• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 List of Figures
 Abstract
 1. Introduction
 2. Literature review
 3. Data collection
 4. Dry beach evolution
 5. Beach cusps
 6. Summary and conclusions
 Reference














Group Title: UFLCOEL-95014
Title: Beach cusp analysis and the dry beach evolution of Longboat Key, Florida, using video monitoring techniques
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Permanent Link: http://ufdc.ufl.edu/UF00085022/00001
 Material Information
Title: Beach cusp analysis and the dry beach evolution of Longboat Key, Florida, using video monitoring techniques
Series Title: UFLCOEL-95014
Physical Description: v, 104 p. : ill., map ; 28 cm.
Language: English
Creator: Sloop, Robert V
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1995
 Subjects
Subject: Beach nourishment -- Florida -- Longboat Key   ( lcsh )
Beach erosion -- Florida -- Longboat Key   ( lcsh )
Coast changes -- Florida -- Longboat Key   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.E.)--University of Florida, 1995.
Bibliography: Includes bibliographical references (p. 100-104).
Statement of Responsibility: by Robert V. Sloop.
 Record Information
Bibliographic ID: UF00085022
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 34549212

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Table of Contents
        Page ii
    List of Figures
        Page iii
    Abstract
        Page iv
        Page v
    1. Introduction
        Page 1
        Page 2
        Page 3
    2. Literature review
        Page 4
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    3. Data collection
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    4. Dry beach evolution
        Page 47
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    5. Beach cusps
        Page 52
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    6. Summary and conclusions
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    Reference
        Page 100
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        Page 103
        Page 104
Full Text



UFL/COEL-95/014


BEACH CUSP ANALYSIS AND THE DRY BEACH
EVOLUTION OF LONGBOAT KEY, FLORIDA USING
VIDEO MONITORING TECHNIQUES






by



Robert V. Sloop




Thesis


1995















BEACH CUSP ANALYSIS AND THE DRY BEACH EVOLUTION OF LONGBOAT
KEY, FLORIDA USING VIDEO MONITORING TECHNIQUES.











By

ROBERT V. SLOOP


A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF
FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF
MASTER OF ENGINEERING


UNIVERSITY OF FLORIDA


1995
















TABLE OF CONTENTS

TABLE OF CONTENTS ....................................................................................................................... ii

LIST O F FIG URES............................................................................................................................... iii

CHAPTER 1....................................................................................................................................... 1
INTRODUCTION ............................................................................ ................................................ 1
1. 1 Objectives................................ .......... .. ... .... ....... ............................................ 2

CHAPTER 2 ....................................................................................................................................... 4
LITERATURE REVIEW .............................................. ........ ...................................................4
2.1 Photographic Monitoring Techniques and Measurements........................................... 4
2.2 Beach Cusps............................................................................................................................. 9

CH APTER 3.....................................................................................................................................34
DATA COLLECTION ....................................... .................................................. ...................... 34
3.1 The Video M monitoring System ......................................................................... ....................34
3.2 Deployment/Data Description............................................................................. .....................36
3.3 Related Deployments............................................................................................ ................... 41
3.4 Project Background and In Situ M onitoring.......................... ............................42

CH APTER 4 ..................................................................................................................................... 47
DRY BEACH EVOLUTION ............................... .................................................................47
4. 1 M monthly Summary............................................................................................. ....................... 47
4.2 M monthly Summary With Storm Events........................................................................................... 49
4.3 Rectified vs. Oblique Image Analysis................................ ..................................................50
CHAPTER 5..................................................................................................................................... 52
BEACH CUSPS .................... ................................................................................................................52
5.1 Background....................................................................................... ...........................................53
5.2 Cusp Formation Description.......................................................................... .....................56
5.3 Cusp Formation Analysis................................................................................ ....................... 73
5.3.1 LBK General Parameters.............................................................. .................................................. 73
5.3.1 Edge W aves ............................................................................................................. ...................... 78
5.3.2 Swash M mechanics .................................................................................................... ....................... 84
5.3.3 Additional M echanisms......................................................................................... ......................... 88
5.3 Toward a Formation Theory .............................................. .................................................90

CHAPTER 6 ..................................................................................................................................... 93
SUM M ARY AND CONCLUSIONS ........................................................................ ...........................93
6. 1 Summary................................................................ ................................ ........................... 93
6.2 Conclusions......................... ..................................................................................... .............94
5.3 Future Work ....................... ..........................................................................................................98

REFERENCES.................................................................................................................................... 100















LIST OF FIGURES
FIGURE 1.1 CUSP NOMENCLATURE AND TYPICAL SWASH PATTERNS. 3
FIGURE 3.1 NOURISHMENT PROJECT AND VMS LOCATION 37
FIGURE 3.2 TYPICAL LBK SCENE 1 IMAGE. 39
FIGURE 3.3 RECTIFICATION OF TYPICAL LBK SCENE 1 IMAGE. 40
FIGURE 3.5 BEFORE, DURING, AND AFTER THE CONSTRUCTION 44
FIGURE 3.6 SIGNIFICANT WAVE HEIGHTS FOR NOVEMBER, 1993 45
FIGURE 3.7 WAVE PERIODS FOR NOVEMBER, 1993 46
FIGURE 4.1 SCENE 1 DRY BEACH WIDTH MONTHLY SUMMARY 49
FIGURE 5.1 ORIGINAL AND RECTIFIED CUSP IMAGES 52
FIGURE 5.2 BEFORE, DURING, AND AFTER THE OCTOBER STORM 54
FIGURE 5.3 LBK BEACH PROFILE, NOVEMBER 2, 1993 55
FIGURE 5.4 NOVEMBER 1, 1993 56
FIGURE 5.5 NOVEMBER 5, 1993 20+ CUSPS 58
FIGURE 5.6 NOVEMBER 7, 1993 STORM AND RAIN 59
FIGURE 5.7 NOVEMBER 13, 1993 WELL DEVELOPED CUSPS 60
FIGURE 5.8 NOVEMBER 14, 1993 OBLIQUE WAVES AND MULTIPLE CUSP SETS 62
FIGURE 5.9 NOVEMBER 15, 1993 ACTIVE CUSP FORMATION 63
FIGURE 5.10 C, D TYPICAL CIRCULATION 64
FIGURE 5.11 NOVEMBER 21, 1993 BI-LEVEL CUSP SYSTEM 66
FIGURE 5.12 NOVEMBER 28, 1993 CUSP DESTRUCTION DUE TO HIGH TIDE AND OBLIQUE
WAVES 67
FIGURE 5.13 NOVEMBER 29, 1993 ATTEMPTED CUSP REORGANIZATION 68
FIGURE 5.14 NOVEMBER 30, 1993 THE END OF A CUSPATED ERA. 68
FIGURE 5.15 WAVE HEIGHT AND CUSP DESCRIPTION 69
FIGURE 5.16 WAVE PERIOD AND CUSP DESCRIPTION 70
FIGURE 5.17 CUSP SPACING VS. SIGNIFICANT WAVE HEIGHT 72
FIGURE 5.18 CUSP SPACING VS. PERIOD 72
FIGURE 5.19 NOV. 17 19 OBSERVED VS. PREDICTED CUSP SPACING 83
FIGURE 5.20 TYPICAL BACKRUSH PATTERN IN EACH BAY 84
FIGURE 5.21 OBSERVED CUSP SPACING VS. SWASH MECHANICS THEORY 87













Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering



BEACH CUSP ANALYSIS AND THE DRY BEACH EVOLUTION OF LONGBOAT
KEY, FLORIDA USING VIDEO MONITORING TECHNIQUES.

By

Robert V. Sloop

August 1995

Chairman: Robert G. Dean
Major Department: Coastal and Oceanographic Engineering




The video monitoring of the beach nourishment project at Longboat Key Florida

provides a unique opportunity to utilize video images to perform coastal engineering

analysis ofnearshore and beach phenomena. Using rectified images and a standardized

selection procedure, the evolution of the dry beach width of the project over its first

fourteen months is presented along with a monthly summary including the effects of

storms. It is determined that the storms cause short-term acceleration of the long-term

beach profile equilibration, and that the project demonstrates evidence of equilibration one

year after its completion. Beach cusp formation and spacing prediction theories are

investigated using data obtained from the video imaging and in-situ wave instrumentation.

It is found that edge wave theories do not accurately predict cusp spacing, but are








accurate in prediction of maximum wave heights for cusp formation. Spacing is found to

have a linear relationship with swash length. Based on observations and analysis from the

video images, is hypothesized that cusp formation and equilibrium spacing are the result

of a complex interaction of energies, beginning with edge waves "seeding" a longshore

variation in swash. The system then develops characteristic nearshore circulation cells and

the cusps proceed to outgrow their edge wave sources. Their equilibrium spacing is

dictated by the swash length, which represents the summation of local energy sources.













CHAPTER 1


INTRODUCTION



Coastal engineers have used various techniques to study nearshore phenomena

throughout history. Surveys, acoustic profiles, aerial photography, satellite imaging,

visual estimation, in situ gauges, and video monitoring have been used to describe the

complex interactions that shape the shoreline into its various forms. Of these, video

monitoring has recently become popular due to the ease of deployment, low cost,

availability, and extensive coverage capabilities.

Perhaps the most obvious and celebrated feature of any beach is its width. From

tourists to developers to naturalists to nesting sea turtles, the amount of beach at any

given time is an item of considerable interest. In fact, the reasons behind changes in beach

width are often the inspiration for debate, speculation and copious amounts of general

holding forth. According to Anders and Byrnes (1991), "quantitative knowledge of

shoreline position change is essential for most planning and design aspects of projects in

the coastal zone." (p. 17)

Similarly, even casual observers of beach cusps have been fascinated by their

regular spacing, temporary nature, and propensity for creating arguments in the scientific

realm. As described by Werner and Fink (1993), "Beach Cusps ..have attracted








investigation owing to their beauty, their effect on sediment transport, and their uniformity

in the presence of complex interactions between waves, currents, and sediment."(p. 968)

Each of these topics, video monitoring, beach width evolution, and cusp

formation, are individually interesting and technical research items, therefore, the

combination of the three should prove to be three times as entertaining. Thus is the

inspiration for the following work.


1.1 Objectives


The primary objective of this paper is to investigate the use of video monitoring

techniques to: 1) evaluate the changes in dry beach width and 2) investigate the formation

of beach cusps during the first fourteen months of a beach nourishment project on

Longboat Key, Florida. The literature review provides background information on the

historical thoughts, perspectives, and work in the field of photographic monitoring and

beach cusp analysis, and includes a categorical summary tracing the development of ideas

concerning beach cusp phenomena. A description of the video monitoring system (VMS)

will be given, including hardware specifics, capabilities, lessons learned, and suggestions

for future work. A method of charting the evolution of a nourishment project through the

dry beach width will be introduced. Beach cusp formation and destruction will be

characterized and compared to popular theories and descriptions using the results from the

video monitoring and offshore wave data. The techniques developed to gain additional

insight on beach activity from the results of the video monitoring will be detailed, along

with suggestions for future work.









In describing beach cusps, a clear and consistent nomenclature is required. For the

purposes of this paper, an adaptation of Bodie's (1974) description is appropriate: "cusps

appear as [regularly spaced,] crescent-shaped, nearly semi-circular cutouts in the beach

face tapering to a point seaward and aligned nearly perpendicular to the surf line". (Bodie,

1974). These points tapering toward the sea are termed horns, with the "semi-circular

cutouts" (Bodie, 1974) separating them as bays. The distance between successive horns

is the cusp spacing or cusp width. The distance from the shoreward base of the horns to

the seaward points is the cusp length. Water that flows from the sea toward the shore will

be referred to as uprush, and the return flow as backrush. A typical circulation pattern

will be described as having an uprush over the horns and a backrush from the bays. Figure

1 illustrates these common cusp

features.


Figure 1.1 Cusp Nomenclature and Typical Swash Patterns.


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~~-TI.I *~u
.j hd- '


L~ * ;
~ ..A1













CHAPTER 2


LITERATURE REVIEW


2.1 Photographic Monitoring Techniques and Measurements


The use of various photographic techniques to map the world's coastlines and

asses their morphological processes has been in vogue since the 1920's. Anders and

Byrnes 1991). The use of video photography, however, has been restricted to the past

several decades, and can be attributed to the mass availability of video cameras, the

economics of video tapes as an image storage medium, and the popularity of personal

computers and digitization software. The techniques developed to glean quantitative

information from still photography are applicable to video images upon digitization.

Almost without exception, the authors of the current literature note that the photographic

systems are simple to use, inexpensive, convenient, and provide increased levels of

coverage in time and area.

Maresca and Seibel (1976) state that "oblique images, taken with a 35-mm single

reflex lens camera from an elevated point such as a bluff are particularly suitable for the

measurement of breaking waves, water level, beach run-up, and current in the surf zone

under storm conditions" (p.681) Using a camera on a 8 m bluff, they found the effective

range to be 250 m with an accuracy in the vertical plane to 10% and to 1% in the








horizontal plane. Techniques are presented to scale distances in the oblique images,

estimate wave heights and longshore currents, and to quantify errors in the measurements.

Using video recording techniques, aerial surveys of over 30,000 miles of Canadian

coastline were carried out by Owens (1983) to "supplement, rather than to replace,

traditional information sources such as maps, charts, vertical air photographs, and ground

truth studies." (p. 29) The system consisted of a video recorder, an audio recorder and

monitors for playback deployed onboard both helicopters and fixed-wing aircraft. Owens

notes the advantages of the video system over other systems include real-time quality

control, cost, availability of replay equipment, transportability, and system simplicity. He

acknowledges, however, that the images are of lower quality than those achieved with

other media, such as 8-mm or 16-mm movie film.

