RICHARD J. RUSSELL WILLIAM G. Mcintire Coastal Studies Institute, Louisiana State University, Baton Rouge, La. Beach Cusps Abstr

RICHARD J. RUSSELL Coastal Studies Institute, Louisiana State University, Baton Rouge, La. WILLIAM G. McINTIRE

Beach Cusps

Abstract: Beach cusps develop along seaward faces posure and state of the sea. Conditions under which of growing berms. They appear early in the transi- cusps disappear are described. Although most steps tional period of decreasing wave energy from in the depositional development and erosional winter- to summer-beach conditions. Growth stages removal of cusps are understood, the theory of their are described and related to currents within the origin will remain incomplete until the reasons for swash zone. Cusp spacing depends on coastal ex- their spacing are known in quantitative terms.

CONTENTS Introduction and acknowledgments 307 3. Number of examples in spacing of cusp apices . 311 Field observations 308 4. Beach changes related to increasing and decreas- Juvenile cusps 311 ing wave energy 315 Well-developed cusps 312 5. Sequential stages of turbidity distribution and Cusp disappearance 312 current flow associated with growing cusps 316 Toward a theory of cusp origin 313 References cited 318 Plate Following Appendix 1. Relationship between apex and bay 1. Cusps on firm beaches slopes 319 2. Juvenile cusps Appendix 2. Relationship of cusp length to de- 3. Well-developed cusps gree of exposure 319 4. Cusp erosion, Preston Beach, south of Perth, Western Australia r-316 Figure 5. Asymmetrical erosion of cusps, Dominica . . . 1. Section across three series of cusps: Cluny, Basse 6. Cusp-originating processes Terre, Guadeloupe 309 7. Current flow into bays, Warnbro Sound, south 2. Comparison between bay and apex slopes . . . 310 of Safety Bay, Western Australia

ment and formulating opinions about their INTRODUCTION AND histories, we turned to the literature, usually ACKNOWLEDGMENTS finding confusion at least as great as our own Our beach-cusp observations started in the during initial stages of investigation. Without West Indies in 1956 and subsequently were exaggeration, practically every idea concerning extended to the coasts of all the continents cusps advanced by one author is directly con- excepting Antarctica, with greatest concentra- tradicted by that of another. The inadequate tion centered on tropical and southern-hemi- theories of origin advanced by Branner, sphere beaches. The main objectives of field Cornish, Jefferson, Johnson, Kemp, Lane, work were investigations of beach morphology, Shaler, and Wilson have been reviewed in beach rock, and eustatic changes of sea level, practically all American beach cusp literature. and the relating of coastal characteristics to Rather than retracing familiar paths we will lithology and structural deformation. We ob- restrict our reference comments to contri- served beach cusps on so many occasions that butions that we consider particularly interest- we decided to record their characteristics in ing or instructive. quantitative terms and to collect sediment Palmer (1834) noted the ability of waves to samples, in the hope that we might learn how drive loose material up a beach and observed cusps originate. In some cases, mainly in the the winnowing effect of backwash. He esti- West Indies and Western Australia, we re- mated that if 10 or fewer breakers arrive per turned to familiar locations during opposite minute shingle accumulates, but with more seasons to make comparative studies. than 10 breakers per minute the beach starts After studying 84 examples of cusp develop- washing away. He noted (p. 572) that after

Geological Society of America Bulletin, v. 76, p. 307-320, 5 figs., 7 pis., March 1965 307

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 308 RUSSELL AND McINTIRE—BEACH CUSPS

