The
spacing of the cusps produced would vary depending upon the wave number
of the standing wave. The major shortcomings of Escher1 s theory were

11

that the features which he observed in the wave tank were not true cusps
and that there was no observational evidence on real beaches to substan-
tiate his theory.

Another early observer of cusp formations was Butler [1937]. Butler
observed and reported on cusps formed on a boulder beach at Lake 01 ga,
Quebec. These cusps, with an average spacing of approximately 18 ft
(5.5m), were thought by Butler to have been formed as a result of selec-
tive erosion of the boundary glacial till present on the beach by swash
from average sized waves striking the beach. An unusual feature of these
cusps was the size of the material in the cusps, which varied from that
of a pea to 3 ft in diameter, with the greatest volume of fragments having
diameters of 1 ft or more. Butler listed the factors relating to cusp
spacing as wave height of the average waves striking the beach and the
size of the component material which made-up the cusps. Butler's theory
was not general in that it was only applied to the cusps at Lake Olga
and additionally, did not adequately explain the regularity of cusp spac-
ing normally observed.

Evans [1938] described beach cusps composed of sand up to 600 ft
(183m) in width. He developed a classification system for various types
of cusps found along the shores of lakes and oceans. These were;

(1) Storm cusps - up to 600 ft (183m) in width

(2) Ridges of sand on lake bottoms

(3) Deposition and erosion due to obstructions on the beach

(4) Very small cusps due to "slop" of a dead sea

(5) Ideal cusps

With regard to "ideal cusps", Evans [1938, p. 621] stated;

"The conditions of adjustment between waves and the shore
under which these cusps form are very delicate, and there
is very little latitude of action in the process."

12

He believed that whenever the proper conditions were present, formation
was very rapid, almost instantaneous. It was also his contention that
once a cusp had formed, a considerable change in wave condition was re-
quired to obliterate it. Initially, Evans postulated that beach cusps
were originated by the swash breaking through a beach ridge (a long ob-
struction parallel to the shoreline). Cusps formed preferentially in
recently built beach ridges which had been broken through by the waves.
A very close adjustment existed in the relationship between height and
uniformity of waves and that of the height and shape of the ridge on
which it acted.

The regularity in spacing of these cusps (ideal) was attributed
to the fact that the initial breaks in the sand ridge were due to a
single wave which was larger than those which had built the ridge. Ac-
cording to Evans [1938, p. 622];

"Now a wave is not of the same height throughout its length, but
varies somewhat, and there is some regularity in this variation. Again
the parabolic swirl of the water when it comes into the openings made
by the wave tends to give a regular spacing to the indentations and
projections. If two small openings happen to be very close together,
they are likely to become one larger opening, while an opening that is
slightly too wide will be partly filled with material washed from the
adjoining incipient cusps. The completion of the process is dependent
on the continuance for a short time of waves of the same size and charac-
ter as the one which caused the original breaks."

In a later paper, Evans [1945] modified his early theory of forma-
tion to include a more complete explanation of the regularity of spacinq
between cusps. After the waves broke through the sand ridge, which Evans
considered necessary for cusp formation, the parabolic swash and backwash
carved out a system of bays and horns. This process continued until equili
brium was obtained with all cusps being relatively the same size.

13

Although Evans1 theory provided an explanation for the regularity
of spacing of ideal beach cusps, it did not provide an explanation for
the formation of cusps on a flat beach where no ridges were present.

A theory similar to that of Johnson [1909] was developed by Kuenen
[1948]. He noted that the horns were depositional areas where the material
being removed from the bays was deposited. This fact was a key factor in
his theory of cusp origin. In Kuenen' s theory, as in Johnson's, cusp
growth commenced at natural depressions in the beach. Refraction of the
swash as it swept into the embayments and fanned out onto the sides of
the protruding horns was an essential element in the production of cusps.
This caused sediment to be washed sideways out of the troughs onto the
horns. Larger material tended to accumulate on the horns while finer
material was carried away. As long as the depth of water sweeping through
the embayments was so small that the amount of water passing in and out of
the bay was able to carry the sediment along, enlargement both vertically
and horizontally of the bays continued. As a result, the channel became
deeper and wider with steeper sides. When the outer portion of the em-
bayment reached a certain limiting depth, erosion tapered off.

The horns were built-up due to refraction of the swash in the em-
bayments and transport of material towards the sides of the bays. Coarse
material tended to be pushed back up the beach of the embayment and out
along the developing cusps. When the maximum depth in the central area
of the bay had been attained, the growth of the bays and horns gradually
decreased.

Because of the closeness of the developing bays a rivalry frequently
developed between two cusps attempting to expand. Eventually > however,

14

equilibrium was established wherein the growth potential of all cusps
was essentially satisfied. The water flow in an embayment as described
by Kuenen is shown in Fig. 2.

Kuenen's description of the mechanism causing horn growth or accre-
tion is based on a water flow pattern which appears to be in disagree-
ment with that observed by other researchers and this author.

Longuet-Higgens and Parkin [1962] were stimulated to conduct re-
search concerning beach cusps by the idea that construction of the cusps
might be due to the occurrence of "edge waves" of the type that can occur
in the neighborhood of a sloping beach. Edge waves are widely spaced
wave crests arranged at right angles to the shoreline [von Arx, 1962].

Although their conclusion was that cusp-spacing is not simply re-
lated to the period of the waves or the wavelength of low edge waves on
a beach, Longuet-Higgens and Parkin [1962] uncovered some enlightening
facts concerning cusps. They noted that the difference between the
permeability of the material in the cusp horns and the bays resulted
in a difference in the relative power of the swash to erode material from
the bay and horn. The backwash tended to be reduced by percolation of
water into the beach. Since the horns are more permeable than the bays,
there is increased percolation in the vicinity of the horns as compared
with the bays. Thus, the backwash and consequently the eroding power of
the swash is reduced near the horns compared with that in the embayments.

They also found the presence of an impermeable layer of material
present within a few inches of the beach surface. This layer was closer
to the surface in the embayment than under the horns. Permeability
measurements showed that the horns were more permeable than the embayments,

15

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Their studies also indicated that this permeability difference was due
to the composition of the material. The horns consisted of coarse shingle,
fairly well sorted, overlying an impermeable mixture of sand and shingle.
In the bays, the surface layer of shingle was thinner. In some places
the impermeable layer actually outcropped.

Longuet-Higgens and Parkin [1962] developed relationships between
mean cusp spacing and wave period, wave height, and swash-length. Swash-
length, as they defined it, was the width of the beach between the break-
ing point of the waves and the highest point reached by the swash, averaged
over long-shore distance and over time. They found little relationship
between cusp spacing and wave period. A close connection between wave
height and an even better relationship between swash length and cusp spac-
ing was obtained.

They believed that there was one other fundamental length of impor-
tance in determining cusp spacing. Two possibilities offered were the
scale of the beach material or the length (v/g) where g is the accelera-
tion due to gravity andi) is the kinematic viscosity of the water.