Many technical advances in the development of video techniques in the coastal

zone have come from the researchers at Oregon State University, beginning with the work

performed by Holman and Guza (1984) in measuring swash run-up. The camera was

placed so that images were taken along the shoreline, allowing for run-up to be measured

in multiple locations on the same picture. The images were then digitized by hand in a

process described by the authors as being tedious and subjective. A comparison was made

between the results from the digitization of video recordings and those of a resistance-wire

sensor. Conclusions were made concerning the advantages and disadvantages of each

system and the intercomparison between the system, as the actual swash run-up was not

known. The advantages of the video system were the "low cost, ease of logistics,

potential for digitizing a number of longshore locations with one film, and ability to "see"

the phenomenon." (p. 138-139)








The all-weather capability of the photographic monitoring system was a primary

reason for the development and testing of methods to determine sand bar morphology by

Holman and Lippman (1987) in the DUCK85 experiment. The camera diligently recorded

nearshore dynamics data in all conditions during the daylight hours, including "storm

situations when scientific interest is at a peak." (p. 929) Their technique involved taking

photographic time exposures (approximately 10 minutes duration) of waves breaking on

the sand bar from a camera mounted on a 14 m scaffold. The lightest intensities were

found to be the regions of maximum wave energy dissipation. Calibration of the

photogrammetry techniques used to convert the distances from the oblique images to land

distances was performed on the Oregon State University football field due to its known

dimensions. Accuracies were found to be within 2% of the distance to the camera. This is

consistent with the observations of Maresca and Seibel (1976) that distance measurement

errors increase as the distance from the camera increases. The authors found that "the

offshore distance to the bar was typically quite accurate at lower tide stages, but showed a

systematic tide dependence with errors up to 15% at high tides." (p. 943) They note that

the Army Corps of Engineers Field Research Facility (FRF) in Duck, N.C., initiated a long

term video monitoring system atop their 43 m tower to quantify long-term beach

morphology.

Wave run-up measurements from video were also made by Aagard and Holm

(1989) using techniques similar to those employed by Holman and Guza (1984), with an

updated method for digitizing the pictures. In the authors' words:

"This computer-assisted technique samples a given line in the video image at
specified time intervals. After the film has been replayed, the picture lines are








displayed below each other on the monitor. Thus a time series of the run-up is
presented." (p. 548)


This procedure takes nearly 2.5 times as long as the manual digitization of Holman and

Guza (1984), but is believed to be more accurate, with the standard deviation between

swash heights determined by different operators to be 5%. Interestingly enough, the

authors note that a standing edge wave of mode 1 may have been present during their

analysis and could have caused the megacusps observed.

Holman, Howd, Oltman-Shay, and Komar (1990) were back on the Outer Banks

with their video equipment for the SUPERDUCK experiment to document swash

phenomena. Their cameras were set atop the 43 m tower at the FRF and were set to

record for 1 hour 55 minute intervals. The digitization technique was completely

automated by this time, eliminating the previously encountered tediousness and operator

subjectivity. The authors note that the "resolution of the technique depends on range from

the camera and focal length of the individual lens. Typical horizontal resolutions range

from 20 cm (swash elevation of 2.0 cm) for close ranges to 0.73 m (swash elevation of 7.3

cm) for the most distant cases." (p. 1244)

A remotely mounted video camera was used by Holland, Holman, and Sallenger

(1991) to determine overwash velocities on a barrier island off of the coast of Louisiana.

The camera was triggered to record the overwash phenomena by a salt water sensor that

also increased the sampling rates of the in-water sensors. The camera diligently recorded

34 events including a significant overwash caused by Hurricane Gilbert in 1988. The

velocities were determined from the video records by calculating the speed of wave fronts.

These fronts had foam on their leading edge, allowing the waves to be identified by








variations in the pixel intensity. The authors note that "this is the first time that such

spatially extensive overwash velocity data have been quantified." (p. 496)

Wave phase speed and breaking angles were determined from video records by

Lippman and Holman (1991) from data obtained at the FRF during the DELILAH

experiment. As many as eight cameras were used at one time to record data from the

dune crest to approximately 200 m offshore. Video records were made for 2 hours at a

sampling frequency of 10 Hz that compared favorably to the records made by in-situ wave

gauge arrays in terms of wave spectra, angle, and speed. The authors comment that "a

new method for sampling waves is available, and is not constrained by logistic difficulties

of adverse surf zone conditions." (p. 555)

In the introduction of their paper, Anders and Byrnes (1991) state that their

"purpose ... is to provide coastal managers, planners, engineers, and scientists with a

comprehensive survey of potential errors associated with measuring shoreline position

from maps and air photos with respect to calculated rates of change." (p. 17) Although

the focus of the paper is toward large scale maps and aerial photographs, the potential

sources of error are similar to those presented in oblique video photography. An analysis

of these errors includes scale considerations, rectification geometry, interpretation of high

water line (HWL), topographic relief, and the location and quality of control points. The

authors emphasize that the shoreline changes recorded must be larger than the combined

sum of possible errors to be considered significant.








2.2 Beach Cusps

A review of the literature available concerning beach cusps provides days, if not

weeks, of entertainment highlighted by controversy, contradiction and capitulation. As

summarized by Dean and Maurmeyer (1980): "The primary efforts have been directed

toward (1) determining a causative mechanism for their formation; (2) describing

qualitatively the associated water motions and sediment transport; and (3) developing a

predicitve relationship for their spacing." (p. 863)

The first beach cusp description and formation theory of note comes from Palmer

(1834) who describes the ability of the wave backrush, having breached a berm, to form

return channels. These channels have the ability to "remove all loose material from them".

(p. 573) and to scour the sediment from the bays, leaving horns between them, forming

cusps.

The concept of formation by breaching was supported by Jefferson (1899), when

he described a "great wave" (p. 239) that had breached a line of seaweed, "leaving

considerable masses of water imprisoned behind the weed."(p. 240) This water "can only

escape through occasional breaks in the wall of seaweed and at these points streams of

considerable strength set outward."(p. 240) These streams eroded the bays, leaving

behind seaweed covered horns. It was his contention that the seaweed was responsible for

changing the behavior of the backrush of the waves, resulting in cusps. His paper includes

comments on the effects of tides, material composition, storm effects, cusp spacing, swash

motion, wave magnitude and wave direction. Although subsequent studies refute the

conclusion that "the cusps must be ascribed to the agency of the seaweed piled up on the








beach",(p. 237) his observations concerning the mechanisms involved in cusp formation

provided the groundwork for many subsequent research efforts.

Branner (1900) provides the first volley in this cusp origin saga when he states that

"seaweeds have nothing to do with the matter". (p. 484) The evidence for this refutation

comes from observations of beach cusps on beaches where "there are no seaweeds or

other "drift" on the beach". (p. 484) His theory of formation was based on the

interference patterns developed between multiple wave sets of equal wave length traveling

toward the shore. At the points of constructive interference, the waves would converge,

transporting material to form horns. Destructive interference would lead to divergence,

and a spreading of the material to form bays. For a shoreline of the proper curvature, he

continues, the cusp spacing would be uniform, whereas a straight shoreline would have a

cusp spacing that gradually increased away from the centers of the locations of wave

generation. As for the origin of these waves, perhaps Branner himself says it best "I am

not sure that I know how the two sets of waves in this hypothesis are produced, but I am

confident that they do sometimes exist, for I have seen them." (p. 484)

Perhaps the most comprehensive summary of early cusp formation theories is

presented by Johnson (1910) in his paper "Beach Cusps". He explores the early theories

presented by Jefferson, Branner, and others, while developing "a theory which differs in

some essential particulars from those already advanced." (p.600) His theory begins with a

description of cusps and formation phenomena gathered from a variety of observations

made by himself and a host of colleagues throughout the country. These observations

were standardized by questionnaire, which encouraged the observer to note:








"Locality; general description of the beach; length of cusps; distance between
points of cusps; size of cusp material; relative steepness of two sides of cusps;
position of cusp axis relative to shoreline; slope of beach; comparison between
beach material and cusp material; whether or not cusps were being fashioned at the
time of observation; any evidence of long-shore current; height of waves; evidence
of more than one set of waves; whether or not waves come in parallel to beach;
direction of wind; stage of tide." (p. 604)


Even today these descriptors encompass many of the phenomena thought to influence

cusp formation. Johnson's conclusions from these field notes can be summarized as

follows:

FORM Various forms, however, all triangular, with the ideal form being that of
an isosceles triangle with its base towards the shore. This shape may be skewed by
longshore currents but retains its principal form with the horn pointing offshore.
MATERIAL Cusps tend to form from all sizes and types of materials. Horns
tend to contain the coarsest material in the region. Material has little influence on
size.
SIZE Cusp lengths were observed to range from one inch to 30 feet or more.
SPACING Cusp spacing ranged from one inch to 100 feet, with relative
uniformity between cusps. It is noted that the spacing is a more significant
parameter than the length.
FLOW PATTERN Landward near the horns and seaward toward the middle of
the bays.
BEACH SLOPE Slope effects insignificant compared to wave size.
WAVE SIZE Very significant in determining cusp spacing. Larger waves
produce larger cusps. Evidence that "doubling the wave height doubles the
length". (This length is equivalent to the "spacing" described in the nomenclature.)
WAVE DIRECTION "the best conditions for cusp formation exist when a single
series of waves advances parallel with the beach."(p. 614)
WAVE PERIOD Insignificant.
LONGSHORE CURRENT Cusps form when no longshore current is present.








WIND DIRECTION Little effect on cusp formation.
TIDE Cusps are evident at all tidal stages.
SCARP The presence of scarps or ridges were not required for cusp formation.
SEAWEED/FLOTSAM Little effect on cusp formation.


The results of these findings led to a rejection of Jefferson's theory due to cusp

formation on debris-free beaches and Branner's theory due to the destructive influence of

waves approaching at angles to the shore and the restrictions of the equal wavelength

requirement. In addition, Johnson proposed his own formation theory:

"Concisely stated, it is that selective erosion by the swash develops from initial
irregular depressions in the beach shallow troughs of approximately uniform
breadth, whose ultimate size is proportional to the size of the waves, and
determines the relatively uniform spacing of the cusps which develop on the
intertrough elevations." (p. 620)


Johnson, (1972), continued his analysis of shoreline processes and beach cusps in his

book, Shore Processes and Shoreline Development, with an edition published as late as

1972.

In 1935, at Lake Olga, Quebec, Butler (1937) observed cusps formed of boulders

with sizes ranging "from that of a pea to three feet in diameter, but the greatest volume of

fragments had diameters of a foot or more." (p. 447). The average spacing of these cusps

was approximately fourteen feet and the length was nine feet. Butler described the

protected nature of the area and its lack of waves large enough to move the boulders in

the cusp building fashion of Johnson (1910). He proposes that these boulder cusps were

"formed relatively slowly by extremely selective erosion ofbouldery glacial drift by swash

from waves of the size that strike this beach most of the time."(p. 451) Although the








waves in question are not capable of moving the boulders into the horns of the cusps, the

swash was thought to be capable of undermining the boulders causing depressions toward

which gravity aided in their motion.

In addition to the size of the boulders at Lake Olga, the lack of tides was another

condition considered by Butler (1938) to be uniquely responsible for the cusps. In his

literature review, Butler quotes Shepard (1935) as concluding that the "tides are the most

important factor in beach cusp development" having "twice the influence of waves."

Shepard (1938), corrected Butler by pointing out that the actual cusps did not respond to

the tides, however, the sand that alternately covered and uncovered them did. He

continues by stating that "this observation did not show that the tides produced the cusps.

On the contrary since it was during the large tidal ranges that the cusps were buried and

during the small tidal ranges that they reappeared, it became evident that waves lacking

the interference of strong tidal currents are favorable for cusp formation."(p. 309)

Shepard extended up his beach cusp work in a book, Submarine Geology (1963).

This work was followed by Evans (1938), whose most significant contribution to

the field was the outlining of a classification system for describing different types of cusps.

The system can be described as follows:

1. CAPELIKE Large (up to 600 ft. wide) cusps rapidly formed and
destroyed by storms.
2. SANDRIDGE Built as a result of a large sand ridge underwater.
3. OBSTRUCTION Built due to an obstruction on or near the shore.
4. SMALL Very small (1 to 6 in.) cusps formed by non-breaking waves
with no tide.
5. IDEAL Rapidly forming cusps in series with nearly regular spacing.










The most relevant of these types, the ideal cusps, form due to a critical "adjustment

between the waves and the shore" (p. 621). Although he does not delve into the details of

this adjustment, he goes on to describe the process by stating that when "the proper

adjustment does occur the formation of the cusps is very rapid, sometimes almost

instantaneous. But after the cusps are once formed, a considerable change in wave

conditions is required to obliterate them." (p.621) His observations led him to believe,

like Jefferson, that a sort of barrier or ridge breach was required for the initiation of cusp

formation. The regularity of the cusp spacing is a result of the non-uniformity in the

height of the breaching wave at regular intervals. Once established, these regular breaks in

the ridge are reinforced by the scouring action of the "parabolic swirl of the water when it

comes into the openings made by the waves." (p. 622) Thus, according to Evans, ideal

cusp formation is the result of the erosion of a ridge breached by a wave with regularly

spaced variations in height. The horns are merely the portions of ridge that are not

eroded. In a follow-up paper, Evans (1945) confirmed his support for the formation of

ideal cusps by stating that "they never form except through the process of breaking a

ridgelike obstruction by the waves ... In the examination of hundreds of such series of

cusps, I have found no exception to this." (p. 404)

The first researcher to contradict the basic erosional assumptions of the day was

Keunen (1948), who described the formation of cusps as being depositional in nature. He

noted that:

"the beach as a whole is not eroded during the formation of cusps, .. Evidently,
accumulation goes on concomitantly with erosion, and the horns must represent








not merely buttresses left standing by the erosive action in the bays but prograded
areas where most of the eroded material comes to rest." (p. 35)


The motion of the eroded bay material, he contends is the result of the "refraction of the

swash" (p. 36) as it enters the bays. The uprush travels through the center of the bays and

spreads outward, carrying the coarser materials toward the horns where it is deposited.