having "struck" pebbles upward, . . . "waves monly destroy cusps. He also emphasized wider instead of returning in dispersed and weakened cusp spacing as resulting from higher waves. form, moved back in columns, which were of Our field work, in connection with Coastal sufficient power to return every pebble that Studies Institute projects, was supported fi- had been thrown up." A succession of waves nancially by the Geography Branch, Office of caused slight depressions that increased in size Naval Research (Project No. Nonr 1575 [03], to localize continuous channels. Having broken, Task Order No. NR 388 002). the waves . . . "are again collected and returned through the channels, and remove all loose FIELD OBSERVATIONS material from them." Between the channels a Horns of cusps consist of softer deposits than series of parallel "banks" (p. 573) developed. occur in the bays between them. Pits dug in Although this is probably the earliest statement freshly formed cusps are likely to reveal con- concerning beach cusp origin, Palmer's considerable interstitial water. Cusps commonly tribution contains a greater number of per- display coarser sediments (in many cases gravel tinent observations than appeared during the or shell fragments) than those on bay floors. succeeding century. Even where beach deposits appear to be quite Kuenen (1948) emphasized the depositional homogeneous, mechanical analyses of samples origin of cusps, noting that the horns com- ordinarily reveal coarser sizes in the horns. If monly are composed of deposits that differ many beaches are examined which are com- from those of beaches upon which they rest. posed of a wide variety of materials, and cusps Guilcher (1949) advanced a theory of origin are observed in various stages of development that differs but little from our own conclusions. and dissipation, it becomes evident that cusps Boye (1954), influenced by Cailleux, correctly are deposits on pre-existing beaches. observed contrasts which he regarded as indi- Cusps appear and disappear within the low cating that horn deposits are "sea-sorted," zone of frequent wave uprush, toward the whereas those in bays between exhibit com- upper limits reached by the swash. Those shown posite "fluvio-marine" sorting. in Figure 1 of Plate 1 appeared overnight along Bagnold (1940), in spite of the fact that a beach sheltered by a reef flat 200 yards wide many writers maintain that tidal influences are on West Island of Cocos-Keeling Atoll. On the involved in cusp formation, presented an ex- preceding evening the low beach consisted of cellent description of their development west fine, calcareous sand which was hard and of Alexandria, Egypt, in the nearly tideless smooth. After a night of moderate but un- Mediterranean. Their spacing averaged 12 m; spectacular wave activity 12 cusps were present. apices of horns sloped seaward at an angle of Each was composed of coral gravel, with frag- 14°, whereas in adjacent bays the slope was ments up to 6 inches in length. Cusp bases only 3°. He noted further that the step line, merged into a fairly continuous depositional where waves break, was unindented. Possibly berm consisting of similar deposits. The tide more effectively than any other observer, he was high, and most of the reef flat was covered described water motions in which the surge of when the picture was taken. A short distance waves piles up quickly toward a cusp apex, below the water's edge gravel similar to that in then divides into streams leading toward adja- the cusps and berm was exposed along the step. cent bays, where the flow attains such down- Berms and cusps of this kind, as well as much slope momentum that surges proceeding di- larger ones, commonly form and may disappear rectly into bays are headed off. Flow down the within a few hours. Their surfaces eventually "hollow" had greater intensity than the op- may culminate in a summit flat, which composed wave uprush. He also noted that, whereas monly exhibits some backslope. the uprush and backwash of waves on a straight Cusps develop in a wide variety of beach beach are separated by a "dead" position, deposits. Examples included in our observations where "sand is at rest," the flow of surges up were distributed percentagewise roughly into cusp apices continues without interruption the following size categories: boulders, 12 per down the slopes leading into bays and back cent; gravel or coarse grit, 16; extremely soft, toward the sea (p. 46). coarse sand, 24; soft medium sand, 40, and Shepard (1963, p. 201) correctly contra- relatively hard fine sand, 8. Petrologic composi- dicted the views of some writers, in observing tions ranged from basalt or other rocks to that diagonal wave approach is inimical to cusp nearly pure shell fragments, including the development, and that longshore currents com- mineral spectrum from black, heavy, ilmenite-