The following conditions for the formation of cusps were specified

by Longuet-Higgens and Parkin [1962, p. 199];

"(1) The incident sea waves were always normal to the beach and
breakers were long-crested.

(2) The surface material was capable of being shifted freely by
the waves but within a few inches of the surface there was always a
compact and relatively impermeable layer of material."

Flemming [1964] conducted wave tank experiments in order to investi-
gate the mechanism of the transport of particles during cusp formation.
He concluded that, in general, each cusp was built on the remains of a
predecessor. An impermeable layer was established soon after the swash

17

began to play over a beach. The initial waves eroded the beach surface
and washed the fine particles down into the interstices of the under-
lying material to form an impermeable layer. Cusps then tended to form
in the coarse material on top of the impenetrable layer.

Flemming observed a water movement pattern in the embayments similar
to that shown in Fig. 3. This pattern differed from that observed by
Kuenen [1948] but agreed with that observed by Russell and Mclntire
[1965], Longuet-Higgens and Parkin [1962], and this author.

Sorting of material by swash resulted in particles with a minimum
settling velocity being found near the back of the bays. According to
Flemming, the permeability of this mixture was low. Particles with
slightly higher settling velocity accumulated on the cusps horns as a
mixture of irregular particles having a higher permeability.

Russell and Mclntire [1965] presented an enlightening article about
beach cusps which supported the ideas of several early researchers. It
was their belief that cusps were of a depositional nature, being deposits
on pre-existing beaches. According to them, juvenile cusps began to form
during a period of decreasing wave height following an erosional period
caused by high waves. Cusps tended to originate and attain maximum de-
velopment during transitions from winter to summer beach profiles. The
cusps having the sharpest apical points seemed to occur where the impact
of the waves was parallel to the shore. The more rounded apices developed
if there were some longshore drift or slight departure of the wave fronts
from a parallel alignment with the shore.

Russell and Mclntire found that the material of which cusps were
composed differed from that found on the underlying beach. The horns

18

UPRUSH

OUT WASH

Figure 3. Typical Swash Pattern Observed in Beach Cusps. Similar
Patterns in Mature Cusps Were Observed By Several Re-
searchers and This Author.

19

were recognized as being areas of deposition. The material of cusp horns
was found to be softer and coarser than that of the bays.

The authors did not specify why cusps began to form at one location
or another. They simply supposed that cusp formation had begun at some
location and described the events which lead to fully developed cusps.
The swash arriving at the cusp horn divided and the water swept into the
bays. Any material which was being carried by the upsurge which did not
come to rest was carried away. Due to the decrease in turbulence and
velocity of the water as it flowed around and sometimes over the horns,
the heavier and coarser entrained material was deposited there. After
the initial removal of loose material from the embayments, the water
flowing back down the bays possessed transportation velocity to keep its
suspended load in motion, but rarely was it capable of entraining new
load across the bay-floor pavement. This pavement was initially estab-
lished at the bottom of the bay when all loose materials had been re-
moved by overflowing waters and was resistant to any further loss of
material .

Juvenile cusps were irregular at first; two to three times larger
than final cusp spacing. The regularity increased as the cusp became
better developed. Cusp forming processes apparently succeeded in shift-
ing the original horns so that irregular members became incorporated into
larger members.

An unusual theory concerning cusp formation was suggested by Cloud
[1966]. According to his theory, a breaking wave may follow Plateau's
Rule. This rule, developed by the Belgian physicist Plateau, states that
under gravity-free conditions a liquid cylinder becomes unstable when

20

its length exceeds its circumference. The cylinder then separates into
nearly equal divisions whose lengths are proportional to the diameter of
the cylinder. A breaking wave approximates a cylindrical form according
to Cloud and breaks into segments which cause the formation of cusps. The
ratio of the cusp length to wave height was 16 or 20 to 1 , as documented
by Cloud.

Dolan and Ferm [1968] proposed the idea that crescentic coastal
landforms, such as the Carolina capes, represent only one order of shore-
line forms in an uninterrupted hierarchal grouping of coastal features.
Smaller forms were grouped within the larger forms with a logarithmic
spacing between groupings. Their hierarchy of spacing is:

(1) cusplet (4.9ft) (1.5m)

(2) typical beach cusp (26-82ft) (8-25m) such as are examined
in this study,

(3) storm cusp (230-394ft) (70-120m), and

(4) giant cusps or shoreline rhythms (2300-4920ft) (700-1500m)

Factors which Dolan and Ferm considered important in affecting cusp
spacing were planetary currents, shoaling and breaking of waves, and eddy
currents which produced the largest of the forms.

Bowen and Inman [1969] investigated the nearshore circulation of
water on a plane beach exposed to a uniform wave train. The wave train
when normally incident on the beach generated standing edge waves of the
same frequency as the incoming waves. These edge waves interacting with
the incident waves produced a steady circulation pattern consisting of on-
shore flow toward the breakers, a longshore current in the surf zone, and
an offshore flow in narrow rip currents. Bowen and Inman theorized that
the combined flow associated with the incoming waves, the edge waves, and
the nearshore circulation would rearrange beach sediment to produce a

21

regular longshore pattern of cusps. Sediment would be deposited in the
surf zone by the slow onshore current. A rip current then tends to erode
a channel for itself. The result of all this should be a system of beach
cusps, whose spacing is equal to the wavelength of the nearshore circula-
tion and dominant edge wave. At locations where the surf zone is wide
and the slope of the beach small, the spacing of cusps is much smaller
than the wavelength of the predominant edge wave. In such situations
it seems likely that cusp formation is in response to the reformed wave,
associated with the bore of the breaking wave, and edge waves traveling
within the surf zone, which have a smaller modal number than that of the
predominant flow pattern. No direct or quantitative measurements of cusp
spacing as related to edge wave wavelength were presented by Bowen and
Inman in support of this theory.

Brueggeman [1971] showed the depositional character of a single
beach cusp horn [p. 36]. Also, the presence of buried cusp horns (shown
by landward dipping layers) points to a depositional character.

22

II. DATA COLLECTION

A. COLLECTION PERIOD AND LOCATION

Data collection was accomplished during the winter months in order
that the maximum number of changes in beach profile would occur. It
is during periods of changing wave parameters such as the winter months
that the beach goes through cycles of erosion and accretion. By making
daily observations during this period it was hoped that a substantial
number of opportunities to observe formation and destruction of beach
cusps would occur.

Three data collection sites were chosen along Del Monte Beach for
several reasons. First, there is a gradient of wave heights due to re-
fraction from north to south with the largest waves at the north end.
Thus cusp formation could be observed over a wide range of wave condi-
tions. Unfortunately, no simple relationship existed between wave heights
observed at various locations along the beach due to the changing re-
fraction pattern associated with the incoming deep water wave angle and
wave period. This necessitated taking wave height observations at all
three observation sites vice just one.

