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Beach cusp analysis and the dry beach evolution of Longboat Key, Florida, using video monitoring techniques

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Title:
Beach cusp analysis and the dry beach evolution of Longboat Key, Florida, using video monitoring techniques
Series Title:
UFLCOEL-95014
Creator:
Sloop, Robert V
University of Florida -- Coastal and Oceanographic Engineering Dept
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Gainesville Fla
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Coastal & Oceanographic Engineering Dept., University of Florida
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English
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v, 104 p. : ill., map ; 28 cm.

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Subjects / Keywords:
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 )
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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.

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University of Florida
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University of Florida
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All applicable rights reserved by the source institution and holding location.
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34549212 ( OCLC )

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 OF FIGURES ............................................................................................................................... iii
CHAPTER 1 ............................................................................................................................................ 1
INTRODUCTION ..................................................................................................................................... 1
1. 1 O bj e c tiv es ....................................................................................................................................... 2
CHAPTER 2 ............................................................................................................................................ 4
LITERATURE REVIEW .......................................................................................................................... 4
2. 1 Photographic M onitoring Techniques and M easurements ............................................................... 4
2 .2 B ea ch C u sp s ................................................................................................................................... 9
CHAPTER 3 .......................................................................................................................................... 34
DATA COLLECTION ............................................................................................................................ 34
3. 1 The Video M onitoring System ....................................................................................................... 34
3.2 DeploymentlData Description ....................................................................................................... 36
3.3 Related Deployments .................................................................................................................... 41
3.4 Project Background and In Situ M onitoring .................................................................................. 42
CEL4,PTER 4 .......................................................................................................................................... 47
DRY BEACH EVOLUTION ................................................................................................................... 47
4.1 M onthly Summary ......................................................................................................................... 47
4.2 M onthly Summary With Storm Events ........................................................................................... 49
4.3 Rectified vs. Oblique Image Analysis ............................................................................................ 50
CELAPTER 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 E dge W aves ......................................................................................................................................... 7 8
5.3.2 Swash M echanics ................................................................................................................................. 84
5.3.3 Additional M echanisms ........................................................................................................................ 88
5.3 Toward a Formation Theory ......................................................................................................... 90
CELAPTER 6 .......................................................................................................................................... 93
SUNffvfARY AND CONCLUSIONS ......................................................................................................... 93
6 1 S u m m a ry ...................................................................................................................................... 9 3
62 Conclusions .................................................................................................................................. 94
5.3 Future Work ................................................................................................................................. 98
REFERENCES .................................................................................................................................... 100




LIST OF FIGURES

FIGURE 1. 1 CUSP NOMENCLATURE AN]) 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 IAGES 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 of nearshore 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 I

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.

L ~

- ....- .,.

'Si




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 3 5 -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. 68 1) Using a camera on a 8 rn bluff, they found the effective range to be 250 rn with an accuracy in the vertical plane to 10% and to I% 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. 13 8-13 9)




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 mn 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 purposee .., 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. Hi-s 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). H~e proposes that these boulder cusps were "formed relatively slowly by extremely selective erosion of bouldery glacial drift by swash from waves of the size that strike this beach most of the time."(p. 45 1) 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 Geolog (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. 62 1). 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.3 13) 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 Smidth and Dolan (1960). Concerning the regularity of cusp spacing, Russel and Mclntire 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-HI-ggins 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 2;'zr, 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. 28 1) 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 of cresentic 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. 1 10) 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. 3 593) 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 -gT2 Sin[(2n + 1)18]
2;r
where L is the edge-wave length, T is the dominant wave period, 83 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 onehalf 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. 113 3)
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(2'r / T) 2 (2.1)
g(tanl)2
where H is the breaker height in meters, T is the wave period in seconds, g is the acceleration due to gravity, and 8i is the beach slope in degrees. A value of -:! 2.5S indicates a reflective beach and a value of e 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, 2, in terms of the swash excursion (4:x) max The following linear relationship was developed;
2 z 3.9-j (-x)max (2.2)
which predicts cusp spacings of same order of magnitude as those observed. 86 describes the cusp geometry such that;
h= -hB (2.3)
(hH + h6)
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. 88 1) 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:
b / (tang gg 2 < 0. 042 (2.4)
where 11b is the breaker height, tan fi 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 crossshore 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, shorenormal, 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 10O-s [period] waves)." (p. 969) The resulting cusp spacing is found to have a linear relationship with swash excursion such that: Ao= 1. ,(2.5)
where A.,~ represents the steady state cusps spacing and 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 McIntire 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