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 FIELD OBSERVATIONS 309

or magnetite-rich sand to white, light, cal- of a new berm is determined. If wave heights careous, organic sand. A bias toward higher have been exceptionally large the new cusps gravel or shell content and poorer sorting than will form high on the upper beach and will be in adjacent bay deposits depends both on dep- widely spaced. ositional processes and the type of material Two levels of cusps may be seen quite com- exposed along the nearby step. When cusps monly, in some cases three or more may be wash away, the sediment may be carried some observed. The spacing between their apices distance offshore, but in most cases coarser invariably is shortest in the lowest series. An materials are soon worked back to the step example of three series was instrumentally zone. surveyed at the west end of the long beach at The literature about beaches ordinarily Cluny, on the northern shore of Basse Terre, stresses contrasts between winter and summer Guadeloupe (Fig. 1). The thickness of deposits characteristics, and indeed the differences are in series designated as I, II, and III is indicated striking. A summer beach typically is higher by shading. The dashed line is an estimated

III

Level Vert.Exag. 5x Figure 1. Section across three series of cusps: Cluny, Basse Terre, Guadeloupe

and wider and displays finer sediments. The beach profile, based on observations in adjacent high, steep-fronted waves of winter commonly bays. One interesting feature shown in the sec- reduce greatly the volume of exposed beach and tion is slight convexity a short distance down- produce low-level flatness. The flats of a winter slope from the apical termination of each cusp. beach ordinarily exhibit residual concentrations These demonstrate the validity of Bagnold's of coarse material. (1940 p. 30-31) idea that a beach consists of While beach characteristics vary appreciably two concave elements separated by a convexity between extreme seasons, tendencies toward just above the step, at the closest breaker line. developing a summer or winter condition ap- The concave element above the step was called pear on lesser scales at any time of year. These the upper beach, and that below, the lower depend on changes in the state of the sea associ- beach. This simple terminology should come ated either with local variations in windiness or into wider use as it has greater genetic merit the arrival of swell from distant areas of storm than more common attempts to formalize activity. Within a few hours there may be con- beach taxonomy, most of which are difficult siderable expansion or reduction in visible beach to apply. The three series of cusps shown in the area at mid-tide. Cusps may form or be washed figure were on the upper beach at the time of away during alternations between these tenden- survey, but such was not the case throughout cies. A somewhat persistent increase in wave their histories. When cusps of series III were height and steepness may result in removing formed, the step was not far below their apices, large volumes of sand, together with surface just seaward from the associated convexity. forms such as cusps and berms. Later on, as seas Lower-energy waves responsible for series II, begin to moderate, a new berm and associated and I, in turn, broke along steps at lower levels. cusps may appear, and the volume of exposed Contrasts in steepness of the fronts of cusp sand may increase. Shoreward flow exhibits horns, as shown in the profile, illustrate a maximum ability to bring large and heavy characteristic of cusp geometry. The slope of materials to high beach levels early in the de- the apex in series III is essentially that estab- clining phase of wave heights. It is then that lished when the cusp was formed. With lower- juvenile cusps are deposited, and the inner level ing of limits of wave uprush, members of that

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 310 RUSSELL AND McINTIRE—BEACH CUSPS