A. second reason for selecting Del Monte Beach was the existence of
a gradient in sand sizes along the beach from north to south. At the
north end of the beach near Holiday Inn, the sediment is a medium sand.
At the south end of the beach, the sediment is a fine sand [Dorman, 1968].

There is essentially no longshore current present at Del Monte Beach
[Dorman, 1968]. Additionally, dye markers placed in the surf at the be-
ginning of this project confirmed this fact. The absence of a longshore
current is caused by a very small breaker angle. Due to refraction, the

23

breakers arrive with their wave fronts almost parallel to the beach
[Koehr and Rohrbough, 1964].

The upper beach as defined by Bagnold [1940, p. 30] also has a
range of slopes, varying from 10-12 degrees at the north end to 2-3
degrees at the south end. This would be expected considering the north
to south gradient in wave heights and beach sediment sizes.

Three locations along the beach were selected for obtaining cusp
data (Fig. 4). These locations were at the upper end of the beach near
the Holiday Inn, in the middle of the beach opposite the Navy Oceano-
graphic Laboratory, and at the lower end of the beach. Henceforth,
these locations will be referred to as the upper, middle or lower site.

These locations were selected due to the differences in wave height
and sand grain size at the various locations while maintaining reasonably
close proximity between sites to facilitate obtaining daily measurements.
A distinct difference in cusp spacing, cusp depth, and frequency of cusp
occurrence was observed at the three locations. A reference cusp was
chosen at each site which initially was close to a reference point es-
tablished by tri angulation on the beach.

Daily observations at all three sites were planned so that short
term changes in wave and beach parameters could be measured and recorded.
The majority of the measurements were obtained at the planned frequency
although extremely severe weather or some other unforeseen event occasion-
ally precluded obtaining readings at the prescribed time. These lapses in
the observation schedule were not considered to have seriously degraded
the results of the project.

24

UPPER
SITE

Figure 4. Locations of the Observation Sites Along Del Monte Beach
on Monterey Bay.

25

B. PARAMETERS MEASURED

The following parameters were recorded daily (Fig. 5):

(1) beach slope,

(2) width of cusp,

(3) depth of cusp,

(4) width of swash zone,

(5) movement of reference cusp,

(6) wave height,

(7) wave period,

(8) tidal information,

(9) depth of loose layer of material on beach, and

(10) remarks and descriptive comments.

The cusp width was measured from horn to horn at a position on or
close to the apices.

Cusp depth was measured approximately two-thirds of the distance
from the apex towards the rear or shoreward edge of the embayment. The
depth was measured by planting a ruled measuring pole in the center of
the embayment approximately midway between the horns, and sighting from
the top of one horn across to the top of the opposite horn. The height
above the sand where this line of sight intercepted the measuring pole
was considered to be the depth of the cusp measured relative to the top
of the horns.

The slope of the beach was measured at the center of the reference
cusp bay. Periodically, the beach slope at other locations was obtained,
Slopes were measured using a large two armed protractor (each arm approx-
imately 3 ft long) with the movable arm fitted with a bubble level. The
fixed arm was placed on the sand, the movable arm was then raised until
level as indicated by the attached bubble level. The angle between the
two arms (the beach slope) was read from a large (1 ft diameter) protrac-
tor scale located at the pi vet point of the two arms. The arms of the

26

APEX

OF -
HORN

CROSS SECTION

CLIFF FACE

UPPER BEACH

PLAN VIEW

Figure 5. Description of the Parameters Associated With Beach Cusps

27

instrument were made sufficiently long to smooth out small discontinui-
ties in the beach profile and thus provide a measure of the average beach
slope.

The swash zone as measured was the distance from the low level of
the backwash to the upper level of runup. This measurement was only re-
corded when the tide level placed the swash zone in close proximity to
the cusps being measured.

In order to measure migration of the reference cusp on the beach, a
set of orthogonal axes with the origin positioned at a reference (fixed)
location were used. Migration of the reference cusp laterally (long-
shore movement) and tranversely (onshore-offshore movement) was measured
daily utilizing this two dimensional coordinate system. Using this sys-
tem, the migration of a reference cusp was traced throughout the lifetime
of the series. Whenever a new series of cusps formed following the de-
struction of an older series, one of the new cusps located near the refer-
ence point was selected as the new reference cusp.

Wave heights recorded were the significant heights of the breakers.
The heights of 20 of the larger breakers were measured over a length of
time corresponding to about 60 wave periods, using the wave pole method
of measuring crest heights. These 20 breaker heights were averaged and
then multiplied by 4/3 in order to correct for depression of the wave
trough below the still-water level.

The wave period was the average significant period or the period of
the large well-defined waves. These periods were calculated by measuring
the total elapsed time required for four or five of these larger waves to
pass a distant point near the seaward edge of the surf zone. Time was

28

divided by one less than the number of waves observed to obtain an average
period. This measurement was repeated until several average periods were
obtained whose values were in good agreement.

The U.S. Coast and Geodetic Survey Tide Table information recorded
daily were the times and heights of high tides. The tide range from lower
low water to higher: high water was also recorded.

An indication of the penetrability of the surface layer of the beach
was obtained at each site by forcing the wave measuring pole into the
beach using approximately the same force (body weight) on the pole each
day. Penetration depth measurements were conducted on both bays and
horns.

In addition to the daily observations, periodic measurements of
several other parameters were found to be necessary. One such parameter
was sand size. Samples for textural analysis were collected at selected
times and locations.

Relative permeability measurements were also made. A plastic tube
with a diameter of 2.62 in (.067m) and a volume of one liter was inserted
into the beach at selected points. The time for one liter of seawater
to drain into the beach under the influence of gravity was measured. The
tube was inserted the same distance (approximately .015 in) into the
beach each time the measurement was conducted. Due to the differences
in tide level, water table height, amount of runup, etc., measurements
obtained on different days and at different times of day probably are not
directly comparable. Readings taken on the same day within the same time
period can be compared directly.

29

Changes in the depth of the beach sediment were measured using a
row of 11 stakes, approximately 2 ft high and 14 ft apart, aligned paral
lei to the beach. When the stakes were first positioned, the beach was
barren of loose sediment following a winter storm. The distance from
the top of each stake to the sediment layer on the beach was measured
daily as sediment returned to the beach. Eventually a series of cusps
were observed to form on the section of beach spanned by the measuring
stakes.

30

III. DATA ANALYSIS AND PRESENTATION

A. CUSP WIDTH AS A FUNCTION OF MEASURED PARAMETERS

Multiple linear regression analysis of the data was performed using
the BMD02R computer program developed for use at the UCLA Medical Center.
This program computes a series of multiple linear equations in a stepwise
manner. At each step one variable is added to the regression equation.
The variable selected is the one which makes the greatest reduction in
the error sum of squares.

The values of the data obtained each observation day were punched
on computer cards and the regression analysis performed. The parameters
of wave height, period, beach slope, reciprocal beach slope, wave height
squared and cusp depth were allowed to remain free as independent vari-
ables. Cusp width was selected as the dependent variable.