The backrush then travels back to the ocean with the finer sand, unable to transport the

coarser material due to frictional velocity losses. This finer sand is then deposited in the

bays with the next wave uprush. The regular spacing of the cusps is explained as an

equilibrium between the horn building potential of adjacent bays. As a bay is eroded, its

spacing and depth increase to a point at which the current can no longer transport

materials toward the horns. At this point, the bay size is in equilibrium. The adjoining

bay, with a similar growth potential, widens and deepens until the shared horn settles into

equilibrium position between the bays. This process continues until a series of equilibrium

cusps is formed or a change in wave climate occurs. This explains the tendency of cusps

formation to be sequential as opposed to instantaneous. While this theory is satisfying in

many aspects, the basic flow pattern described is opposite if that detailed the majority of

the literature.

In contrast, Smith and Dolan (1960), from observations on the outerbanks of

North Carolina, state that "they (cusps) are solely the product of wave erosion of the

lowest berm edge." (p. 1979) They also note that the points of the horns did not move

when subjected to oblique waves, contrary to the findings of Johnson (1910) and Evans

(1938).








Russell and Mclntire (1965), presented findings from observations of 84 cusp

formation situations on six continents over a nine year period that convinced them of the

depositional nature of cusp formation. They noted that the horns are made up of the

coarsest materials on the beach and that these materials ranged in size from boulders to

hard fine sand. The coarse material was not found to be "a stratigraphic layer that can be

traced into nearby beach sections, as would be the case were the cusps erosional in

nature." (p. 313) They recognized the validity of the work done by Kuenen (1948), but

highlighted the contradiction in the direction of flow in the bays as previously indicated.

Perhaps they describe it best by stating: "If cusps are forming, the inflow along the sides

and over tops of adjacent cusps swings into the bays; where the two streams meet, the

water piles up, attains considerable turbulence and flows rapidly down the bay." (p.313)

In addition, they identified the changes in wave conditions that encourage cusp

development, claiming that: "favourable conditions arrive soon after a decrease in local

storminess or a lessening in the intensity of heavy swell." (p. 313) In a climatic sense, they

equated this period to the transition from typical winter to summer wave patterns. In

addition, waves striking the coast obliquely cause longshore drift, and lead to asymmetry

of the cusps and their eventual destruction, in contrast to the findings of Smith and Dolan

(1960). Concerning the regularity of cusp spacing, Russel and McIntire detail the

evolution of cusps from their juvenile stage, with many irregularities and varied spacing, to

their well developed state, characterized by regular spacing and similar dimensions. The

authors conclude by stating that "we are confident of our conclusions, [but] it is apparent

that we have not been able to explain something vital to a complete theory of cusp origin,








the reason for cusp-width uniformity." (p. 317) They suggest that the regularity may be

connected to wave dimensions, rip currents, and/or irregularities in the offshore bar.

Longuet-Higgins and Parkin (1962) observed cusp formation and wave breaking

on two British beaches and attributed their formation to a combination of swash dynamics

and the existence of a layer of impermeable material on the beach face. Cusps were seen

during all stages of the tidal cycle, however, it is noted that the most likely time for the

formation of well developed cusps was "just after the turn of the [high] tide." (p. 195)

The authors note that "the cusp-spacing is not simply related to the period of the waves or

to the wavelength of low edge-waves on a beach of the same mean gradient." (p. 195) In

contrast, they contend that "a close correlation exists between the cusp-spacing and the

and the height of the waves which form them, . and an even closer correlation exists

between the cusp-spacing and the width of the swash zone." (p. 194) In addition, an

atypical circulation pattern is described, along with a mention of the requirement for

shore-normal, regular waves in the formation process.

In perhaps the most unique formation theory since Jefferson's (1899) seaweed

theory, Cloud (1966) offers Plateau's Rule for the origin of beach cusps. Plateau's rule

states that "a liquid cylinder becomes unstable when its length exceeds 2nr, and that it

then separates into subequal divisions whose lengths are proportional to the diameter of

the cylinder." (p.890) Cloud notes that cusps tend to form on a beach that has been

steepened by a period of increased wave activity. This steepened beach would tend to

create plunging breakers directly on its face, which would essentially simulate a cylinder.

The cusps could be the result of the separation of this unstable cylinder, as given by








Plateau's Rule. The segmentation to diameter ratio predicted in such a case varies from

15.5 to 16.7, and the author encourages comparison to observed cusps.

From his observations of beach cusps in "Soviet waters" (p. 282), Zenkovich

(1967), finds himself supporting the view that "the development of cusps is usually

preceded by the formation of a beach ridge, [with] the cusps being formed in its

subsequent erosion." (p.281) He also observed that "the size of cusps, the distance

between them, and their outline in plan section differ greatly in relation to the steepness of

the slope, the composition of the beach material, and the nature of the wave disturbance."

(p. 281) Concerning the relative heights between cusps formed on beaches of different

material, he notes that cusps formed on shingle beaches are only half the size of sandy

beach cusps in a similar wave climate, primarily due to the difference in material transport

phenomena. The author infers that cusps encourage the surf to dissipate energy at its

lowest energy level, and suggests that man-made coastal structures be shaped into cuspate

forms.

Cusp spacing was the subject of a dimensional analysis performed by Dolan and

Ferm (1968). Their findings indicate a hierarchical grouping ofcresentic coastal

landforms that range in size from the smallest of beach cusps to the capes of Florida and

North Carolina. They suggest that the different orders of features respond to different

magnitudes of coastal processes. The smallest cusps respond to the daily changes in

shallow water waves, while the large capes are influenced by the long term patterns

generated by Gulfstream eddys.

While investigating the regular spacing of rip currents in the nearshore surf zone in

the field and laboratory, Bowen and Inman (1969) noted "that the combined flow








associated with the incoming waves, the edge waves, and the nearshore circulation may

rearrange the sediment to produce a regular longshore pattern of beach cusps." (p. 5490)

This interaction leads to a complex set of circulation cells within the surf zone capable of

producing cusps and rip currents with variable characteristics depending on the beach

slope, wave size, and surf zone width. For a steep beach, the authors indicate that the

spacing of the cusps is equal to one half of the wavelength of the trapped edge waves and

the circulation cells. On a gently sloping beach, the spacing of the cusps may be small

compared to the rip current spacing, and is thought to be a function of smaller circulation

cells responding to the reformed waves of a lower modal number.

While performing laboratory investigations into the formation of giant (>500m)

beach cusps in the presence of rip currents, Komar (1971) was apparently surprised to find

a circulation pattern opposite to his hypothesis. He had expected to find that horns

formed at the point of null transport between two successive rip currents. Instead, in both

the laboratory and subsequent field observations, the horns of the cusps formed directly

shoreward of the rip currents. It was surmised that the transport within the rip current is

not exclusively offshore, and that a back-eddy is formed. It is this shoreward flowing

component of the rip current that deposits sand upon the horns. Komar also presents an

interesting description of an equilibrium situation that occurs during the formation of the

cusps. "Having produced the shoreline configuration ... with a large cusp in the lee of

the strong rip current and smaller cusps by the weaker rips, all cell circulation and other

longshore currents suddenly ceased to exist; the rip currents completely disappeared." (p.

2648) He proposes that an equilibrium between the nearshore cell circulation and the

longshore currents has been achieved, and remains stable. "The significance of this








equilibrium condition is that it is possible for cusps to have been produced by rips

currents, though the circulation is no longer present... at the time of observation." (p.

2649)

A straightforward application of "thin" flow phenomena is presented by Gorycki

(1973) to explain cusp formation without the requirements of seaweed, ridges, initial

beach irregularities, intersecting waves, cylindrical fluid instabilities, rip currents, or edge

waves. The phenomena is known as a sheetflood structure and it "is initiated by the

tendency of the edge of fluids traversing flat surfaces to extend laterally and invaginate at

regularly spaced intervals." (p. 109) Gorycki suggests that the swash produced by

breaking waves is predisposed to separation into "equally spaced zones of fast currents

separated by zones of lower velocity" (p. 110) which form cusps. His experiments in the

laboratory confirmed that a thin sheet of water flowing down an incline indeed separated

and formed cusp-like features. In nature, he contends that "beach cusps will only form if

waves of rather uniform size approach the beach with their crests parallel to the shoreline

.. and are not confused by winds or currents." (p. 116)

Wave height at the time of formation was the single most significant factor in

determining cusp spacing according to Smith (1973) after a regression analysis of data

gathered at Monterey Bay, California. He continues with: "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." From his field observations he concludes

that cusp formation is a depositional process created by perpendicular waves of uniform

size acting upon a beach with loose material. The cusps remain intact unless a period of








large and/or oblique waves occurs. Water circulation patterns were observed to be

typical.

Extremely small ( 11 to 59 cm) beach cusps were observed at Mono Lake,

California by Komar (1973), and were determined to be the result of "edge waves, trapped

by refraction to the nearshore." (p. 3593) The cusps formed quickly and regularly under

conditions of no wind and small surging waves that did not break. The flow pattern

observed consisted of an uprush split by the horns and a backrush down the center of the

bays. The support for edge waves formation is summarized as follows: "The unusual

formation of beach cusps at Mono Lake under wave surge, their sudden appearance with

regular spacing, and a correspondence with the expected range of edge-wave lengths all

lead to the conclusion that edge waves were responsible for their generation." The

correspondence Komar spoke of was with edge waves of mode n = 0 and occasionally n =

1 in the equation:

L = T2 sin[(2n + 1)f]
2;r

where L is the edge-wave length, T is the dominant wave period, f is the beach slope, n is

the offshore modal number. In this situation, it is assumed that the edge waves have the

same period as the surge, and that the cusp spacing is equal to one half of the edge-wave

length.

Bodie (1974) provides a complete description of cusp formation, maturation and

destruction with conclusions similar to those made by Smith (1973). Factors contributing

to the likelihood of cusp formation included a smooth, clean, uniformly sloping breach

with permeable sand and shore normal waves with a consistent period. The process was








described as being depositional and stable upon maturation, with a typical water

circulation pattern within the cusps. Sequential cusp formation normally occurred within

one day, and large wind and storm waves were found to destroy the cusps in the same

amount of time.

In what may be the most often cited work on edge waves and beach cusps, Guza

and Inman (1975) state that "edge waves, both directly and via their interactions with

other water motions, are responsible for many cases of cuspate topography." (p. 2998).

In addition, they provide a clear and concise definition of edge waves as "the normal

trapped modes of longshore periodic wave motion that occur along the edge of water

bodies, and they may be standing or progressive." (p. 2998) (For completeness, it should

be recalled that edge waves decay exponentially away from shore.) In relating the

importance of edge waves in nearshore sediment transport, the authors link theories

together demonstrating the existence of edge waves on all types of shorelines, the

excitability of edge waves from normally incident deep water waves, and the requirement

of edge waves to dissipate energy through friction and interactions with currents and other

waves. The distinction is made between reflective systems with surging waves and

dissipative systems with plunging waves, and the authors restrict their focus to the

reflective systems. They performed extensive laboratory experiments and noted field

observations to conclude that cusps are formed by :"(1) subharmonic edge waves (period

twice that of the incident waves) of zero mode number or (2) synchronous (period equal

that of incident waves) edge waves of low mode number." (p. 2997) In describing the

edge wave and cusp interaction, it is noted that the embayments are present at the location

of maximum runup, or the wave antinodes, and that the horns are positioned at the








location of no runup, the nodes. The spacing of the horns, therefore are at exactly one-

half the length of the edge waves (zero mode subharmonic).

Dalrymple and Lanan (1976) revisited the intersecting wave formation theory of

Branner (1900) in a series of laboratory experiments. They demonstrated that that cusps

could be formed by the intersection of two wave trains of equal wave length, although the

mechanism was not one of interference patterns but a function of the generation of rip

currents. The intersecting waves, it was determined, were capable of creating rip currents,

which then generated beach cusps with equal spacing. In addition, the water circulation

was described as being atypical, that is, with the uprush at the center of the bays and the

backrush along the horns. The dependency of cusp spacing on wave height was

determined to be only loosely correlated through wave length.

A qualitative description combining the thoughts of the breached ridge, sheetflood

flow, and topographic variations in the formation of beach cusps along the Delaware shore

is given by Dubois (1976). He provides the following description of the genesis of a series

of cusps:

"Beach cusps developed as follows: After an erosional event on a sandy beach, a
berm developed at low tide. The swash extended over the berm and ponded
between the berm and the backshore. The stream flow from the ponded water to
the sea cut loosely spaced channels through the berm. As the tide rose, the berm
and channels migrated landward. When the tide fell, the swash could no longer
overtop the berm, and no water ponded landward of the berm. Since no water was
returning seaward through the channels, the channel form could not be maintained,
and the swash flared the channels into bays. A series of beach cusps appeared on
the beach as the tide continued to fall." (p. 1133)

In addition, the cusp spacing is described as irregular, and the wave direction as oblique.