series were left high and dry, perched above the they developed lies behind a wide shoal, much level of subsequent modification by wave ac- of which is less than 2 fathoms deep and from tivities. Apex slopes of other series are steeper, which Tete a 1'Anglais and Kahouanne rise as an effect related more to subsequent erosion islands. than to original inclination. The spacing between cusp apices of 106 Measurements of slopes in bays is straight- measured examples is shown in Figure 3. The forward, and all parts of the profile are likely number of examples is plotted horizontally, and to be meaningful. Profiles across surfaces behind the distance in feet between adjacent cusps is apical slopes are also significant. But slopes of shown on the vertical scale. In more than two cusp margins, and particularly those near horn thirds of the cases cusp apices were less than apices, in nearly all cases exhibit steepening by 63 feet apart; others fell 96-186 feet apart. In subsequent wave erosion. The first effect of ero- a sense these examples were random because sion typically is the creation of scarplets from they were taken from beaches in the West a few inches to several feet in height. These are nearly vertical at first, but as the sand dries they change so that their slopes tend to assume angles of repose characteristic of loose sand. After measuring hundreds of these steepened M f slopes and finding little or no association with o> parameters such as grain size, we became con- vinced that their extreme variability results < 4 from postdepositional events. In Figure 2 slopes of cusp apices are plotted horizontally and slopes in adjacent bays vertically. The 16 8 9 10 11 12 13 14 15 16 17 18 19 pairs used in this illustration were selected as APEX(degrees) among the most reliable of our observations be- Figure 2. Comparison between bay and cause in all cases points of measurement lay apex slopes close together and were equidistant from the water's edge. Although at first glance it might appear that a cloud of points suggests a slope Indies, New Zealand, Australia, and South relationship, statistical analysis of 20 pairs as Africa. The frequencies and spacing, however, shown in Appendix 1 proved otherwise. There indicate a wide departure from the result of is none, even if the two or three extreme cases of truly random sampling, in which every possible steep apex slope are disregarded. kind of exposure, size of material, and other If a berm is present, this berm and any associ- pertinent parameters are represented ade- ated cusps attain a level determined by limits quately. In that case the numbers of examples of wave uprush possessing sufficient velocity should establish a normal probability curve, and turbulence to transport the materials to be rather than clustering into two distinct groups. deposited. On sheltered shores of lakes or Our sampling did not include any observations estuaries, where limited fetch is present, berms around small ponds, along lake shores, or on are low, and cusps lie closely spaced. Beaches sides of estuaries, and thus completely excluded facing open seas and exposed to high waves and all the smallest cusps. When we divided our swell are characterized by higher berms and data upon the basis of exposure to open oceans, broader cusps. In the examples of cusp devel- we found very significant correlations, as shown opment studied, the lowest berm ordinarily in Appendix 2. The cluster with shorter spacing ranges from about 4 to 12 feet in elevation represents mainly observations on Caribbean above mean sea level, and averages about 7 feet. beaches, and widest spacing was measured on Striking regional contrasts are present. Berms beaches south of Perth, Western Australia. along the Caribbean coasts of the Lesser Antilles Where more than a single series of cusps is and the south coast of Puerto Rico are con- observed, the spacing of horns is wider at higher sistently lower than those on opposite sides of levels. In the Cluny example (Fig. 1) the the islands where shores locally are not pro- lowest-series horns were spaced at intervals tected by reefs. ranging from 22 to 28 feet and averaged 25. The cusps surveyed and illustrated in Figure Series II ranged from 32 to 38 feet, and series 1 attained a maximum elevation of 8 feet, a III, from 52 to 69. relatively low value because the beach on which Two series were present along a sand and

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 FIELD OBSERVATIONS 311

gravel beach about a mile south of Precheur, of axial directions and other deformities in on the coast of Martinique west of Mt. Pelee juvenile cusp shapes are evident, but this (PI. 1, fig. 2). The upper series was indistinct, condition disappears in a comparatively short and its wider horns were associated with a berm time if the thickness increases fairly rapidly. about 6 feet above sea level. A highly de- The irregularities in shapes of juvenile cusps teriorated condition suggested that it had been should not be confused with asymmetry that formed many months before the picture was develops when cusps are being eroded by waves taken. The series about 2 feet lower was fresh arriving at an angle to the shore line or when and appeared to be experiencing continuing de- pronounced longshore drift occurs. velopment. Maximum shingle size increased The most persistent survival of irregular southward, away from the camera, from about spacing from the juvenile stage occurs in the 6 to 12 inches, but most of the gravel fell within case where widths of bays between three adjacent horns are approximately half of the distances characteristic of other members of the series. "Half-cusps" are not uncommon. 15'r They are smaller and lower than others as a 30' rule. The sum of distances across bays on either