The regression analysis was performed separately upon data from each
observation site. The data from the lower beach site was determined to
be too inaccurate with respect to wave heights to produce meaningful
results. Wave heights at the lower site were on the average 1 to 2 ft
in magnitude. Small errors in visually determining these wave heights
produced a large percentage error in the data. For example, a 0.5 ft
error in wave height at the lower site constituted a 25% error. At the
upper site where the average waves were much larger (6.6 ft) a 0.5 ft
error in wave height represented only a 7.6% inaccuracy. Similarly, a
0.5 ft error' at middle beach represented a 12.5% error. For the above
reasons, the data obtained at the upper site was considered to be the
most accurate.

31

Due to the substantial percentage of error in wave height data at
the middle beach and the close correlation existing between wave height
and period, the regression analysis program showed a slight preference
for wave period over wave height (wave period measurements were less
prone to error). However, when the same analysis was performed on the
data from the upper beach where a close correlation between wave height
and period was also present, wave height was selected as the most im-
portant parameter in the regression equation. Since wave height measure-
ments at the upper site were more accurate than at the middle site, the
regression relationship developed from the upper site data was considered
more accurate.

When wave period information was surpressed at the middle site, the
results of the regression analyses for both upper and middle sites were
in fair agreement. In both of these cases, wave height was selected as
the primary variable, followed by beach slope.

The regression analysis was performed using both filtered and unfiltered
data from the upper and middle site. The filtered data were more represen-
tative of waves and beach conditions at the time of actual cusp formation.
The criteria utilized in selecting the data were;

(1) The data represented the wave and beach conditions when cusps
first appeared followinq a period when cusps were absent.

(2) There was a significant change in the wave or cusp parameters
during a period when cusps were already present.

Based on this analysis the regression equation containing the two

variables which best fit the data is:

W. = 80 + 7.4 H + 1.6S,

32

where W = cusp width in feet, H = significant breaker height at the
time of cusp formation or modification in feet and S = beach slope in
degree's.

In an attempt to find the best single parameter which would have the
highest correlation coefficient, the parameters, h2/s . H/s. H, H2, and
H /s" (m and n representing values between 0 and 4) were transgenerated
and a regression equation for each parameter then calculated (H and S
represent the same parameters as defined above) .

The results of this analyses (Table I) indicate that H alone provides
the best fit in a single variable regression equation. It also indicates
that the slope of the beach cusp is a relatively unimportant parameter in
determining variability of the data. The value of the regression coeffi-

2

cientforthe wave energy, H , was only slightly less than that of the wave
height, H.

There is most likely at least one additional parameter important in
describing the variability of cusp spacing. As pointed out by Lonquet-
Higgens and Parkin [1962], cusp spacing is proportional to the width of
the swash zone or wave height and one other parameter having the dimension
of length. It is possible that this parameter is the mean grain size of
the sediment on which the cusp is formed. Because the regression equation
presented doesn't contain the additional linear dimensional term which was
discussed, it is not considered to be a general equation which could be
expected to be valid on any beach other than Del Monte. Due to paucity
of sediment size data, this parameter was not included in the regression
analyses.

33

TABLE I
TABULATION OF THE REGRESSION ANALYSES RESULTS

Multiple

Regress.

Multiple Regress.

Parameters

Coefficient

Parameters

Coefficient

H.S
H2, 1/S

0.5659

m=2.2

0.4834

0.5251

m=2.4

0.4813

H.l/S

0.5596

m=2.6

0.4781

P.l/S

0.5157

m=2.8

0.4743

P.H.l/S

0.6401

m=3.0

0.4701

P,H,S

0.5854

m=3.2

0.4655

H,D,1/S

0.6861

m=3.4

0.4608

D,P,1/S

0.6579

m=3.6

0.4560

H.D,S,P,1/S
H^/S

0.7030

m=3.8

0.4511

0.4839

H/S

0.4176
0.5591

H0

H2

0.5242

The Following

is a Tabulation of

P

0.4785

H2/Sn Where;

n=.05
n=.10

0.5242

0.5240

The Following

is a Tabu"

lation of

n=.15

0.5237

Hm/S Where;

n=.25
ii=1.2

0.5224
0.4648

m=.2

0.0183

n=1.5

0.4309

m=.4

0.1566

n=1.8

0.3931

m=.5

0.2267

n=2.0

0.3670

m=.6

0.2841

n=2.5

0.3040

m=.8

0.3666

n=3.0

0.2492

,2
.4

.6

Where: H=Wave Height (ft), S=Beach Slope (degrees)
P=Wave Period (seconds), D=Cusp Depth (ft)

34

B. SEDIMENT ANALYSIS

Standard grain size analyses were performed on sediment samples with
a one-half phi increment between each screen in the stack. Samples were
washed in fresh water, dried, and shaken for 10 minutes on a ROTAP machine.
Fraction weights were determined using an electronic balance. Folk and
Ward [1957] size distribution statistics were determined and are tabulated
in Table II.

C. RELATIVE PERMEABILITIES

The permeability measurements were normalized to provide a more mean-
ingful analysis. An average permeability time (434.4 seconds) was calcu-
lated and divided by each individual time. Values greater or less than
unity represent cases where the relative permeability is greater or less,
respectively, than the average permeability. The values of normalized
relative permeability are shown in Table III.

D. BEACH PROFILE

The differences between the thickness of sediment observed each day
and the thickness of sediment initially covering the beach were calculated
and plotted in Fig. 12 and 13.

35

TABLE II

SEDIMENT SIZE DISTRIBUTION STATISTICS FOR SAND SAMPLES TAKEN ALONG

DEL MONTE BEACH

Sample Location
Cusp bay, upper site
Cusp horn, upper site
Cusp bay, middle site
Cusp horn, middle site
Cusp bay, lower site
Cusp horn, lower site
Cusp bay, middle site
Cusp horn, middle site
Stake No. 11, middle site
Stake No. 6, middle site
Stake No. 1, middle site

Date of Sample
4/12/73

Folk

Mean
(Ph

and VJard
Diameter
i Units"}"
1.48

Description
Medium Sand

4/12/73

1.33

Medium Sand

• 4/16/73

2.06

Fine

Sand

4/16/73

2.02

Fine

Sand

4/12/73

2.13

Fine

Sand

4/12/73

2.10

Fine

Sand

5/12/73

2.21

Fine

Sand

5/15/73

2.12

Fine

Sand

e 5/ 8/73

1.96

Medium Sand

i 5/ 8/73

2.04

Fine

Sand

i 5/ 8/73

2.10

Fine

Sand

36

TABLE

III

TABULATION OF RELATIVE PERMEABILITY MEASUREMENTS
BAYS ALONG DEL MONTE BEACH

OF BEACH

CUSP HORNS AND

Location

Sample Date

Relative Permeability

Upper beach, bay

5/ 2/73

1.81

Upper beach, horn

5/ 2/73

2.95

Beach above cusp, upper site

5/ 2/73

1.95

Lower beach, bay

5/ 2/73

0.34

Lower beach, horn

5/ 2/73

0.47

Middle beach

5/ 8/73

Stake No. 1
Stake Mo. 4
Stake No. 6
Stake No. 8
Stake No. 11

1.66
2.41
1.33
1.64
1.69

Middle beach, bay

5/15/73

.88

Middle beach, horn

5/15/73

1.03

Beach above cusp, middle site

5/15/73

.72

37

IV. DISCUSSION AND INTERPRETATION

A. CUSP FORMATION

A very critical balance of wave and beach conditions are necessary
before cusps can form. Long periods exist, especially during summer
months, when conditions are not favorable (as described below) for cusp
development and none appear on the beach. Even when conditions appear to
be ideal , cusps may not always form.