The cusps described were on the order of 30 m in spacing and 20 m in length. Dubois

details the relationship between the length from the backshore to the berm crest (L) and








cusp formation by stating that, "at high tide where L was greater than 12 m, no beach

cusps formed." (p. 1133)

The southeastern coast of Nigeria was the site selected by Antia (1989) to collect

"systematically-obtained field data on beach changes under the different cusp phases over

a prolonged period of time." (p. 264) For a two year period, beach profile changes were

recorded every two weeks and the effects of beach cusps on erosion, accretion, and linear

beach change were detailed. The perspective is rather unique in that the author

investigates the effects of the particular stage of cusp development on other beach

parameters, specifically volumetric and linear change. An evaluation of the beach state -

reflective, intermediate, or dissipative is made using the reflectivity parameter, 6 ,given by

Wright and Short (1983) as:

H(27n /T)2
& = (2.1)
g(tan) ()2

where H is the breaker height in meters, T is the wave period in seconds, g is the

acceleration due to gravity, and /f is the beach slope in degrees. A value of e < 2.5

indicates a reflective beach and a value of e 2 33 indicates a dissipative beach.

Intermediate values represent transitional conditions between reflective and dissipative

beaches. Antia (1992) concludes that beach cusps tend to form on reflective beaches

during the transition from high to low energy wave conditions, and that cusps can exist in

equilibrium on beaches undergoing both erosion and accretion. The suggestion is made

that erosion occurs more rapidly on reflective beaches, and cusps tend to form on

reflective beaches, so that a relationship between the increased formation of cusps during

erosion or the increased erosion of the beach during cusp formation can be inferred. The








data indicate however, that this point is better applied to linear beach changes and scarp

motion than to volumetric changes, due to the notion that linear changes may simply be

the result of sand shifting within the profile and not being transported out of the

volumetric calculation area.

Dean and Maurmeyer (1980) present observations and yet another spacing

prediction relationship from their observations of beach cusps at Point Reyes Beach and

Drakes Beach, California. In addition to documenting the typical water circulation pattern

and noting no apparent difference in material coarseness between the horns and bays, two

unique observations were made. The first "is that in cases of most effective beach cusp

formation, the wave period and swash period are nearly equal." (p. 866) The second is

that "there is a consistent increase in cusp spacing with increase in berm height" (p. 873)

for multiple sets of cusps. An idealized cusp topography model was combined with

frictionless water particle trajectory model to create a simple analytical prediction of cusp

spacing, A, in terms of the swash excursion ( x) max. The following linear relationship

was developed;

A 5J 3.9.- (x) (2.2)

which predicts cusp spacings of same order of magnitude as those observed. 6 describes

the cusp geometry such that;

hH hB
h-= (2.3)
(h + hB)

where h represents the heights of the horns (H) and bays (B) from a given datum. The

authors investigate the possibility of edge wave formation and note that "these

subharmonic oscillations entail alternating uprush and backrush in adjacent cusp swales;








this was clearly not occurring in any of the cusps observed." (p. 881) In addition, edge

wave formation is rejected due to the variations in incident wave periods, the validity of

small displacement linear wave theory assumptions, and the uncertainty of using a single

value for beach slope. They conclude that "swash mechanisms govern beach cusp

formation and spacing." (p. 881)

Laboratory experiments with glass beads on a variable slope beach led Kaneko

(1985) to relate cusp formation to breaking wave type. He found that beach cusps formed

when:

Hb /(tanf)gT2 < 0.042 (2.4)

where Hb is the breaker height, tan f is the beach slope, g is acceleration due to gravity,

and T, is the incident wave period. The author notes that this value is approximately

midway in the region defining plunging breaking waves as given by Galvin (1968). At

values larger than 0.042, cusps do not form, having been replaced by a longshore bar. At

values less than 0.042, Kaneko credits the building and spacing of cusps to edge waves.

In a compilation of the several sources of data, the cusp spacing is determined to be one

half the wave length of a zero mode subharmonic edge wave or equal to the wave length

of a zero mode synchronous edge wave.

In the introduction of their paper concerning edge waves, Schaffer and Jonsson

(1992) specify that they would like to address some of the confusion often associated with

edge waves. Specifically, they note that "Few people claim ever to have actually seen an

edge wave in nature ... [and] accordingly many coastal engineers .. regard them as a

mathematical curiosity rather than a physical reality, and a touch of mystery in the notion

of edge waves is not unusual." (p. 349) They provide comparisons of the full linear and








shallow water wave approximations, suggest dispersion relations for sloping beaches and

sloping beaches with a shelf, and estimate the maximum possible edge wave amplitude for

given conditions. Most importantly, however, they provide clear diagrams of reflected

edge wave fronts of various modes and their trapping in the surf zone.

A field experiment was performed by Sato, Kuroki, and Shinohara (1992) in an

attempt to quantify the time scale of cusp formation, and whether the process is erosional

or accretional in nature. A section of the beach with cusps was surveyed and contour

mapped. The section was then bulldozed flat at low tide and a set of 168 iron rods were

driven into the sand at intervals of 4m in the alongshore direction and 2m in the cross-

shore direction. Leveling measurements were taken at every low tide until the cusps

regained their previous size and shape. In addition, dyed sand was placed within the grid

to trace the motion of the sand. The contour mapping revealed that the cusps required

approximately three high tides to completely form and the process "purely accretionary .

. with the horns experiencing more deposition than the bays." (p. 2215) The authors also

mention that the removal of the rods from the horns was relatively easy, while removal

from the bays often required two or three people, suggesting a variability in density and

permeability caused by the cusp formation.

Paton (1993) presents a compilation of observations on beach cusp phenomena at

several New Zealand beaches. To this she combines statistical analysis, current meter

spectral analysis. and wave refraction analysis to develop a cusp formation theory that is

based on edge waves and nearshore circulation. In the presence of long period, shore-

normal, surging waves on reflective beaches with steep slopes, a periodic longshore

variation in wave height is developed. This variation leads to the initial disturbance that








creates the nearshore circulation cells that continue the cusp formation process and the

maintenance of the cusps. The author notes that the cusp spacing determined by this

method should be half of the edge wave length, with the horns at the edge wave nodes.

However, Paton also acknowledges that several inconsistencies in the data exist which

dispute edge wave theory. Specifically, the lack of correlation between the incident wave

periods and the cusp spacing disputes edge waves as a causative mechanism, as

subharmonic edge waves are exactly twice that of the incident wave period. Other

inconsistencies included a prediction of edge wave excitation at wave heights less than the

minimum for observed cusp formation, lack of formation under conditions expected to

generate cusps, and the variable nature of the selection of wave periods, beach slopes and

edge wave modes in developing correlations.

The latest installment in the cusp formation saga arises from the computer

simulation work done by Werner and Fink (1993) to develop their self-organization

theory. The authors "show that uniform beach cusps can develop by local flow

morphology feedback, [and] examine the implications of this self-organization model." (p.

968) A comparison is made between their model and the swash mechanics model of Dean

and Maurmeyer, and the numerous edge wave models. In the self-organization model,

swash trajectory is modified from a linear path to a parabolic path due to longshore

depressions in the beach topography. The depositional nature of decelerating flow and the

erosional nature of accelerating flow are modeled in the swash zone. The combined

effects of "(i) positive feedback between morphology and flow that creates relief and (ii)

negative feedback that inhibits net deposition or erosion on well formed cusps" (p.969)

generate regularly spaced cusps in a time frame that "requires 50 to 1000 swash cycles








(corresponding to 0.1 to 3 hours for 10-s [period] waves)." (p.969) The resulting cusp

spacing is found to have a linear relationship with swash excursion such that:

so = 1. 7 (2.5)

where Aso represents the steady state cusps spacing and x is the swash excursion. This

relationship agrees with that determined analytically and observationally by Dean and

Maurmeyer (1980). It also agrees with the data from the edge wave models given by

Guza and Inman (1975). To compare the mechanisms behind the edge wave theory and

the self-organization theory, the authors modeled cusps at spacings determined by edge

waves dissimilar to those predicted by the self-organization theory. The simulation was

run for "hundreds of swash cycles" (p. 970), after which it was noted that the cusps had

modified their spacing to that predicted by the self-organization theory. As a result,

Werner and Fink contend that:

"The conditions that are necessary for self-organized cusp formation, coupling
between alongshore surface gradients and flow, are unfavorable for cusp formation
in the standing wave model. Therefore, we conclude that the standing wave and
self-organization mechanisms are incompatible." (p. 970)


They acknowledge, however, that insufficient data on natural cusps exist to separate the

two models.

The following series of tables summarize the thoughts on beach cusp phenomena

presented by the authors of the various papers reviewed. The dates appearing by the

authors names are not necessarily indicative of the origination date of the theory, but refer

to the dates of the literature included in the reference section of this paper, and as such,

provide only a rough estimation of lineage.











FORMATION/SPACING CONSIDERATIONS


Berm or Ridge Breach Palmer 1834

Jefferson 1899

Evans 1938

Smith and Dolan 1960

Dubois 1978

Material Differences on Beach Face Johnson 1910
Butler 1937

Kuenen 1948

Longuet-Higgins and 1962
Parkin
Sheet Flood Flow/Wave Form Cloud 1966

Gorycki 1973

Rip Currents Shepard 1963

Russel and Mclntire 1965

Bowen and Inman 1969

Komar 1971
Hinon 1974

Dalrymple and Lanan 1976

Edge Waves Bowen and Inman 1969

Komar 1973

Guza 1975
Kaneko 1985

Paton 1993

Intersecting Waves Shaler 1985
Branner 1900

Shepard 1963








Dalrymple and Lanan 1976

Swash Mechanics/ Self Organization Longuet-Higgins and 1962
Parkin
Dean and Maurmeyer 1980
Werner and Fink 1993



Table 2.1 Literature Summary Cusp Formation/Spacing Considerations



WAVE DIRECTION


Shore Normal Johnson 1910
Kuenen 1948
Longuet-Higgins and 1962
Parkin

Russel and Mclntire 1965

Cloud 1966
Zenkovich 1967

Gorycki 1973
Smith 1973

Bodie 1974

Dubois 1976

Dean and Maurmeyer 1980
Kaneko 1985
Sato, Kuroki, and 1992
Shinohara

Paton 1993
Werner and Fink 1993

Oblique Evans 1938
Smith 1960








Dolan 1960



Table 2.2 Literature Summary Wave Direction During Cusp Formation





NATURE OF FORMATION


Erosional Jefferson 1899
Butler 1937
Evans 1938
Smith and Dolan 1960
Zenkovich 1967
Dolan and Ferm 1968
Dubois 1978

Depositional Kuenen 1948
Russel and Mclntire 1965
Zenkovich 1967
Smith 1973
Bodie 1974
Kaneko 1985

Sato, Kuroki, 1992
Shinohara


Table 2.3 Literature Summary Nature of Cusp Formation Erosional/Depositional


CIRCULATION PATTERN








Typical Uprush on horns, Backrush in Jefferson 1834
Bays

Longuet-Higgins and 1962
Parkin

Russel and McIntire 1965

Zenkovich 1967

Komar 1973

Smith 1973

Bodie 1974

Guza and Inman 1975

Werner and Fink 1993

Paton 1993

Atypical Uprush in Bays, Backrush on Kuenen 1948
Horns

Longuet-Higgins and 1962
Parkin

Bowen and Inman 1969

Komar 1971

Dalrymple and Lanan 1976


Table 2.4 Literature Summary Water Circulation Pattern in Cusps













CHAPTER 3


DATA COLLECTION




3.1 The Video Monitoring System

The basic components of the video monitoring system (VMS) are the camera, the

pan/tilt mechanism, the timer, and the video capture devices with corresponding software.

The VMS employed for the monitoring of the Longboat Key beach nourishment project

was designed, built, and installed by Erdman Video Systems of Miami Beach, FL, and

represents the latest evolution in a series of systems specifically developed to monitor

coastal phenomena. The major components of the VMS are commercially available and

relatively inexpensive.

The camera utilized in this study was a color Sony Hi8 FX 710 with automatic

exposure control, automatic focus, variable zoom, and a polarizing filter. The use of Hi8

tapes allowed for increased quality recordings and ease of transport due to their small size.

The camera was mounted in a surveillance type environmentally protected housing on the

parapet of the Longboat Harbor Towers 11th floor roof. The pan/tilt mechanism was a

digitally controlled stepper motor with a repeatability of better than 0.1. The camera and

the pan/tilt motor are the only components exposed to the weather.

Two distinct types of video capture devices were employed and were remotely

located within the condominium, connected to the camera through weather-proofed








cables. The first was an analog video tape recorder, which recorded 8 frames at each

designated scene location during each sampling interval. The analog format of the tapes

allows for continuous replay on typical home or office VCRs. The time lapse nature of

the photography lends itself well to viewing long term phenomena and patterns in a

reasonable amount of time.

The second video capture device was a 486/33 personal computer (PC) which

captured and stored the images in digital format. This format is required for almost all

types of numerical analysis. In addition, the PC was employed to control the stepper

motor and provide remote access through telephone lines via modems. This access

allowed for the addition and/or deletion of scenes, downloading of real-time or past

images, and camera adjustments. Up to 34 different scenes can be monitored at user

specified frequencies, from any PC location with modem access.

Throughout this paper, the video monitoring system will be referred to as the VMS

and includes all of the hardware and software required to obtain images. An image is the

"picture" or "photograph" of a particular scene. The scenes are fixed views, and are

always the same. The multiple images of these scenes are unique due to their differences

in time. Analog images are those contained on a VHS tape. Digital or digitized images

have been converted to matrices which represent the relative pixel intensities of the analog

image, ranging from 0 (black) to 255 (white). Rectification is a process in which an

oblique image is artificially "stretched and rotated" to appear as an image taken from

directly overhead. Details of the rectification process are given by Mason (1993).








3.2 Deployment/Data Description

In accordance with a requirement by the Florida Department of Environmental

Regulation (FDER) in permits numbered 41 & 581938039, the video monitoring system

(VMS) for the beach nourishment project at Longboat Key (LBK), Fl. was installed atop

the Longboat Harbor Towers. This condominium is an eleven story building located at

4401 Gulf of Mexico Dr., Longboat Key. This location is slightly north of the center of

the project and the border of Manatee and Sarasota Counties, between Manatee County

survey markers R-65.5 and R-66, and samples the project at a location that corresponds to

the in situ monitoring site LBK2. Stubbs 1994). Figure 2.1 presents the project area along

with the locations of the VMS and the in-situ monitoring site.