60' side tends to equal the median distance be- 75' tween apices of regular members. Cusp-forming 90' processes apparently succeed in shifting the 105' original horns so that irregularly spaced mem- 120' bers of a series become incorporated in larger 135' and regular members, reducing initial contrasts 150' in bay widths. If bay widths on either side are 165' 180' approximately equal, the task is apparently 195 more difficult to accomplish, and "half cusps" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 tend to persist. EXAMPLES JUVENILE CUSPS Figure 3. Number of examples in spacing of cusp apices Early signs of cusp development may be illustrated by an example from the coast of northwestern Australia (PI. 2, fig. 1). Patches a size range of from 2 to 4 inches, and no rela- of shell have accumulated at somewhat irrtgu- tionship of maximum shingle size to cusp larly spaced intervals. These juvenile cusps spacing was apparent. Basalt pebbles covered formed roughly along the upper limits of wave hard, black sand. No similarity existed between uprush (plainly shown as recently wetted sand, horn positions of cusps of one series and the which is darker in the photograph). An indica- other. This is ordinarily the case and is a natural tion that a new berm is developing at the level consequence of the fact that the older series of cusp bases is shown by a fairly continuous was first to form and had been perched above line of coarse shells. The slight depressions the reach oi swash by the time the newer series described by Palmer had not become con- developed. spicuous channels, nor had columns of return- When a cusp series begins to form, juvenile ing water removed all loose material from horns are spaced somewhat less regularly than intercusp areas. In the two examples shown in later on. if the initial accumulations are ob- Plate 1, this task had been more nearly com- served when only a few inches thick, gravel, pleted. In the Australian example the spacing shell, or other coarse material occurs in patches of nearby cusps was considerably less regular that lie upon the pre-existing beach, but their than that farther away, where cusps were spacing provides only a rough idea of what it larger, and their apices may be noted as ex- will become when the deposits are 3 or more tending farther toward the water's edge. A feet thick in apical areas. At first the distances small "half-cusp" beyond the juvenile cusp in between some adjacent accumulations may be the foreground was being shifted toward the two or three times longer than between other observer, and its materials undoubtedly became pairs in the series. Signs of increased regularity incorporated with those of its neighbor if cusp- in spacing appear rather promptly as a result of forming conditions continued. The berm of lateral shifting of the initial deposits. Skewing this series was 8 feet above sea level. Indistinct

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 312 RUSSELL AND McINTIRE—BEACH CUSPS

remnants of an earlier berm occurred about is associated with conspicuous berms at approxi- 4 feet higher. mately the level of the higher points along cusp In a slightly more advanced stage of develop- tops. Cusps are best regarded as forms that ment, cusps begin to develop the flat tops that appear along the seaward side of advancing and characterize them throughout the rest of their broadening berms associated with an adequate life (PI. 2, fig. 2). Those shown in Figure 2 of supply of sediment. Well-developed cusps are Plate 2 developed on a rather steep beach likely to retain their spacing, apical patterns, toward the end of a refraction bay in northern and maximum surface elevations while they Luzon. The limits of wave uprush at about 6 thicken seaward and increase in volume. feet are emphasized by drifts of seaweed. After adjustments characteristic of their Various other flotsam accumulations that juvenile stage, which result in appropriate falsely suggest sand stratification occur along spacing, cusps grow seaward across a beach. swash'lines below. Beach slope in the bay next When they attain moderate size the pre-exist- above the center of the picture was 6°, and the ing beach remains exposed in bays. The con- sand was fine and hard, as was also the case trast between cusp and bay materials gradually farther along the beach, beyond the limit of diminishes. The stage shown in Figure 1 of cusp development. These Philippine cusps have Plate 2 exhibits a predominance of original more rounded apices than the juvenile cusps beach surface and deposits. A somewhat more from Australia. They also exhibit slight but advanced stage is illustrated in Figure 2 of Plate consistent asymmetry which undoubtedly ex- 2, but the floors of developing bays are still pressed an effect of gentle longshore drift distinct. Similar conditions are present along toward an extremity of the nearly circular bay. both of the beaches in Plate 1. Beaches with Thus a factor that ordinarily is associated with well-developed cusps (Pi. 3) ordinarily have a cusp removal was present, but it was over- different appearance. An example from Puerto shadowed in intensity by factors favoring cusp Rico (PL 3, fig. 1) exhibits almost homogeneous development. coarse sand, whether on the berm, cusp tops, While statistical support is lacking, it seems apices, slopes toward bays, or down the bays that most cases of distinct apical pointing indi- toward the water's edge. The South African cate the impact of waves parallel to the shore example (PL 3, fig. 2) is similar. Its more line, and that more rounded apices develop if distinct berm displayed much finer and firmer there is some lateral drift or slight departure of sand than in the Puerto Rican example. wave advance from a direction normal to the The spacing of well-developed cusps varies shore. considerably, depending mainly on exposure conditions and the dimensions of the waves that WELL-DEVELOPED CUSPS formed them. Once established it tends to The criteria for recognizing a well-developed remain unchanged. stage of cusp development are poorly defined because the forms may not develop in an CUSP DISAPPEARANCE orderly way during the interval between their Any deposit of loose sand tends to lose its earliest appearance and final obliteration. Cusps initial form when the factors responsible for its may be erased soon after appearing in juvenile accumulation disappear, unless it is stabilized condition or may persist for considerable length by vegetation. Cusp disappearance, however, of time without further development. Cusps of ordinarily is accomplished by marine processes an upper series may have originated during —very similar to those that cause cusps to some extraordinary state of the sea that may form—and occurs so rapidly and completely not be duplicated for many years and may that cusps are among the least persistent of remain undisturbed by marine processes. How- landforms. A cusp more than 2 or 3 years old ever, they may be altered by the effects of is rare. wind, rain, trampling of animals, activities of Cusps originate and attain maximum de- man, or other processes. Cusps at lowest levels velopment during transitions from winter- to are decidedly ephemeral features with life summer-beach conditions. They commonly are histories that may be limited to a few hours. erased when the transition occurs in the oppo- A well-developed series of cusps charac- site direction. These transitional periods may teristically occupies considerable area, shows occur at intervals of some months or a few notable reduction in sharpness of boundary hours. Although seasonal in a gross way, cusps contrasts between horns and adjacent bays, and may appear at any time of the year. Local