In order to determine if cusps were erosional or depositional features,
two attempts to cause cusp formation were carried out. The first try, on
31 January 1973, entailed digging a trench perpendicular to the shoreline
19 ft long and 1 ft deep to simulate a bay on a beach where cusps frequently
form. All wave and beach conditions appeared to favor cusp formation but
none were found. Again, on 2 February: 1973, an artificial ridge (or horn)
of sand 22 ft long, 2 ft wide and 20 in high was constructed perpendicular
to the shoreline on the beach. As in the first attempt, no cusps were in-
duced to form. These results reveal the difficulty of inducing cusp for-
mation. While it is probably possible to cause cusps to form, it would
require a great number of trial and error attempts and a considerable a-
mount of luck to be successful.

Based on the observations at Del Monte Beach, one important require-
ment for cusp formation is that a plentiful supply of loose and permeable
sediment be present. This observation is in agreement with the idea that
the surface material be capable of being shifted freely by the waves as
specified by Longuet-Higgens and Parkin [1962] and with the observations
of Fleming [1964], and Russell and Mclntire [1965].

38

Another very important condition for cusp formation is the angle of
the breakers as they approach the beach. Only when the wave fronts are
nearly parallel to the beach can cusps form. In addition, from observa-
tions made along Del Monte Beach, it appears that long crested swell with
a period of 14-15 seconds also enhance the development of cusps.

It appears that in the study area cusps form most often in the coarse,
loose sediments such as those deposited on the beach following a winter
storm. Although the winter season is usually an erosional period, the in-
terval between storms is sometimes long enough for the sediment which has
been carried offshore to be partially redeposited on the beach. There is
a definite lag between the time of occurrence of a winter storm and the
reappearance on the beach of the sediment which was moved offshore by the
storm waves. It is in this first layer of coarse sediment that the initial
formation of beach cusps is observed. This observation of initial cusp
development is supported by the contention of Russell and Mclntire [1965]
that cusps form following a decrease in wave height.

Another condition which seems to be important in cusp formation is the
requirement for a clean smooth beach. Heavy deposits of seaweed or debris
appear to interfere with the water motions over the beach. Similarly the
beach should have a fairly uniform slope without sharp discontinuities such
as steep sided holes or ridges.

Cusps frequently commence formation at some location on the beach
where accretion of sediment has taken place. This build-up may be due
to either upper beach topography or some process occurring in the surf
zone such as described by Bowen and Inman [1969]. Initially an embryo

39

horn is formed at the point of accretion with the rest of the cusp being
developed later. As will be subsequently shown, cusp development is a
progressive occurrence.

Under certain conditions where old or relic cusps have been left on
the beach, new series of cusps can begin to form as a seaward extension of
a previous cusp horn. The new series then propagates up or down the beach
in much the same manner as will be described below. The cusps in the new
series are spaced at intervals determined by the concurrent wave condi-
tions. When the location of a horn from the new series is close to, but
seaward of, a relic cusp horn, a connecting ridge may angle down from the
relic horn towards the new horn forming a connection between the two.

Contrary to the theories of Jefferson [1899] and Evans [1938], cusps
were not observed to commence formation on seaweed, debris or in a sand
ridge. Frequently, following a winter storm, the beach was heavily littered
with kelp torn from the sea bottom and various other types of debris. Not
until these items were almost completely buried and the beach was relatively
smooth were cusps observed to form.

Usually, cusps started to form near the high water position on the beach
near a point of accretion. This depositional area on which cusp growth
commenced was continually enhanced until the area was of sufficient height
and width to visibly perturb the swash moving around and over the elevated
area or rise. As the swash moved up the beach, the uprush of water slowed
and frequently stopped on the sides of the embryo horn. On both sides of the
rise the uprush continued further up the beach. This characteristic water
motion can be observed in Fig. 6.

40

Figure 6. Characteristic Water Motion Near
Monte Beach.

a Cusp Horn on Del

41

The energetics associated with cusp development may be explained
as follows: the kinetic energy of the uprush is dissipated by three
major processes;

(1 ) bottom friction

(2) conversion of kinetic energy into potential energy due to an
elevation increase, and

(3) percolation losses into the sand.

It is easy to understand why the uprush slows and ultimately stops
on the rise while it continues landward on both sides. The relatively
steep sides of the rise or embryo horn causes an elevation of the water
sweeping up its sides and a corresponding loss of kinetic energy by the
water. The water moving landward on either side of the rise must travel
a considerably greater distance up the beach profile before a comparable
transition of kinetic to potential energy occurs.

In addition, as observed by Longuet-Higgens and Parkin [1962] and
substantiated by the relative permeability values shown in Table III,
horns are more permeable than bays. Thus more percolation of water into
the beach occurs at the horns than in the bays. This reduces the erosion-
al capability of tie backwash in the vicinity of the horns.

Material being transported by the swash remains in motion either as
bed load or in suspension as long as the velocity is sufficient to main-
tain a turbulent regime. As either velocity or turbulence of the water
decreases, sediment is dropped, the heavier and larger material first. This
process occurs both on the horns and in the bays. However, since the horns
are more permeable and more of the uprush percolates into the beach, there
is less backwash to return sediment back towards the surf. That material
which is entrained again by the receding fluid is small in size, thus the
heavier, coarser material remains on the horn. Kuenen [1948], Longuet-

42

Higgens and Parkin [1962], and Russell and Mclntire [1965] also found the
material in the horns to be coarser than in the bays. Table II shows the
results of size analyses of the material from the cusp horns and bays.

.The formation process discussed above is regenerative in that the higher
the horn becomes, the more pronounced is the effect of the horn on the in-
coming swash. Additionally, as the tide level decreases, the horn building
process progresses seaward developing a horn of considerable length, often
extending midway down the beach face.

A small angle of incidence of the breakers or possibly just the pres-
ence of the horn itself modifies the upwash or surge. The water, instead
of moving directly shoreward, swings in an arc across the beach face (Fig. 7).
This uprush of water tends to have more erosional capability than would
be the case if no horn were present. The uprush of water divides around
the horn and the flow is deflected to the right and left. This water erodes
the loose material, depositing coarser material at the periphery of the arc
and carrying much of the finer material seaward with the backwash. Because
of the deposition at the outer edge of the swash arc, a second rise or em-
bryo horn commences formation at a location on the opposite side of the
arc from the original horn.