From this location and elevation, images can be obtained throughout a 180 degree

arc from Northwest to Southeast, at distances approaching one mile. The VMS system

was in continuous operation during daylight hours from May 27, 1993 through July

31,1994, with two basic sampling schemes. The first scheme was in place while the

project was in its initial phases, and was programmed to follow the construction crews,

sampling on an hourly basis. The post-construction scheme established fourteen fixed

scenes from North to South and sampled each scene hourly. In addition to the single

digitized image records, an averaged image made up of eight individual images is

generated at hourly intervals. The averaged images are useful for determining wave

breaking conditions, especially over offshore sand bars.










Lon
NORTH













Anna Maria


WAVE GAUGES (LBK 2)




CAMERA LOCATION,
LONGBOAT HARBOUR TOWERS

Longboat





Siesta Key


gKey






..t Tampa Bay


Bradenton


Key


Sarfta


Figure 3.1 Nourishment Project and VMS Location
(Modified from Stubbs 1994)



The data base generated consists of over eighty thousand (80,000) digitized

images of the project, and over 15 continuous hours of analog tape. The data represents

an extremely large volume of information with challenges concerning storage, handling,








transmission, evaluation, and application. The digital images were archived for retrieval

on a compact disk (CD) by Erdman Video Systems. Differences in file formats determine

the amount of compression for an image and the amount of storage space required.

Different formats are compatible with different software applications. Table 3.1 details the

amounts of storage required for the same LBK scene 1 image in six popular formats. It

should be noted that color images typically require at least three times as much storage

space as grayscale images.

FILE FORMAT NUMBER OF BYTES
.JPG 31,535
.GIF 205,910
.PCX 287,393
.TGA 309,659
.TIF 692,117
.BMP 737,334


Table 3.1 Single Image Storage Requirements by Format



An effort to convey this information in a condensed and meaningful fashion has

lead to the generation of a VHS format tape labeled with time and date and a CD

containing all digital images. To reduce the volume of information, only the images from

scene 1 will used for digitization, scaling, rectification and analysis. Scene 1 is a wide

angle view looking northwest from Manatee County Survey markers R-65.5 to R-63.5.

Each image contains a scene designation and Eastern Standard timecode printed at the

bottom. Figure 3.2 presents a typical data set image from scene 1.


































iPrUh N inme






Figure 3.2 Typical LBK Scene 1 Image.


In this image, the point of maximum swash uprush and waves breaking on the sand

bar are clearly visible. In addition, the reference point used for rectification and relative

beach change measurements is indicated. This point represents a fixed position on the

beach with known coordinates and was selected due to its visibility in the digitized images

and construction drawings and its presence before and after the beach nourishment. To

locate the reference point for scene 1 on the construction drawings, begin at Manatee








county survey marker R-65.5 and proceed along the survey baseline toward marker R-65

approximately 313 feet. The reference point is at the base of a tree located 81 feet toward

the west at a 90 angle.

In addition to the original oblique images, scaled rectified images have been

generated using an in-house program developed by Erdman Video Systems. A 20 ft. by

20 ft. grid has been created and overlaid on the rectified images for scaling purposes. An

example rectification of Figure 3.2 appears in Figure 3.3.


Figure 3.3 Rectification of typical LBK scene 1 image.








In addition to the features visible in the oblique image, the rectified image allows

for direct measurements of distances and wave angles. It should be noted that the quality

of the hardcopy images, in both original and rectified formats, suffers due to multiple

transformations from the original digital color versions to the grayscale images as printed.

Many details visible in color, on a high resolution PC monitor are lost in the final hardcopy

outputs.




3.3 Related Deployments

The initial tests of a VMS system with remote access capabilities took place on

Hollywood Beach, FL from 1990 to 1992 (Mason, 1993). The system was designed to

monitor the beach nourishment activities occurring during the summer of 1991 and to

assess the nearshore turbidity impacts of the project. The camera was installed inside of a

private residence on the 21st floor of a condominium near the project site and recorded

analog images at 30 and 60 minute intervals. The height of the camera and the wide

(8mm) angle lens used allowed for scenes to be sampled over a 6.5 mile range.

Researchers were impressed with the performance of the system and the usefulness of the

data obtained.

This project was quickly followed by a semi-permanent installation in Miami

Beach, FL in 1992 (Mason 1993). The VMS was deployed to collect long term nearshore

activity on Miami Beach and to test hardware and software upgrades to the system. The

camera was placed in a water-proof housing with an upgraded pan/tilt mechanism on the

16th floor of the Rooney Plaza. Software advances included automated digitization with








remote camera control and scene selection. It was at this time that the time-averaging of

images from a particular scene was developed. A version of this system is in place today.

At present, there are related VMS installations in Palm Beach, FL (PEP reef

monitoring), Tennessee (fog formation), and Italy (harbor monitoring). Plans are in place

for installing a VMS at the FRF in Duck, NC and in Jacksonville, FL. In addition, another

camera is being added to the deployment at Longboat Key, FL.




3.4 Project Background and In Situ Monitoring



Longboat Key is a barrier island in the Gulf of Mexico and is approximately 10

miles in length and varies from 1/2 to 1 mile in width. The average shoreline alignment of

LBK is 326 west of north, and the shore normal is 236 (ATM 1992). The twenty year

wave hindcasts from the USACOE Wave Information Study (WIS) indicate a mean

significant wave height of 0.8 feet and a mean peak period of 4.8 seconds at WIS station

41. (Hubertz and Brooks 1989). The local tides are characterized as semi-diurnal, with a

range of 1.63 feet. Mean low water is located at 0.47 NGVD and mean high water is at

1.16 feet NGVD (ATM 1992). Figure 3.4 presents the tides at LBK for the month of

November 1993.










Tides at LBK November 1993


3

2.5

2

1.5

1

0.5

0

-0.5

-1

-1.5


Figure 3.4 Tides at LBK November, 1993



The beach nourishment project at Longboat Key began on February 28, 1993, and

continued until August 12, 1993. The construction crews appear in the images from scene

1 during the later parts of May and the beginning of June, 1993. The project consisted of

approximately two million, eight hundred and ten thousand (2,810,000) cubic yards of fill

material, spread over 9.28 miles of beachfront. The material was excavated from two

separate sources. The southern portion of the island was nourished with material from the

New Pass ebb-tidal shoal, while the northern portion was nourished with material from the

Longboat Pass ebb-tidal shoal (ATM 1994). Figure 3.5 provides a before, during and after

view of the construction.









































Figure 3.5 Before, During, and After the Construction

The in-situ monitoring site was designated LBK2 and was part of an ongoing

sedimentation and turbidity monitoring project (Stubbs 1995). The wave and turbidity

instrumentation packages were made up of a watertight PVC body with associated

peripheral sensors located on pipes jetted into the sea bed on steel frames at an average

depth of 18 ft. The wave data were measured with a Transmetrics P-21 pressure

transducer, and were translated into wave amplitude, wave period and tidal stage






45


information. The system sampled at one Hertz for 1024 seconds every two hours (Stubbs


1995). Figures 3.6 and 3.7 present the wave data from the instrumentation.



Wave Heights


6.00
October Storm
5.00 -

4.00-

3.00 December Storm

2.00 -

1.00

0.00
S0 0 000 00 00 0 0 Date Time0
000000000000000 00000000 00000


Date Time


Figure 3.6 Significant Wave Heights for November, 1993












Wave Periods


10.00

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00
0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
000 O O 0000 0 0 u C i M i

Date Time


Figure 3.7 Wave Periods for November, 1993













CHAPTER 4


DRY BEACH EVOLUTION




As previously indicated, the amount of dry beach resulting from a nourishment

project is of primary concern to the public and the coastal engineer. The degree of project

success is often judged by this single parameter by the media and amongst individuals who

do not recognize the volumetric and profile modifications that determine a project's

technical merit. To help clarify the situation, a method has been developed to track the

evolution of the dry beach width throughout the nourishment period using the data

obtained by the VMS. This method is intended to augment traditional techniques such as

surveying and aerial photography. The data from the VMS cover a broader area than is

possible with surveying, and samples much more frequently than both techniques. Hourly

images are available during all daylight hours, in all weather conditions, and in real time, if

desired.




4.1 Monthly Summary



A series of images was selected to generate a monthly summary according to the

following criteria:










TIDAL HEIGHT The times of all images are within +/- 2 hours of Mean Low
Low Water (MLLW) +1.0 feet. (+/- 0.1 feet)_
STORM/WAVE ACTIVITY To avoid the effects of storm wave set-up, no
images containing breaking waves were selected.
RAIN Images with visible raindrops on the environmental housing portal were
eliminated.
LIGHTING The images selected were required to have proper light exposure to
illuminate the beach and waterline in both the original and rectified views.
CAMERA LOCATION Due to slight variations in camera position due to wind
loading and repeated repositioning, the images were also required to reflect
consistent camera positioning.


These strict image selection criteria help ensure that the dry beach width measured

accurately represented the relative status of the project on a monthly basis. The dry beach

width is determined from the point of maximum uprush on the rectified versions of the

images selected, and verified with the original images. Three distances between this point

and a shore parallel line through the reference point are measured and averaged to obtain

the width. Figure 4.1 presents the summary of these results on a monthly basis. It should

be noted that the reference point is clearly visible on all construction drawings and aerial

photographs, so that distances to known monuments or local features (buildings,

intersections, etc.) can be determined. Appendix 1 contains both the original and rectified

images used in this analysis.










Dry Beach Width Monthly Summary
500.00 ----
450.00 ourihme 6t 6/'/93
450.00
& 400.00
8 350.00
300.00
250.00
S200.00
150.00
100.00
50.00
0.00

ooFigure 4.1 Scene 1 Dry Beach Width Monthly Summary
(N (N NS NS aS (S (S (S CS N N 1 N S N N NN
Ifr4o C-4 O N C- N C 4 rO C'4


Figure 4.1 Scene 1 Dry Beach Width Monthly Summary


4.2 Monthly Summary With Storm Events



The VMS captured several large storm events during the monitoring period. The

addition of these images and their corresponding dry beach width to the monthly summary

plots provides additional insight into the driving mechanisms behind the shoreline

evolution. The storm images included in this analysis show the maximum high water mark

on the beach during the event, in addition to meeting the lighting, rain, and location

criteria of the monthly summary images. The dates of the storms included are 10/30/93-

11/1/93, 12/11/93-12/16/93, 1/04/94-1/05/94, and 3/02/94-3/04/94, and are referred to as

the October, December, January and March storms, respectively. The procedure used for

obtaining the distances from the rectified images is identical to that used in obtaining the

monthly summary measurements. The images from the monthly summary (Appendix 1)









can be used for a before/after visual review of the impact of each storm. Figure 4.2

depicts the monthly dry beach width summary with the inclusion of storm events.

Appendix 2 contains the original and rectified storm images utilized.


Monthly Summary With Storms








_De cember Storm



r____t____ Maich Storm
Jan uary St orm


Date


Figure 4.2 Dry Beach Evolution With Storm Events
(Note: The storm widths reflect storm surge and run-up.)


4.3 Rectified vs. Oblique Image Analysis


The question of evaluating images in the oblique frame of reference arises after one

has processed several dozen images and obtained measurements. Although the process is

not overly difficult, it is tedious, and requires a considerable amount of time. In addition,

dual sets of images (original and rectified) more than double the required computer

memory space. In an effort to provide "quick and dirty" measurements from oblique

images, a set of correction factors has been developed to convert the number of pixels

measured on an oblique image to feet on the beach. These scaled distances are only valid


500.00
450.00
400.00
350.00
300.00
250.00
200.00
150.00
100.00
50.00
0.00








at the specific longshore location where the calibration is conducted. This method is not

intended to be exact, but it may be useful in screening large numbers of images to select

those with significant changes, before applying the rectification techniques. As the images

are produced hourly, and available in real-time, the method could also be used to quickly

evaluate current beach activity to make image downloading decisions. Figure 3.3 presents

the monthly dry beach width summary with the addition of the distances determined from

this modified oblique method for comparison.


Rectified vs. Oblique Summary


500
450 -- ----





2 300 -.MAGES





50
0350 ---


250---

200 '
o IODI =IED OBL QUE 1

100 "



0

100 -- - --- --- --- -- ---Date -
50 ---- -- --




Date


Figure 4.3 Rectified vs. Oblique Dry Beach Width Summary













CHAPTER 5


BEACH CUSPS



The documentation of beach cusp patterns and size characteristics, along with the

environmental conditions surrounding their formation and destruction is not new, nor is

the use of the combination of video systems and in-situ instrumentation for monitoring

beach phenomena. What is unique, however, is the combination of the three for the

purpose of gaining insight into the mechanisms underlying beach cusp formation. The

images from the LBK nourishment project provide cusp measurement capability in

rectified form, and the in-situ instrumentation (Stubbs 1995) provides significant wave

heights (Hs) and peak periods (Tp). The original images provide an hourly record of the

formation and destruction processes in action. Figure 5.1 provides a typical set of original

and rectified images with visible cusps.


Figure 5.1 Original and Rectified Cusp Images










5.1 Background



During the first fourteen months of the beach nourishment project at LBK, the

VMS faithfully recorded all nearshore events on an hourly basis. Interestingly enough,

significant beach cusp formation was only apparent during the month of November, 1993.