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 CUSP DISAPPEARANCE 313

storminess resulting in high winds and the to account for many of their characteristics, development of high, steep waves occurs most such as the contrast between cusp and under- frequently in winter in many parts of the lying beach materials. The coarser sediments world. That is the most likely season both for present on most cusp horns are not part of a accelerated beach erosion and depositional stratigraphic layer that can be traced into conditions favoring cusp disappearance. How- nearby beach sections, as would be the case ever, cusps develop early during the subsequent were cusps erosional in origin. transition toward a summer beach. Favorable Kuenen (1948) reported cusp characteristics conditions arrive soon after a decrease in local faithfully but apparently failed to recognize storminess or a lessening in the intensity of that his theory of origin involved a serious heavy swell. contradiction. The washing of pebbles side- Plate 4 illustrates the disappearance of cusps ways from bays to horns implies directions of on Preston Beach, north of Bunbury, Western transport that oppose those of water flow. Australia. Vigorous wave attack was driving Guilcher (1949) observed flow directions but scarps up to 3 feet high into cusp deposits. The did not quite explain their relationship to rapidity of the process is suggested in Figure 2 depositional accumulations. Bagnold (1940) of Plate 4, where footprints less than 20 minutes came closer to presenting an adequate theory. old lead directly to a 3-foot dropoff. On nearby On several Australian beaches we found Binnengup Beach we determined that wave essentially spherical, tightly compacted ac- approach just beyond the step differed 10° cumulations of Posidonia filaments (PI. 6, fig. from the shore-line trend. The erosional scarps, 1). These algal balls ranged up to baseball size however, formed at an angle of 25°. and provided a simple tool for identifying Where waves strike obliquely and considera- current directions. When placed at various ble longshore drift is established, cusps develop positions within the swash zone or thrown out asymmetrical shapes and wash away. Plate 5 into the breakers, these buoyant floats com- illustrates this. In Figure 1 of Plate 5, the out- monly returned to an adjacent cusp apex, line of the original, rounded cusp apex appears regardless of the position from which they dimly toward the right above the middle of the started. Where there was some longshore drift picture. The scarp across the horn diminishes a ball failing to lodge on one cusp commonly in height with increasing distance from the arrived on the next and in rare cases came to observer. No suggestion of a scarplet was evi- rest in any part of an embay men t up to 10 dent on the opposite side of the horn, in lee of feet from an apex. As these objects floated with the direction of wave attack. In extreme cases a freeboard of about three quarters of their asymmetry of this kind develops cusp remnants diameters, their drift paths indicated current as angular as the teeth of a ripsaw. The earliest directions on the water surface. Shell fragments indication of asymmetrical change on tropical and other coarse materials, however, were coasts is often the accumulation of coconut being concentrated in the immediate vicinities husks and other flotsam on stoss sides of cusps, of cusp apices or on flats behind them, in as shown in Figure 2 of Plate 5. patterns implying similar drift directions at Asymmetrical features are relatively rare on depth. boulder beaches. Longshore currents ordinarily Observations on drift of algal balls and fail to develop velocity sufficient to shift heavy localization of sediment accumulations amply objects. Any kind of beach is subject to re- support Bagnold's observation that surges pile moval, however, if it experiences sufficient up on the face of each cusp apex and swing erosion, whether or not there is a longshore around into adjacent bays, uninterrupted by component in wave advance or development of any period of rest. All objects that fail to come longshore currents. Waves approaching directly to rest on a cusp are swept away rapidly and toward the shore accomplish this if they have returned through the bays to the sea. When enough energy. there is considerable wave energy the flow down the bays is sufficient to "remove all TOWARD A THEORY OF CUSP ORIGIN loose material," as observed by Palmer (1834, p. 573). If cusps are forming, the inflow along Older theories of cusp origin postulating the the sides and over tops of adjacent cusps presence of rows of seaweed or low beach ridges swings into the bays; where the two streams were readily disproved. More recent theories meet, water piles up, attains considerable tur- that regard cusps as the product of erosion fail bulence, and flows rapidly down the bay (PI.