I 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 M18 FX 710 with automatic
exposure control, automatic focus, variable zoom, and a polarizing filter. The use of iE8 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 11Ith floor roof The pan/tilt mechanism was a digitally controlled stepper motor with a repeatability of better than 0. 10. 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 Ccpicture" 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.




NORTH Ln
Anna Maia WAVE GAUGES (LBK 2) CAMERA LOCATION, LONGBOAT HARBOUR TOWERS Longboat
Siesta Key

Key
L.... Tampa Bay

Key

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
TIE 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.




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 I 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 21 st 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 3260 west of north, and the shore normal is 2360 (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 (2,8 10, 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-2 1 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
SD 0 0 0 0 0 0 Date Time 0 0 0 0 0
00 o0 0 0 0 0 0 0 0 0 0 0 W W 0 0 0 0 0 0 0 0 0W
Date Time

Figure 3.6 Significant Wave Heights for November, 1993




Wave Period (s)
0 0 0 0 0 0 0 0 0
D CD 0 0 0D 0 0 0D 0
10/28 800 10/29 800 10/30 800 10/31 800 11/1 800 11/2800 11/3 800 11/4800 11/5 800 11/6r800 11/7 800
11/8 800 11/9 800 11/10 800 D 11/11800 11/12 800
11/13 800 11/14 800 11/15 800 11/16 800 11/17 800 11/18 800 11/19 800 11/20 800 12/1 800 12/2 800 12/3 800 12/4 800 12/5 800




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 Summga
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 ;our lhe t6/' /93 & 400.00
350.00
250.00 X. 200.00 150.00 .
Cz
100.00 50.00
0.00
Fu 4.1 ON cn ON Dry BN ea*, ON O oly Ou m 0ar
00 t-- rl 0 W) N Mf C1 It M r~n N N
00 ccON 0 M It W) z et- N~.
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 10/30/9311/1/93, 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.

500.00
450.00
400.00 350.00 300.00 250.00
200.00 150.00
100.00 50.00
0.00

Monthly Sumimary With Stormis
December rStorm
______Maich Storm
Jan uary Strm

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




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 Sumnmay
500
450
400 r- REC'lIFr hIUAGES
350 ,
S300
250 -200 '
IODI IED OBL QUE
-150 i 8,c N N .o1 ,
100 --
50
Date
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 (10/30/93-1 1/1/93) 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 (f8 = 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 c
CUSPS
6.0
- 4.0
2.0
0.0
00 5(.0 10).0 15.0 2 25.0 30).0 350.0 400.0
-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 ,8 3.250 given by Komar (1973), and ,8 2.29' 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 (19 10), Kuenen (1948), Smith (1973), and Bodie (1974). The average spacing was 3 8.8 ft. and the average width was 17. 0 ft. During this period, there were I11 tidal cycles with a maximum range of 2.5 ft. The waves had a range of Hs 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
8.0 s.
A slight increase in tidal range, (3.1 ft.) and wave height (HS = 0.75 Tp = 8.0Os) 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 25'. 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 semni-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 of uprush 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 180 220 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.
FigureI 5.12 - oeme 28 199 Cus Detuto Du To H.g Tid an Oblique.. ..
W av s.......
............
g g 0 0 1. .... .....
...............
--------------- --".:i
Figure5.12 Noveber 2, 199 Cup Desruct.n.DueTo.Hih.Tid.and.bliqu W a..v........s