At this point, the project had been in place for 5 months, and a review of Figure 3.1

indicates that over one half of the total evolution had occurred. This portion of the

evolution curve also has the steepest slope, with an average rate of reduction in dry beach

width of over four feet per day during the month. An inspection of Figure 3.2 provides an

indication of the forcing mechanism behind the rapid loss in beach width, as the October

storm (10/30/93-11/1/93) influence is readily apparent. This storm was characterized by

waves with heights as large as 5.82 ft., and periods of 9.1 seconds, (Stubbs, 1995) and

was the most significant wave event of the deployment. Wave breaking is evident on the

beach face, the nearshore sand bar, and an offshore sand bar that is rarely observed. The

storm run-up levels approached those of the beach in its pre-nourishment state and a large

scarp was carved out of the beach face as a result of this wave activity. The sequence of

images in Figure 5.2 provides a visual record of the magnitude of the storm.




















































Figure 5.2 Before, During, and After the October Storm









Figure 5.3 is the beach profile at Manatee County survey marker R-65 as surveyed

by Applied Technology and Management (ATM) on November 2, 1993. On this chart,

the scarp indicated on the images is labeled and appears to be approximately two feet in

elevation. From this point seaward, the beach face is relatively smooth and flat with a

consistent slope of approximately 1:15 (f = 3.80) from +2.5 NGVD to -2 NGVD. Also

visible is the profile change corresponding to the nearshore sand bar where the storm

waves were breaking in the images.





LBK R65 Beach Profile
November 2, 1993
12.0

10.0

8.0 -
CUSPS

6.0-

4.0




00 5(.0 101.0 15).0 2 25).0 301.0 35).0 401.0
-2.0 ---- ----

-4.0 _

-6.0


Distance Offshore (Ft.)


Figure 5.3 LBK Beach Profile, November 2, 1993








The planar beach face was a condition described as conducive to cusp formation

by many researchers, although the slope is shallower than the majority of the slopes found

in the literature reviewed. The exceptions are f = 3.250 given by Komar (1973), and

f = 2.290 reported by Dean and Maurmeyer (1980). Thus the stage was set for the

subsequent cusp formation that was to characterize the beach face for the entire month of

November.




5.2 Cusp Formation Description


The early morning hours of November 1st saw a low tide (-0.1 ft.) and waves with

Hs = 2.66 ft. and Tp = 8.5 s. These waves are breaking on the nearshore sand bar and are

clearly visible on the images.(See Figure 5.3) During the day, the waves diminished to Hs

= 1.31 ft. and Tp = 8.0 s. There are no evidence of cusps or periodic variability in the

swash zone.


Figure 5.4 November 1, 1993








November 2nd followed the same pattern of diminishing waves (Hs = 1.31 0.46

ft., Tp = 8.0 6.7 s) and no cusps. By noon of November 3rd, however, 9 cusps in sets of

6 and 3 had formed with an average spacing of 32.7 ft. and an average length of 18.3 ft.

These cusps continued to form throughout the day while tidal range was constant, until

they made up one continuous set of 16. This set of cusps continued to develop and

increase in number to 20+ for the next two days and achieved their most distinctive form

at 1600 hrs. on November 5th. The formation appeared to be sequential, with the

formation of one cusp following the formation of an adjacent cusp, as described by

Johnson (1910), Kuenen (1948), Smith (1973), and Bodie (1974). The average spacing

was 38.8 ft. and the average width was 17.0 ft. During this period, there were 11 tidal

cycles with a maximum range of 2.5 ft. The waves had a range ofHs = 0.33 0.88 ft.

with Tp = 3.1 8.0 s, and appeared to be shore-normal. Figure 5.4 presents these cusps at

nearly high tide (+1.4 ft.).

It can be seen in Figure 5.4 that there are no waves breaking on the sand bars. In

addition, there is no evidence of the uprush reaching the scarp, contrary to the berm

breaching formation theories presented by Palmer (1834), Jefferson (1899), Evans (1938),

Dubois (1978), Smith and Dolan (1960).

































Figure 5.5 November 5, 1993 20+ Cusps


The final image from the series on the 5th gives an inkling of things to come as a

squall line with rain can be seen approaching from the north. During the night of the 5th

and the early morning of the 6th, the tides reached their maximum at +2.1 ft. and the

waves increased to Hs = 1.31 ft. and Tp = 3.9s, approaching the beach at an oblique angle

from the northwest. Following this event occurrence of this, the images show little or no

cusps, and evidence of rain. The only trace of the cusps that were so well defined just the

evening before were small indentations at the previous embayment locations. Without the

previous days' video data would it have been difficult to identify these features as relict

cusps. The storm continued through November 7th, with a maximum Hs = 2.03 ft. with a








Tp = 5.1 s. Figure 5.6 illustrates the weather conditions and beach face, devoid of cusps.

(note the raindrops on the environmental housing portal.)
















Figure 5.6 November 7, 1993 Storm and Rain



The storm abated on the 8th and wave conditions returned to Hs = 0.65 ft. and Tp

= 7.1 s. By noon, with the rising tide, rhythmic variations in the wave run-up are present.

At noon the following day (November 9th), seven cusp forms can be identified, which

were not evident at 900 hrs. These cusps, in contrast to previous cusps, appear to have

developed simultaneously. By 1600 hrs., the number of cusps had increased to nine, and

were clearly visible at low tide (+0.8 ft.). Their average spacing was 37.7 ft. and their

average length was 14.6 ft.

The following days (November 10 12) were a transitional period for the cusps.

The increasing tidal range (2.6 ft.) associated with the spring tide, encouraged the

development of the cusps seaward, increasing their spacing to 44.9 ft. and their lengths to

15.8 ft. During this period, the height of the cusps appeared to increase as well, although

quantitative values for height are not discernible from the images. (Cusp height, however,








can be estimated by comparing the cusps to the pedestrians walking along the beach.) The

wave conditions during this time were consistent, with Hs = 0.33 0.43 ft. and Tp = 5.3 -

8.0s.

A slight increase in tidal range, (3.1 ft.) and wave height (Hs = 0.75 Tp = 8.0s) on

the 13th and 14th seems to have solidified the cusps and increased their numbers to 20+.

Several images of interest arose from this particular group, beginning with the image at

1000 hrs on the 13th. (Figure 5.7) This image presents one of the clearest views of the

cusps at LBK. The average spacing of these cusps is 54.6 ft. and the average length is

24.6 ft. There are over 19 visible. The tide at this time is rising and passing through an

elevation of +1.0 ft.


Figure 5.7 November 13, 1993 Well Developed Cusps








An additional tidal range increase (3.3 ft.) and larger waves (Hs = 1.2 ft., Tp = 4.6

s) were recorded on November 14th. The cusps began to separate into two distinct

groups, one at the waterline, and one farther upland. (See Figure 5.8) In addition, the

wave direction seemed to have rotated to the southwest as the waves were building,

causing a shift of the lower cusps to the north. In figure 5.8, the two sets of cusps are

visible, as are the obliquely incident waves. From the rectified image, the offset of the

cusp sets is 8.5 ft. and the angle of the wave fronts in relation to the shoreline is between

200 and 250. It is interesting to note that the cusps seem to be adapting to the new wave

direction, as opposed to being destroyed, as has been suggested by several previous

researchers. The seven upper cusps have an average spacing of 58.2 ft. and an average

length of 28.7 ft. The nine lower cusps at the waterline have an average spacing of 49.3

ft. and an average length of 12.9 ft. Thus, the active cusps at the waterline are

significantly smaller than the cusps located higher on the berm. This is consistent with the

findings of Komar (1973) and Dean and Maurmeyer (1980) concerning the sizes of

multiple sets of cusps. The tide at the time of this image was rising and passing through

+1.4 ft. The tides for the period between the 14th and the 18th shift from semi-diurnal to

diurnal, with an increased range, extending from -0.6 to 2.7 ft. NGVD.
































Figure 5.8 November 14, 1993 Oblique Waves and Multiple Cusp Sets


Images from the 15th provide a measure of the time required for cusps to form, as

the high tide from the night of the 14th virtually eliminated all evidence of the lower set of

cusps. The visualization of this is simplified by the presence of seaweed at the waterline at

1000 hrs. As can be seen in the right hand image of Figure 5.9, the seaweed has formed

an unbroken line parallel to the shore with very little periodic variation. Relict, inactive

cusps can be seen shoreward, outlined with seaweed, implying that the tide reached this

level. It is interesting to note that the breaking waves appear to have a periodic longshore

variation, as does the swash, although they are not of the same length. This seems to rule

out the influence of edge waves in this instance. As seen in the left hand image four hours

later, the longshore periodicity of the waves is not apparent, but the active cusps seem to








have self-organized, in alignment with landward relict cusps. It is not clear if the

formation of the cusps changed the appearance of the waves, or the change in the waves

encouraged the cusp formation. It is known that the tide is rising from 0 to +1.2 ft.

NGVD corresponds to a shoreward displacement of 18 ft. which moves to water into the

upper cusp areas. This implies that the swash processes within the upper cusps may have

facilitated the rapid development of the lower cusps.


















Figure 5.9 November 15, 1993 Active Cusp Formation


For the period between November 16 19, the cusp system remained stable

throughout the tidal cycles, and no unusual wave patterns were observed. The average

spacing of the cusps was 53.16 ft with a standard deviation of 5.75 ft, and an average

length of 36.96 with a standard deviation of 5.01 ft. The wave climate averaged Hs = 0.61

ft. and Tp = 7.55 s. What is interesting about this data set is the visible circulation patterns

within the cusps. At different times, the circulation patterns appear to switch from the

typical pattern ofuprush on the horns and backrush in the bays, to the atypical pattern

with the flows reversed. Researchers have previously noted both circulation patterns,








although the pattern termed "typical" is the most prevalent. (refer to Table 1.4 for

details.)


Figure 5.10 A, B Atypical Circulation


Figure 5.10 C, D Typical Circulation










Figure 5.10 presents four views of circulation phenomena. As still images, the

direction of flow is not readily determined, however through careful observation, the foam

and breaking whitewater can be used as flow tracers. The rectified versions of these

images provide insight to the longshore alignment of the cusp features and flow tracers.

In Figure 5.10 A, the swash appears to be extending into the bays, as opposed to flowing

landward at the horns. In figure 5.10 B, The swash also appears to be uprushing into the

bays, although there is evidence of longshore convergence in the cusps in the near field.

Figure 5.10 C clearly demonstrates the splitting of the uprush on the horns and its

convergence in the bays to flow back to the sea. It can be seen that the maximum uprush

is on the horns. Figure 5.10 D is a slightly more subtle view of typical circulation. The

cross-shore white streaks in the bays are lines of convergence from the flow being diverted

into the bays from the horns. For this to occur, the flow must have come up the horns

before converging in the bays.

The period between November 20 27, was a very stable time for the cusp system,

which continued to fluctuate between one and two levels of active cusps. Wave records

for the period are unavailable, however, the activity level was assumed to be relatively low

due to the lack of breaking waves on the sand bars in the images, except for a short period

on the 24th. Figure 5.11 presents an excellent view of the cusps evident during this

period.




































Figure 5.11 November 21, 1993 Bi-Level Cusp System


The active set at the waterline number twenty or more and has an average spacing of 53.2

ft. with a standard deviation of 4.64 ft. The average length is 26.5 ft. with a standard

deviation of 4.15 ft. The "relict" cusps farther landward on the berm number between six

and eight, with an average spacing of 57.7 ft. and a standard deviation of 5.21 ft. Their

average length is 17.5 ft., with a standard deviation of 2.20 ft. These upper level cusps are

extremely stable and appear in successive images at nearly the exact same pixel address.

When the two systems are connected, the spacing remains at approximately 55 ft. and the

lengths combine to become approximately 35-40 ft.








The color image of the early morning on the 28th has an eerie red glow, reminding

one of the old adage, "red sky at morning, sailors take warning" (Hendrickson 1984). The

prophecy was to bode well for the cusps in this case. What appear to be large, long period

waves are visible approaching from the northwest, forming an angle of 18 22 with

respect to the shoreline. In Figure 5.12, these waves are clearly visible. In addition, it can

been seen that the lower set of cusps has been virtually eliminated, and only three small

"relict" cusps remain on the berm. The tide is high (+1.4 ft.) at this time, and it is the high

water produced by the combination of waves and tide that appear to have destroyed the

cusps. Unfortunately, wave records are not available for this day.

The cusps attempted to re-organize late in the day on the 29th as can be seen from

the periodic modification of the swash patterns in Figure 5.13. However, by the morning

of the 30th, their fate was sealed, leaving Figure 5.14 as their final record, with no visible

longshore variation in the beachface.




















Figure 5.12 November 28, 1993 Cusp Destruction Due To High Tide and Oblique
Waves




























Figure 5.13 November 29, 1993 Attempted Cusp Reorganization


Figure 5.14 November 30, 1993 The End of A Cuspated Era.











Figure 5.15 presents the wave heights from the instrumentation as seen in Figure

2.5, modified to include the times during which cusps were evident. The cross-hatched

areas represent these times. From this chart, it is evident that there no cusps when the

wave heights exceeded approximately 0.8 ft. Figure 5.16 presents the wave periods,

cross-hatched with the visible cusp days. A correlation is not as apparent from this data.

It should be noted that the extremely stable period of cusp development from November

20 -27 is not shown, due to lack of wave data.