The process is mainly one of deposition. Loose material from the em-
bayments and from sediments which were transported from the surf zone by
the uprush is deposited either on a cusp horn or at the shoreward edge
of the swash.

The width between horns at the time of formation depends upon wave
height and at least one other parameter. As discussed previously, this
missing parameter is likely to be the mean grain size of the sediment covering

43

Figure 7. Movement of Swash in Arc Within the Embayment of a
Beach Cusp.

44

the beach. Ultimately it is the height of the great waves (those waves
which are substantially larger than the significant breaker height) which
determines the cusp spacing. Additionally, a series of large waves arriv-
ing with the proper phase sequence results in a maximum runup and the
widest arc of swash between cusps. A series of waves of this nature could
also be termed "great waves".

The time required for a cusp or a series of cusps to form can vary
greatly. A whole series of cusps may progressively form in a few hours
(less than 24) or require several days. The formation time is a function
of how closely the wave and beach conditions approach the conditions listed
above as necessary for cusp formation and/or the amount of sediment in
motion in the surf zone.

The generation process continues up or down the beach laterally as
long as no major obstacles or discontinuities are encountered either in
the beach profile or in surf zone conditions.

As a complete cusp (two horns connected by a bay) is formed and the
angle of incidence of the breakers approaches zero, the arc of water
sweeping around the bay from one side meets a similar stream of water
from the opposite side of the bay as shown in Fig. 3. The reinforced
backwash formed by the joining of these two streams of water frequently
reacts with and retards the uprush of water in this center area between
the horns. After this stage has been reached, there is a small amount of
shifting and equalization of distances between horns and depths of the bays
until the ability of the swash to further erode the bay is nil.

The uniform width observed in a series of cusps is attributed to forma-
tion of the cusp series while essentially the same size waves are striking

45

the beach. A typical series of cusps had the following spacing; 28-40-
47-46-42-46-43-40-40-44-44 paces (width of average pace, 2.5 ft). If
a gradient in sand size or wave height occurs along the beach, one can
expect a change in cusp spacing. If a cusp series propagates slowly,
over a period of several days, and the wave heights change significantly
during that period, then the cusp spacings in the series will vary. In-
creasing widths will occur with increasing wave heights.

Cusps grow serially as have been described above. They do not all
appear simultaneously. The formation of the next cusp in the series
depends upon the perturbation of the swash by a previously formed horn.
Cusps were observed to form in this manner during the study. Specifically,
during the period 20-23 February, 1973, cusps were observed propagating
south to north along the beach. Again on 25 February, 1973, a cusp
series was observed to propagate south to north at the middle site.

An experiment was conducted at the middle site in which the horn
of one of a series of well formed cusps was smoothed off into the ad-
joining embayment (Fig. 8). Partial success was achieved in observing
the reformation of the destroyed horn. The dislocated material was
washed out of the bay and redeposited at the location of the original
horn by the action of the swash. The experiment was hampered by the
weather as severe local winds occurred on the morning on which the ex-
periment was carried out.

Several of the ideas previously discussed were evident throughout
the course of the above experiment. It was obvious that the cusp horns
were areas of deposition. Heavy concentrations of seaweed collected at
the seaward ends of the horns (Fig. 9). The arc of the swash which re-
moved the material from the bay and reformed the horn is visible in Fig. 10,

46

The experiment was hampered due to the large wind waves which were
generated by a local storm. Wind waves, in general, tend to mishape
and have a destructive effect on cusps. This destructive effect is possibly
a function on the high initial steepness ratios of wind waves as compared
to those of swell .

B. MEASUREMENTS DURING THE FORMATION OF A CUSP SERIES

In another experiment conducted in early May a series of 11 stakes
were driven into the beach in a line parallel to the beach as shown in
Fig. 11. The distance from the top of each stake to the sand was measured
daily. The results of these measurements are shown in Fig. 12 and 13.

When the stakes were first driven into the beach, it was barren of
loose sediment. Winter storm waves had removed the upper layer of sedi-
ment from the beach approximately 10 days previously. The beach was
smooth with the majority of the seaweed and debris either washed away or
buried. On the second day of observation, a thick layer of sediment was
deposited uniformly over the beach. Size analyses of this sediment and
relative permeability measurements showed that this sediment was of a
relatively coarse material. It was this layer of loose sediment which
supplied the material for future cusp formation.

The differences in height between the initial (barren) beach profile
and those existing on each observation day are plotted in Fig. 12 and 13.
Curve No. 1 shows the change between the initial profile and that exist-
ing on the second day of observation; curve No. 2 shows the same parameter
for the third day of measurement, etc.

By the third day an area of accretion had begun to form in the vicin-
ity of stake No. 9. This area continued to be enhanced throughout the

47

Figure 8. Destruction of a Cusp Horn at Del Monte Beach.

48

Figure 9. Collection of Seaweed at a Horn Apex on Del Monte Beach,

49

■:r:;;':;v::::;:;.o::;;.;:->:v; V-:

Figure 10. Arc of Swash Removing Loose Material from the Bay and
Rebuilding of the Horn.

50

Figure 11. Row of Measurement Stakes Embedded in Del Monte Beach,

51

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53

experiment, becoming initially a rise, then an embryo horn and finally,
a fully developed cusp horn. The area of accretion was the starting
point for a series of cusps which initially propagated north away from
the measuring stakes. Later, probably due to a change in the breaker
angle, the series propagated south in the measurement zone. The cusp
heights indicated in Fig. 12 and 13 represent heights at the location of
the measuring stakes and are not the maximum heights attained as the
stakes were located towards the rear of the cusps.

An embayment began to form on the third day with the center near
stake No. 7. Erosion of this bay and accretion at the horn near stake
No. 9 continued as indicated by curve No. 3. Little change occurred in
the vicinity of stake No. 1-5.

On day five (curve No. 4), the start of development of a horn was
visible near stake No. 3. Additionally, a layer of finer beach material
was deposited over the beach between days five and six as indicated by
the uniform increase in profile height of approximately 0.2 ft.

By day eight (curve No. 7), a definite horn had developed near stake
No. 3 with an embayment being generated south of stake No. 1. Between
days eight and nine, another layer of finer material arrived on the beach,
enhancing and smoothing the cusp profiles. This process of finer material
changing the outlines of the initially formed cusps had been noted in
many previous instances. The tendency is for the finer sediment to smooth
or obscure the sharp profiles of the initial cusps. This process can be
referred to as "defocusing" of the cusps.

During days No. 10 and 11, a combination of continued sediment de-
position and slight reorganization of the series occurred. By day No. 11

54

(curve No. 10) the series had reached equilibrium and showed somewhat
smooth or defocussed profile of mature beach cusps.