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
7
6
5
4
3
.- 2
1
o o 0 0 C0 0 0 0C0 0 0 0 In 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 o o 0 0 0D 0 0 0 0D 0 0 (0 0 0 0 0 0 0 0 0D 0M 0 0 0 0D 0 0 0 0 0 000 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 "10 Z' Q e O~ 0 0M: 4 0'' !! 2:
000
- -- - -
Date Time
Figure 5.15 Wave Height and Cusp Description




Wave Period and Cusp Descritption 15
14 13 12
-11
0
r. 9
P- 8
7
6
5
4 3
00 00 0000 000000 00 000000 00 000000 00 0000 00000000 00 0000 0000 00 00
00 C 0- c. :!! tn "D 00 C" 0 N M 't~ kn r- 00 0, 0- 7!t W) 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 5 1. 0 to 5 5. 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
Cusp Spacing (ft.)
Figure 5.18 Cusp Spacing vs. Period

55.00

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

* **** ***
* ** *** ** *




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 (f8i 3. 8') 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 seni-




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: Ur = gk tanh kh (5.1)
where u- is the frequency, g is the acceleration due to gravity, and h is the water depth. The wave number, k is given by k = 27c IL, 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- g T2 tanh(2 rh) (5.2)
27r 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 199 1)
H 0. 612H, (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:
HB = hB (5.6)
where the B subscript denotes breaking conditions and Kc 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(2;r/T2 -.4 57
g(tan 674)(.7




Using the significant wave height, the reflectivity parameter is 0. 81. Using the average wave height, the reflectivity parameter is 0.5 1. 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 / (tan3)l;' < Hb / 88.2 <0. 042 (5.8)
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/I6 0.96(59
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 8 = 3.80 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 a = 0.133 Hz a = 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 L= 211.0 ft. L= 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. H. = 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 Edgze 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:
HMX= g~i tan 2fi =O0.59 ft. (5.10)
2
where Tj is the incident wave period. For the conditions at LBK, with T = 6.42s and f8 = 3.80, 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:




HmN = T 102-= (5.11)
where v is the kinematic viscosity, equal to 1. 5 1E-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: Le= T'2 sif[(2n + 1),8] (5.12)
2;r
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 (T. = 2 Ti) edge wave, mode n = 0 Subharmonic (Te = 2 Ti) edge wave, mode n = 1

g
Le = -& T2 sin38 L = 2 sin 3,9
7C

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
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 form-ing 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 3 2.7 ft. and their average spacing in their well-developed form was 3 8.8 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 11Ith, 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=O) Prediction
60
Observed Spacing (Avg. 53.16 ft.)
50
45 Predicted Spacing (Avg. = 38.86 ft.)
.= 45
5 XX-X-X-X-X-X-rJ) 40 I
3 0 1 I ...I
o CN C 0 0 0 0
o0 0 00 0 0 00 0 0 O0
Date Time
Figure 5.19 Nov. 17 19 Observed vs. Predicted Cusp Spacing
As can be v5.19, 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:

A = 2.0( y)Amx + 5.97

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 ( )mx 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

(5.13)




A" 3. I9-- ( rm (5.14)
where 6 describes the cusp geometry such that; hH -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
= (5.16)
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 r 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 selforganization theory. Cusp spacing is found to have a linear relationship with swash excursion such that:
Aso = 1.7 r (5.18)
where Aso represents the steady state cusps spacing and is the swash excursion.




87
Observed vs. Predicted Cusp Spacing Based on Swash Length

> o 0 0 01 0 0
z, z, z,4 z
M r-.
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:
2 =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 (19 10), Butler (193 7), Kuenen (1948), and Longuet-HiFggins 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 (0)
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 of uprush 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

SUMM4ARY and CONCLUSIONS
6.1 Summar
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 platform 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.