Wave Height and Cusp Description


10
9
8
.P 7
6
5


3
2



00000000 0 00000000 000 00000


Date Time


Figure 5.15 Wave Height and Cusp Description










Wave Period and Cusp Descritption


15 --
14 -
13
12
S11
S 10

7
6

4 -
3
2 innin nnin. mm,
0000000000000000000000000000o
00 0 0 0 000000 00 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 0 0-- :N!t'^ W -i 00 a,0 N Mw -tr'n "o r- 00 a, 0 N !t

Date Time


Figure 5.16 Wave Period and Cusp Description


In summation, it can be said that the formation of cusps began at LBK after the

high water from the October storm had receded, leaving the beach face planar and with a

consistent slope. This is in agreement with the description provided by Antia (1992), who

noted that cusps tend to form during the transition from high to low energy wave

conditions. The cusps formed sequentially in most cases, often in small groups of similar

number and size, although cases were noted in which significant cusp formation occurred

in the hour between successive image recordings, leading the observer to believe that the

formation was simultaneous. The equilibrium state of the cusps in terms of spacing was

extremely regular, with the average standard deviation being less than 10 % of the actual

spacing. The lengths, however, were more variable, and appeared to be a function of the

tide. At high tide, the lengths were shorter, and at low tides, the receding water seemed to








draw the cusps seaward, extending their length. The tides did affect the spacing of the

cusps, leading one to believe that spacing is a more stable and significant parameter than

the cusp length in terms of formation mechanisms.

Wave height and period did not appear to have a direct correlation with the

spacing, as can be seen in Figures 5.17 and 5.18, although it is noted that shore-normal

waves were consistently present in the formation phase of the cusp systems. The scale of

the plots should be noted, as the cusp spacing at steady state only varies from 51.0 to 55.0

ft. It is not known if this small variability is masking a correlation between the spacing

and/or the wave height and period. The action of waves in the destruction of the cusps,

however, is more clear. As can be seen in Figure 5.15, the cusps were not present when

the wave height exceeded approximately 0.8 ft. In addition, oblique waves tended to

modify the cusp dimensions in one of two ways. The first was the simple destruction of

the cusps if the waves were of sufficient height. The second modification occurred when

the oblique waves were not of sufficient size to eliminate the cusps, but were large enough

to begin displacing them to the north or south. As the active cusps were modified at

higher tide levels, they were merged with the relict cusps at the berm. As the tide receded,

the cusps formed a single system, with a spacing midway between the previous spacings of

the systems, and lengths equal to the sum of the previous lengths. In situations where the

cusps were destroyed, cusps reformed in locations that corresponded to the same pixel

address on the images. It is believed that small differences in beach face levels,

indistinguishable from the images, remain, aiding in the rapid development of cusps at the

same location as their ancestors.











Cusp Spacing vs. Wave Height


0.80

0.75

0.70-

0.65

0.60

0.55

0.50

0.45
50.00


56.00


Cusp Spacing vs. Wave Period


51.00


52.00 53.00 54.00 55.00

Cusp Spacing (ft.)


Figure 5.18 Cusp Spacing vs. Period


56.00


51.00 52.00 53.00 54.00 55.00

Cusp Spacing (ft.)


Figure 5.17 Cusp Spacing vs. Significant Wave Height


.. .



*






0


9 -


8.5


8


7.5


7-


6.5


6-
50.00


()~ *** *** ~


I I I I I


I I I I I








Although atypical circulation patterns were observed in the well-developed cusps,

the typical circulation pattern, with the uprush on the horns and the backrush in the bays,

was by far the most prevalent. In general, the circulation within the cusps appeared to be

of low energy, with very little visible white water.

Other factors influencing the formation of the cusps can be inferred from the

images, although they are not directly measurable. The lack of whitecaps and limited

motion in the treetops indicates that wind was not a factor in the cusp development.

Similarly, formation theories based on seaweed/floatsam, intersecting waves, rip currents,

and/or berm breaching can be discounted in this instance, as none of these items appeared

in the images. Analytical investigation into the theories based on edge waves, swash

mechanics, material differences on the beach face, and wave form are considered in the

following section, as is the depositional vs. erosional nature of the cusp formation.




5.3 Cusp Formation Analysis

This section will examine several of the major cusp formation theories and asses

their applicability to the cusps observed at LBK using the results from VMS and wave

instrumentation.


5.3.1 LBK General Parameters

As previously stated, October storm surge resulted in a smooth beach face with a

consistent slope of approximately 1:15 (f = 3.80) from +2.5 NGVD to -2 NGVD. The

long-term average tidal pattern is semi-diurnal, with a range of 1.7 ft. During November

1993, the maximum tidal range was 3.3 ft. and characteristics of both diurnal and semi-








diurnal patterns. The twenty year wave hindcasts from the USACOE Wave Information

Study (WIS) indicate a mean significant wave height of 0.8 feet and a mean peak period of

4.8 seconds at WIS station 41. (Hubertz and Brooks 1989) From the wave data given by

Stubbs (1995) during the month of November 1993, the average wave height (Hs) was

equal to 0.76 ft., and the average peak period (Tp) was equal to 6.42 s. The average

depth at the instrument site is 18.0 ft. The results of all background calculations are

summarized in Table 5.1 at the end of this section.

Using linear wave theory, (Dean and Dalrymple 1991) the dispersion relationship

between the wavelength and period of a wave is given by:

2 = gktanhkh (5.1)

where ao is the frequency, g is the acceleration due to gravity, and h is the water depth.

The wave number, k is given by k = 2r /L, with L being the wave length. Rearranging,

the wavelength can be expressed as a function of the period I and water depth h as:

L=- T2 tanh( h) (5.2)
2r L

For the measured waves in November, using h = 18 ft., and TP = 6.42 s, The wavelength

is equal to 113.1 ft..

The deep water characteristics of the waves can be calculated from conservation of

energy considerations, assuming normally incident waves, with: (Dean and Dalrymple

1991)


EoCgo = ECg


(5.3)








where E is the total average energy per unit surface area of the wave and Cg is the group

velocity of the wave train. The o subscript indicates deep water characteristics. The

energy can be calculated using:


E pgH2 (5.4)
8

where p is the water density, and H is the wave height. The offshore and breaking wave

information was calculated using both the significant wave height (Hs) and the average

wave height (H) from the November data. The relationship between the two is: (Dean

and Dalrymple 1991)

H= 0.612Hs (5.5)

The breaking wave characteristics can be calculated using the Conservation of Energy

equation previously given, along with the relationship between breaking wave height and

water depth:

H, = KhB (5.6)

where the B subscript denotes breaking conditions and c is an empirically derived

constant with a value equal to 0.78.

The reflectivity of the beach was evaluated using both the significant and average

wave heights at the instrument for the November data with the formula given by Wright

and Short (1983) as:

H(27 / T)2
E = = 6.74H (5.7)
g(tan/)2








Using the significant wave height, the reflectivity parameter is 0.81. Using the average

wave height, the reflectivity parameter is 0.51. Both values indicate a reflective beach,

found by Antia (1992) to be conducive to cusp formation.

Kaneko (1985) specified that wave breaking type dictated cusp formation, and that

this formation was likely when:

Hb /(tanl)gT2
For the breaking wave height based on the significant wave height at the instrumentation,

this value is 0.0050, and for the average waves, this value is 0.0034. Both of these values

are well below 0.042, indicating that cusp formation should be likely.

The surf similarity parameter is defined by Battjes (1974) as:

tan/? 0.96
o -(5.9)


Using the average significant wave height, the surf similarity parameter is 1.0, and the

value using the average wave height is 1.28. These values indicate plunging and/or

collapsing breakers with a breaking index between 1.1 and 1.2, and 0 1 wave in the surf

zone.

All of the background values discussed are summarized in Table 5.1. Calculations

were made based on both the significant wave height, and average wave height for

November, 1993.










PARAMETER SIGNIFICANT AVERAGE
Beach Slope = 3.8 f= 3.80

Wave Height at Instrument Hs = 0.757 ft. HAV= 0.470 ft.
Depth of Instrument h = 18.0 ft. h = 18.0 ft.
Peak Period Tp = 6.42 s Tp = 6.42s
Angular Frequency o = 0.133 Hz o = 0.133 Hz
Shallow Water Wave Length L= 113.1 ft. L= 113.1 ft.
Shallow Water Wave Number k = 0.0556 ft' k = 0.0556 ft-1
h/L @ Instrument 0.159 (Shallow) 0.159 (Shallow)

Shallow Water Celerity C = 24.07 ft/s C = 24.07 ft/s
Deep Water Wave Length Lo = 211.0 ft. Lo= 211.0 ft.
Deep Water Celerity Co = 32.87 ft./s Co = 32.87 ft./s
Deep Water Group Speed Cg = 16.43 ft./s Cg = 16.43 ft./s
Deep Water Wave Height Ho = 0.92 ft. Ho = 0.57 ft.
Wave Breaking Depth hB = 0.57 ft. hB = 0.40 ft.
Breaking Wave Height HB = 0.46 ft. HB = 0.30 ft.
Reflectivity Parameter 6 = 0.81 e = 0.51
Reflectivity Classification Reflective Reflective
Kaneko's Parameter 0.0050 0.0034
Surf Similarity Parameter = 1.00 = 1.28

Surf Characteristics Plunging Plunging


Table 5.1 Background Wave Characteristics








5.3.1 Edge Waves

The formation of cusps through the mechanism of edge waves has been supported

by Bowen and Inman (1969), Komar (1973), Guza (1975), Kaneko (1985), and Paton

(1993) through both field observations and laboratory experiments. Edge waves can be

described as waves trapped at the shoreline by refraction or reflection. They can exist as

either standing or progressive waves with maximum amplitudes at the shoreline,

exponentially decaying toward deep water. The energy of an edge wave can only be

dissipated through friction or interaction with other waves, and can not radiate offshore.

The consensus opinion of these authors is that the cusps form as a result of the sinusoidal

variation in the run-up created by the edge waves. In this scenario, the horns are formed at

edge wave nodes, and the bays at the edge wave anti-nodes where the excursion is the

greatest. The cusp spacing, therefore, is a function of the wavelength of the edge waves.

Guza and Inman (1975) define the maximum and minimum wave heights that can

lead to edge wave excitation in the surf zone. As modified by Paton (1993), the maximum

wave height is defined as:

gi2 tan2 f
H. = J2 t = 0.59 ft. (5.10)


where T, is the incident wave period. For the conditions at LBK, with T, = 6.42s and f/

= 3.8, the maximum wave height is found to be 0.59 ft. This is close to the wave height

of 0.8 ft. noted in Figure 5.16. When the wave heights exceeded this value, no cusps were

present. The minimum wave height for edge wave excitation, as modified by Paton

(1993), is:








vT
HN = 10.2(-L) (5.11)


where v is the kinematic viscosity, equal to 1.51E-5 ft2/s. The minimum wave height for

edge wave excitation at LBK is 0.06 ft.

Edge waves can exist in several modes (n), where the mode indicates the number

of zero crossings of the amplitude in the offshore direction. An edge wave of mode n = 0,

simply decays exponentially away from the shore, with an amplitude approaching, but not

crossing zero. An edge wave of mode n = 1 contains a single zero crossing in amplitude

directed away from the shore. These modes, n = 0 and n = 1, are the modes considered to

be the most influential in cusp development by Guza and Inman (1975), due to damping of

the higher mode edge waves by friction in the surf zone.

In addition to the two edge wave modes, there are two distinct types of edge

waves, distinguished by differences in period, described in the literature as being

conducive to cusp formation. The first type is a synchronous edge wave. Synchronous

edge waves have periods equal to those of the incident waves. The second type is a

subharmonic edge wave, with a period equal to twice that of the incident waves. All types

of edge waves of all modes have wave lengths described by:

L = g T2 sin[(2n + 1)/] (5.12)
27r

where the e subscript denotes the value of the edge wave, and n denotes the modal

number (Guza and Inman 1975). From this, four distinct wave length equations relating

the incident wave period to the edge wave length can be generated, as follows:









* Synchronous (Te = Ti) edge wave, mode n = 0


* Synchronous (Te = Ti) edge wave, mode n = 1


* Subharmonic (Te = 2 Ti) edge wave, mode n = 0


* Subharmonic (Te = 2 Ti) edge wave, mode n = 1


L, = T2 sinf
2K


L, =g T2 sin 3,
2g



L, 2g sin f

L, = 2g 2 Sin 3


From the wave data presented by Stubbs (1995), the incident period has a

maximum of 9.8 s and a minimum of 3.3 s, with an average over the month of November

at 6.42 s. The twenty year hindcast wave data has an average of 4.8 s. Table 5.2 presents

a summary of the possible edge wave lengths for all of the reported wave periods at LBK.

Table 5.3 summarizes the possible cusp spacing due to the edge waves, as given by Guza

and Inman (1975) to be 1/2 of the edge wave length.


Edge Wave Lengths at LBK

Wave Period Synchronous, Synchronous, Subharmonic, Subharmonic,

(s) Mode n = 0 Mode n = 1 Mode n = 0 Mode n = 1

(ft.) (ft.) (ft.) (ft.)
3.3 3.70 11.03 14.79 44.12
4.8 7.83 23.34 31.30 93.35
6.42 14.0 41.75 55.99 167.00
9.8 32.62 97.28 130.48 389.13


Table 5.2 Edge Wave Lengths at LBK










Cusp Spacing Due to Edge Waves at LBK

Wave Period Synchronous, Synchronous, Subharmonic, Subharmonic,

(s) Mode n = 0 Mode n = 1 Mode n = 0 Mode n = 1
(ft.) (ft.) (ft.) (ft.)
3.3 1.85 5.52 7.40 22.06
4.8 3.92 11.67 15.65 46.68
6.42 7.00 20.88 28.00 83.50
9.8 16.31 48.64 65.24 194.57



Table 5.3 Cusp Spacing Due to Edge Waves at LBK



From these calculations, it can be seen that edge wave theory is capable of

predicting cusp spacing at LBK ranging from 1.85 ft. to 194.57 ft. Indeed, this is one of

the attractions of the theory. The average spacing reported from the images ranged from

32.7 ft. to 57.7 ft. From this perspective, the formation theory based on edge waves

covers the range of spacings observed, although there is not an obvious type or mode of

edge wave for a given period that provides a direct correlation. To define the type and

period of edge wave thought to be capable of forming the LBK cusps requires further

investigation.