It should be noted that the height of accretion of the horns above
the initial level of coarse sediment (difference between curve No. 10
and curve No. 1) is greater than the depth of erosion of the bay below
this initial layer. This supports the contention that cusp formation is
primarily a depositional vice on erosional process.

C. CHANGES OCCURRING DURING THE LIFETIME OF CUSPS

The spacing of cusps is determined initially by the wave heights
at the time of formation. A significant change in wave heights is re-
quired to alter the spacing of the cusps after formation. For example,
at the lower site, the spacing of the cusps changed from 54 ft to 112 ft
following a change in significant breaker height from 1.5 ft to 2.5 ft.

The cusp shape may be altered slightly from a sharp, well defined .
crescentic shape due to defocussing. Defocussing is caused by the de-
position of fine sediments over the beach following initial cusp devel-
opment. In addition, the porosity of the horns and bays decreases
greatly when the finer material collects over the beach.

As frequently happens, wave heights may decrease to very low values
following cusp formation and before the forerunners from the next winter
storm approach. During this time, the spacing of cusp series tends to
decrease.

The maximum depths of the cusps do not vary much once they have
reached maturity. Once the erosion of the bays progresses to pavement
level (that level of beach below the loose permeable sediment) no further

55

erosion occurs [Russell and Mclntire, 1965]. Any depth changes which
occur are a result of deposition or erosion of the horns or a uniform
deposition of fine material over the entire beach. The latter occurrence
frequently takes place soon after the formation of the cusp series.

A change from the nearly perpendicular angle between wave crests and
beach or the presence of severe local winds may cause truncation or a-
symmetry of the horns. The axes of the horns are then no longer per-
pendicular to the shoreline, but are skewed at some angle. Wind waves
may also cause scarping of both horns and bays.

Occassional ly, one may see a new series of cusps form seaward of
an existing series. This is especially prevelant when existing cusps
have been cut back to near the top of the upper beach berm by storm
waves and high tides. These storm waves and high tides widen existing
cusps and reposition them landward on the beach profile.

Waves which are \/ery much smaller than those which initially cause
cusp formation may cause juvenile horns to begin to form. These new
horns are usually centered midway between the older horns. A new series
then forms whose spacing is nearly one-half of that of the original series,
As an example, during the period of 4-6 April, 1973, the significant
breaker height decreased by a factor of four and cusp spacing decreased
from 134 ft to 54 ft.

Once cusps establish their positions on the beach, they tend to re-
main very stable, the horn positions shifting only a few feet over their
lifetime.

56

D. DESTRUCTION OF CUSPS

In general, wind waves tend to truncate and destroy cusps. Cusps
are also obliterated by very large breakers washing over the cusp site.
If not completely destroyed, cusps may be driven to the back of the
beach into the storm berm where they become large, mishapen storm cusps.

\lery high tides and/or storm surges can remove nearly all sediment
from the beach. Erosion continues until all loose sediment is removed
and there is no material left to form cusps. Only after wave heights
decrease and sediment is returned to the beach can cusp formation commence
again.

57

V. SUMMARY AND CONCLUSIONS

The spacing between horns of a beach cusp is a function of the height
of the great waves breaking at the time the cusp is formed. Wave height
was determined to be the single most important parameter in describing
the variability of beach cusp spacing.

The formation of beach cusps is a complex process. The conditions for
formation are critical and a delicate balance of wave height, breaker angle,
beach slope and sediment size must exist before cusp formation occurs.
Initially, a supply of loose permeable material overlying an impermeable
layer is required. The waves must approach the beach with a nearly zero
breaker angle. Additionally, long-crested waves with a period of 14-15
seconds enhance the development process. The beach must be smooth and
relatively clear of debris. The slope of the beach should be continuous
with no sharp discontinuities.

Cusp formation is essentially a depositional process. It starts with
the deposition of sediment which has been entrained in the swash, at a
rise or area of accretion on the beach. As this area is built-up, it
perturbs the swash causing the erosion of an embayment and the formation
of a new rise or horn. Erosion of the embayment continues until the smooth
impermeable pavement is reached. Thus, all the cusps of a series are not
formed simultaneously, but develop sequentially.

The formation process results in the horns being composed of coarser,
more permeable material than the embayment or surrounding beach. The
increased permeability of the horn in turn aids the formation process by
causing greater percolation losses of kinetic energy from the swash over
the area of the horns than in the bays.

58

The uniformity in the width of a series of cusps is essentially a
result of the fact that the same size waves were present at the time of
formation of all the cusps. If a gradient in wave height or mean sedi-
ment size occurs along the beach, then a gradient in cusp spacing can be
expected with the larger cusps associated with the area of greater wave
height.

A change from the nearly perpendicular angle between wave crests
and the beach or the presence of severe local winds may cause truncation
or asymmetry of the horns. Wind waves may also cause scarping of both
horns and bays.

In order to change the spacing of a cusp series once it has formed, a
large change in wave height is required. Wave heights must change by
approximately a factor of two before a change in cusp spacing occurs.

Cusps tend to maintain the same position as at the time of initial
development migrating only a few feet during their lifetime.

Cusps are destroyed by prolonged exposure to large wind waves or
very large breakers which wash over the cusp site removing the accumu-
lated sediment. Very high tides and/or storm surges are also effective
in removing sediment from the beach. If erosion continues until all
loose sediment is removed, cusps cannot reform until conditions are
altered to permit deposition of sediment.

59

VI. RECOMMENDATIONS

Additional study of the origin and development of beach cusps is
necessary in order to develop universal relationships among cusp, beach
and wave parameters. Further observation of the cusp forming process
is needed in order to quantify the conditions necessary for cusp forma-
tion-. Additional refinements of the theory of cusp formation should
be developed.

At least two observation sites should be selected. The sites should
be as dissimilar with regard to breaker characteristics, wave height,
beach slope and sediment size as possible, and still permit frequent
cusp formation such that sufficient opportunities to observe the forma-
tion process will occur. In this regard, observations should be made
during the winter months.

Capacitance, resistance or a similar type of wave gage should be
used in order to obtain accurate wave height readings. A rapid method
of analyzing the wave records obtained such as the cummulative frequency
distribution method would decrease the time to process each wave record.

Only when cusps are in the process of forming or when some signifi-
cant change in wave or beach conditions occurs is it necessary for measure-
ments to be taken. When observations are made, in addition to the daily
measurements, relative permeability measurements and sand samples from
the bays and horns should be obtained. The sediment analyses should be
performed in one-quarter phi size steps instead of one-half phi size incre-
ments. This will add significance to the mean sediment size data.

60

At both observation sites, a grid of measurement stakes should be
constructed. These stakes should be made of metal strong enough to with-
stand the wave energy of winter storms. Each stake should be labelled
with a tag indicating its purpose to minimize vandalism. The stakes should
be arranged in at least three parallel rows each at a different distance
from the water. The length of the rows should be at least two cusp widths
in extent. Sediment depth data should be obtained from this grid whenever
cusps are forming within its boundaries. If possible, the swash zone
parameter as defined by Longuet-Higgens and Parkin [1962] should be ob-
tained daily when other cusp observations are being taken.