The initial set of cusps were formed between the last image on November 2nd

(1700 hrs.) and 1200 hrs on November 3. The cusps were actively forming throughout

the rest of the day on the 3rd, and continued through the 5th. The first cusps visible had a

spacing of 32.7 ft. and their average spacing in their well-developed form was 38.8 ft, with








an average length of 17.0 ft. An inspection of the wave data indicates that the average

wave period over this interval is 6.21 s with a standard deviation of 1.73 s. The spacing

predicted by edge wave theory for a subharmonic edge wave of mode n = 0 is 26.2 ft.

This type and mode of edge wave provides the closest spacing prediction to the observed

value, and is also the edge wave most commonly associated with cusp formation (Guza

and Inman 1975, Kaneko 1985, Paton 1993). The difference between the predicted and

the observed cusp spacing in their well developed state is nearly 50%.

After the cusps were temporarily eliminated on the 7th, the cusps reformed with a

spacing of 37.7 ft. on the 9th. They would eventually grow to a spacing of 44.9 ft. on the

10th and 11th, and to a final spacing of 54.6 ft. on the 13th and 14th. A very stable era

for the cusps through the 19th of November followed. The average cusp spacing

observed over this period was 53.2 ft. A detailed hourly analysis of observed cusp spacing

vs. that predicted by a subharmonic edge wave of mode n = 0 was performed and the

results appear in Figure 5.20.






83



Nov 17 19, Cusp Spacing Comparison, Observed vs Subharmonic
Edge Wave (n=0) Prediction
60
Observed Spacing (Avg. = 53.16 ft.)
55 ._

S50

45 Predicted Spacing (Avg. = 38.86 ft.)
S 45

40
x-x-x-x-x-x-x-x-x-x-x-x-x-
35
350 ----X---X--X--X--X--X-X

30
o 0 0 0 0 0 0 0 0 0 0 0
o 0 0 0 0 0 0 0 0 0 0 0



Date Time


Figure 5.19 Nov. 17 19 Observed vs. Predicted Cusp Spacing


As can be see in Figure 5.19, edge wave theory does not accurately predict the

cusp spacing or the changes in cusp spacing observed at LBK for steady-state cusps.

An additional aspect of edge wave theory can be investigated using the images

from LBK. According to the theory as described by Dean and Dalrymple (1995), "the

edge wave motion permits the incident water to run up in every other cusp per wave

period. This alternating run-up at the alternating frequency is not often observed in

nature." (p. 266) Indeed, in all of the images recorded at LBK, this pattern was never

observed. Figure 5.20 presents the run-up pattern most commonly observed.


































Figure 5.20 Typical Backrush Pattern in Each Bay





5.3.2 Swash Mechanics

Various relationships between the swash excursion and cusp spacing have been

advanced by Longuet-Higgins and Parkin (1962), Dean and Maurmeyer (1980), and

Werner and Fink (1993). As defined by Dean and Dalrymple (1995), the swash zone is

the "region on the beach face delineated at the upper level by the maximum uprush of the

waves, and at the lower extremity by the maximum downrush." (p. 118) With cusps

present, this region on the images is calculated from the difference between the point

where the incoming waves break on the shore, and the average of the uprush on the horns








and bays. Table 5.4 presents the maximum swash excursions scaled from the rectified

images for November 1993.


Table 5.4 Observed Swash Excursions



The linear relationship given by Longuet-Higgins and Parkin (1962) can be

rearranged to yield:


S= 2 0(Y)4x + 5.97


(5.13)


where A is the cusp spacing and ,y is the swash length in the onshore direction. The

units of this equation are in feet.

Dean and Maurmeyer (1980), present an idealized cusp topography model

combined with frictionless water particle trajectory considerations to yield a simple

analytical prediction of cusp spacing, A, in terms of the swash excursion ( ) max. The

following linear relationship was developed;


DATE TIME SWASH
EXCURSION (ft.)
11/3 1252 20.7
11/9 1300 25.9
11/10 1401 29.7
11/13 1111 28.2
11/16 1103 30.8
11/17 1203 25.0
11/22 1801 26.3
11/27 1302 27.5








A 3.9 ( 5 ,) (5.14)

where 6 describes the cusp geometry such that;

hH -h
6= hB (5.15)
(hH + hB)

where h represents the heights of the horns (H) and bays (B) from a given datum. This

relationship can be modified for use with rectified images to read:

YH
e=-- (5.16)
1+YH
YB

where Y is the cross-shore distance between the waterline and the horn (H) or embayment

(B). For the images reviewed at LBK, this value is 0.211, so that a linear relationship

between swash length and cusp spacing can be derived, such that:

A = 1.79~, (5.17)

where A represents the steady state cusps spacing and ry is the swash excursion.

An additional relationship between cusp spacing and swash excursion comes from

the computer simulation work done by Werner and Fink (1993) in developing their self-

organization theory. Cusp spacing is found to have a linear relationship with swash

excursion such that:

Aso = 1.7 y (5.18)

where Aso represents the steady state cusps spacing and r, is the swash excursion.





87



Observed vs. Predicted Cusp Spacing Based on Swash Length


^z z

Date


Figure 5.21 Observed Cusp Spacing vs. Swash Mechanics Theory


Figure 5.21 presents a comparison of the various cusp spacing predictions based

on swash length and the observed spacing for several days. The relationships are labeled

with the initials of their authors. It can be seen that the observed spacing is not exactly

predicted by any single relationship, however it is encapsulated within the envelope of all

of the techniques. The relationship between the average cusp spacing and the average

swash length is given by the formula:

A = 1.85(r) (5.19)

which is between the values given By Longuet-Higgins and Parkin (1962) and Dean and

Maurmeyer (1980).








5.3.3 Additional Mechanisms

Material differences on the beach face form the basis for theories on cusp

formation and spacing presented by Johnson (1910), Butler (1937), Kuenen (1948), and

Longuet-Higgins and Parkin (1962). As previously stated, the cusp formation at LBK

occurred approximately five months after a beach nourishment project was initiated. The

sediment characteristics of the nourishment and the native materials are presented in Table

5.5 (Stubbs 1995). The lack of significant variation in these parameters leads to the

conclusion that material differences are not the mechanism behind the cusp formation at

LBK.


Location Mean Diameter (mm) Sorting (0o)
Longboat Pass Borrow Site 0.19 0.78
Native North Beach 0.21 0.57
New Pass Borrow Site 0.22 1.52
Native South Beach 0.19 1.20


Table 5.5 LBK Nourishment Material Characteristics



Cloud (1966) notes that cusps tend to form on a beach that has been steepened by

a period of increased wave activity, as may be the case at LBK. This steepened beach

would tend to create plunging breakers (Refer to Table 5.1) directly on its face, which

would essentially simulate a cylinder. The cusps could be the result of the separation of

this unstable cylinder, as given by Plateau's Rule. The segmentation to diameter ratio

predicted in such a case varies from 15.5 to 16.7, corresponding to the ratio between








height the cusp spacing and the wave breaking height. At LBK, the average cusp spacing

is on the order of 50 ft., and the significant wave height averages 0.46 ft. The resulting

ratio is on the order of 100. As the observed values are nearly full order of magnitude

different than Cloud's hypothesis, it must be discounted in this case.

The question of the erosional or depositional nature of the cusp formation poses an

interesting problem when using the image data set from LBK. An examination of the

monthly dry beach width summary in Figure 3.1 indicates that November was a period of

steady beach width loss, implying that the cusps formed during an erosional era in the

beach equilibration. The monthly summary of dry beach width including the storms

(Figure 3.2), however, indicates that the initial cusp formation occurred during a period of

extremely rapid accretion on the beach face. It should be noted at this point that the

measurements of linear beach width do not necessarily represent the volumetric changes in

the amount of material available to the nearshore system. These measurements more

accurately reflect the equilibration of the beach profile to the changing environmental

conditions. It is the author's opinion that this evidence is not as contradictory as it may

seem, due to the difference between the volumetric and linear measurement of erosion and

accretion. The scenario may be as follows. The October storm removed large amounts of

sand from the beach face and deposited it on the nearshore bar, as can be gleaned from the

profile survey in Figure 5.3. The cusps were then formed during the massive redeposition

of the material from the sand bar on to the beach face, corresponding to the peak of the

dry beach width curve in Figure 3.2. If the profile were in equilibrium at this point, the

amount of sand transported to the beach face from the sand bar would be negligible,

forcing the horns of the cusps to utilize another source of sand to continue to build. This








source could be the eroded sand from the bays, recirculated to the cusps after successive

waves. If the deposition on the horns was larger than the erosion from the bays, profile

would be steepened on the average, resulting in reduced dry beach width, even during a

period of volumetric accretion on the horns. In this scenario, the excess sand deposited on

the horns comes from the upland portion of the bays. In summary, the formation of beach

cusps is a balanced function of local erosion and deposition, that can occur during various

phases of general volumetric erosion or deposition.




5.4 Toward a Formation Theory



From the description of the formation of cusps and the analytical investigations in

to the prediction of their spacing, a formation theory must surely be drawn. Cusps formed

at LBK after a storm had created a planar, reflective beach of shallow slope. The waves

present during formation were shore-normal, and had relatively small heights and varying

periods. Circulation within the cusps consisted of an uprush on the horns and a backrush

in the bays. Uprush and downrush was concurrent in adjacent respective horns and bays,

as opposed to alternating. Cusp spacing was best predicted by swash length relationships.

Cusp destruction came about as a result of oblique and/or unusually large waves. The

formation of cusps is a balanced erosional/depositional process.

One of the keys to cusp formation that has not been adequately addressed thus far

is the sequential nature of the formation. In nearly every case at LBK, the cusps formed

from a central location and proceeded outward, growing in length and number, until an








equilibrium was achieved. It is this growth, accompanied by the contradiction in

circulation pattern and that the lack of predictive capability for LBK that eliminates edge

waves from being a viable formation mechanism. If standing edge waves were present,

why didn't the formation occur in all cusps at the same time? If progressive edge waves

were present, why did the cusps form in both directions from the center? In addition, as

the incident edge waves vary in period, why don't the equilibrated cusps cause visible

destructive interference with edge waves of different wave lengths?

Unfortunately, swash mechanics theories are also incomplete. These theories are

easily applied to cusp systems in equilibrium, but they do not provide for an initial

formation mechanism. That is, what initially created the swash patterns and periodic

variability in the swash? Variations in the longshore profile of the beach provide a starting

point for these theories, but don't provide a reason for the sequential development from

cusp to cusp or for the cusps' regular spacing.

Perhaps a solution lies in the combination of these theories, as edge waves could

provide the initial periodic variation in swash patterns which evolve into steady-state

nearshore circulation system with a spacing predicted by swash length. In this scenario,

edge waves are trapped in the nearshore zone by the reflected waves and result in periodic

disturbances in the longshore run-up distances. These disturbances are further varied by

differences in longshore elevations, causing cusplets to develop in certain areas before

others. As the sand is re-arranged by this variable swash, nearshore circulation patterns

are generated by the constructive and destructive interference ofuprush and backrush

timing with incident waves. This constructiveness vs. destructiveness is a function of the

wave period, wave height, and the longshore location. Areas where the uprush has a








maximum velocity become the horns, as sediment is deposited as the uprush decelerates.

When it decelerates to zero velocity, it become backrush and returns to the sea, scouring

out the bays. At all times, the cusps are striving to form into equilibrium sizes, based on

the regular dissipation of the various energies present within the system. As the cusps

form, their spacing "outgrows" that predicted by edge wave lengths, and becomes

dominated by the swash length, as it represents the summation of the various energetic

influences. The sources for the energy within the system include gravity, tides, friction,

and waves and can exist independently or in a coupled fashion.













CHAPTER 6


SUMMARY and CONCLUSIONS




6.1 Summary



The VMS installed at the Longboat Key beach nourishment project remained in

continuous operation for 14 months with minimum maintenance, while producing

extensive amounts of visual data and serving as a backup to the other monitoring

instruments and techniques. As a supplement to regular surveys and aerial photography,

the VMS provides increased amounts of spatial and temporal coverage of both the beach

and the nearshore environment. Similarly, the VMS provides a visual confirmation of any

large or unusual wave data readings for the in-situ instrumentation. Images were recorded

on an hourly basis during all daylight hours, in all weather conditions.

The employment of rectification techniques transforms the system capabilities from

descriptive to analytical, as the rectified images can be used to scale distances and angles.

This provides for a powerful combination of information, capable of documenting beach

morphology and changes accurately, in real time, and from a remote location. In fact, the

analysis presented here was actually a by-product of the original goal of the VMS

deployment, namely the nearshore turbidity monitoring associated with the LBK

nourishment project. The remote capability of the VMS and the permanence of the image








storage system on CD allow for analysis to continue after the completion of the project at

any location with a PC or VCR. It should be noted that the work presented here was

performed almost a year after the end of the VMS deployment without the author having

set a foot on the beach at LBK. The only data used that was manually collected was the

beach profile survey. (Figure 5.3)




6.2 Conclusions



Some of the most useful and applicable data to coastal engineering studies

obtained by the VMS concern the profile and planform evolution of the project as

indicated by the changes in dry beach width. The VMS recorded 3575 images of scene 1,

all of which were reviewed and contributed to the over-all picture of the evolution of the

nourishment project at LBK. From the monthly summary chart of the dry beach width,

(Figure 4.1) several major conclusions can be drawn.

* The initial project sediment placement represents a significant increase in the original

dry beach width. This is manifested in the charts as the large peak in beach width

between May and June 1993.

* The over-all slope of the plot is negative, that is, the beach is decreasing in width. The

rate of loss however, is reducing as a function of time, indicating the approach to

equilibrium, and the stabilization of the beach.




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