Using the above measurements, a more refined regression analysis can
be performed with mean sand diameter and Longuet-Higgens' swash zone
parameter as two of the variables considered.

61

REFERENCES CITED

Bagnold, R.A. 1940. Beach formation by waves; some model experiments in
a wave tank. Journal of the Institution of Civil Engineers, 1:27-52

Bowen, A.J., and D.L. Inman. 1969. Rip current. Journal of Geophysical
Research, 74[23): 5479-5490

Branner, J.C. 1900. The origin of beach cusps. Journal of Geology, 8(6):
481-484

Brueggeman, J.L. 1971. Beach Cusps of Monterey Bay, California. M.S.
Thesis, U.S. Naval Postgraduate School, Monterey, California

Butler, J.W. 1937. Boulder beach cusps, Lake Olga, Quebec. American
Journal of Science, 233:442-453

Cloud, P.E. 1966. Beach cusps: response to Plateau's rule. Science,
154:890-891

Dolan, R. , and J.C. Ferm. 1968. Crescentic landforms along the Atlantic
coast of the United States. Science, 159:627-629

Dorman, C.E. 1968. The Southern Monterey Bay Littoral cell: A preliminary
sediment budget study, M.S. Thesis, U.S. Naval Postgraduate School,
Monterey, California

Escher, B.G. 1937. Experiments on the formation of beach cusps. Leidse
Geologische Medeleelingen, 9:79-104

Evans, O.F. 1938. The classification and origin of beach cusps. Journal
of Geology, 46(4) :615-627

Evans, O.F. 1945. Further observations on the origin of beach cusps.
Journal of Geology, 53:403-404

Flemming, N.C. 1964. Tank experiments on the sorting of beach material
during cusp formation. Journal of Sedimentary Petrology, 34(1): 112-
122

Folk, R.A. and W.C. Ward. 1957. Brazos River bar, a study in the signifi-
cance of grain size parameters. Journal of Sedimentary Petrology 27:
3-27

Jefferson, S.W. 1899. Beach cusps. Journal of Geology, 7:237-246

Johnson, D.W. 1909. Beach cusps. Geological Society of America Bulletin,
21:599-624

62

Koehr, J.E., and J. D. Rohrbough. 1964. Daily and quasi-weekly beach
profile changes at. Monterey, California. M.S. Thesis, U.S. Naval
Postgraduate School, Monterey, California

Kuenen, Ph. H. 1948. The formation of beach cusps. Journal of Geology,
56:34-40

Longuet-Higgens, M.S., and D.W. Parkin. 1962. Sea waves and beach cusps
Geog. Journal , 128:194-201

Russell, R.J., and W. G. Mclntire. 1965. Beach cusps. Geological
Society of America Bulletin, 76:307-320

von Arx, W.S. 1962. An Introduction to Physical Oceanography, Addison-
Wesley Publishing Co., Reading, Massachusetts. 422p.

63

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Naval Postgraduate School

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3. Professor R. Bourke, Code 58 Bf
(Thesis Advisor)

Department of Oceanography
Naval Postgraduate School
Monterey, California 93940

4. Professor R.S. Andrews, Code 58 Ad
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

5. Professor W. C. Thompson, Code 58 Th
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

6. Professor H. A. Titus, Code 52 Ts
Department of Electrical Engineering
Naval Postgraduate School
Monterey, California 93940

7. Dr. R. E. Stevenson
Scientific Liaison Office

Scripps Institution of Oceanography
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65

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENTATION PAGI

READ INSTRUCTIONS
BEFORE COMPLETING FORM

I. REPORT NUMBER

2. GOVT ACCESSION NO

3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Sublllle)

ORIGIN AND DEVELOPMENT OF BEACH CUSPS AT
MONTEREY BAY, CALIFORNIA

5. TYPE OF REPORT 4 PERIOD COVERED

Masters Thesis
(September. 1973)

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORfs;

Dan Howard Smith

8. CONTRACT OR GRANT NUMBERfs.)

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS

11. CONTROLLING OFFICE NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

12. REPORT DATE

September 1973

13. NUMBER OF PAGES

EL

14. MONITORING AGENCY NAME ft ADDRESSfy/ dltterenl trom Controlilni Otllce)

Naval Postgraduate School
Monterey, California 93940

15. SECURITY CLASS, (ot this report)

unclassified

15«. DECLASSIFICATION/ DOWN GRADING
SCHEDULE

16. DISTRIBUTION STATEMENT (ol this Report)

Approved for public release; distribution unlimited

17. DISTRIBUTION STATEMENT (ol the abstract entered In Block 20, it dltterenl trom Report)

IB. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide II necessary and Identity by block number)

Cusp formation, Beach features, Breaking waves,
Beach sediment distribution,

20. ABSTRACT (Continue on reverse side It necessary and Identity by block number)

Beach cusps were observed daily on Del Monte Beach and measurements
obtained so that a quantitative description of the parameters which
affect formation and size of cusps could be determined. In addition
a theory of cusp formation was formulated and an insight obtained into
the factors which influence the shape and size of cusps throughout their
lifetime. Finally, the events leading to cusp destruction were examined,

DD 1 JAN*™ 1473 EDITION OF 1 NOV 65 IS OBSOLETE

(Page 1) S/N 0103-014-6601 I

SECURITY CLASSIFICATION OF THIS PAGE (When Data Bnlered)

66

i'bt-IJRlTY CLASSIFICATION OF THIS PAGECVhon DetB Entered)

20.

It was determined that beach cusps are depositional in nature,
forming most easily in coarse, loose sediment. Cusp development
commences at a rise or area of accretion on the beach. A series
of beach cusps forms sequentially rather than simultaneously.

The width of beach cusps are a function of wave height; the larger
the waves producing wider cusp spacing. Uniform spacing of cusps in
a series can be attributed to the same size waves striking the beach
during the formation period of the cusps.

Once formed, cusps are stable and tend to maintain their dimen-
sions unless a large change in wave or beach condition occurs.

DD

Form 1473
. 1 Jan 73
S/N 0102-014-6G01

(BACK)

SECURITY CLASSIFICATION OF THIS PAGEfl«i»n 0»(» Enffd)

67

Jr

R 7/1
14 NOV 78

r 2 2 5 6 2
S1033 U

Thesis -.S^.j-.-J.

S5758 Smith

c.l Origin and development

of beach cusps at Mon-
terey Bay, California.

I 4 W A R 7 * v 2 2 b

14 NOV 78 S10 33U

Thesis i*» 37 VI

S5758 Smith

C.l Origin anH Hpvelonment
of beach cusps at Mon-
terey Bay, California.

thesS5758

Origin and development of beach cusps at

inn1 1 1 hi i

3 2768 002 00896 3

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