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 314 RUSSELL AND McINTIRE—BEACH CUSPS

6, fig. 2). The upsurge of any incoming wave is even coarse materials are entrained, if present. overpowered by the return current in the bay, This is why cusps consist of coarser sediments and its water becomes incorporated in rapid, than those of the beaches below them. highly turbulent flow toward the step. Berms and cusps grow and widen where Potential bay locations are suggested when reached by upvvash carrying suspended load. juvenile cusps start forming. These areas On a straight summer beach the uprush quickly become better defined, and during that velocity decreases and transportation velocities stage there is some erosion of their floors. The pass critical limits, allowing deposition to growing cusps divert uprush water toward the occur, ordinarily with heavier materials being bays, localizing return flow. Loose materials first to settle. At the "dead" period forward are removed by outflowing waters, but a motion ceases and deposition continues. The pavement becomes established that is resistant backwash increases in velocity and is able to to further loss. By the time that cusps approach transport load but is not likely to entrain much well-developed condition practically all the sediment until it approaches the step zone. sedimentary load transported down bays is The heavier and coarser deposits along supplied by upsurge water that sweeps around berms of many beaches accumulated during from the horns. The introduction of this flow times when waves had higher energies and is shown in Figure 1 of Plate 7. The two swash was more turbulent than was the case areas where upsurge reaches farthest inland are later on, when lower parts of the beach were cusp positions. Flow toward the bay between deposited. Many coarse objects arrived with is well shown in the bay left of the center of the sufficient forward momentum to roll to posi- picture. The same wave in advancing toward tions where they remained untouched by later the bay presents a relatively straight front surges. Limits of uprush dropped as wave and it progresses at a slower pace than the energy diminished. flow coming toward the bay from the cusps. The sequence of changes experienced by a These opposed masses of water meet centrally beach associated with an arrival and decline of in the bay producing the interference illus- high wave-energy conditions is illustrated in trated in Figure 2 of Plate 6. The outflow is Figure 4. Following a period of relative tran- concentrated toward the middle of the bay quility, when little happens to change the (PI. 7, fig. 2). In Figure 2 of Plate 7 the recently beach within the swash zone, increasing energy wetted bay floor appears dark, and the inner causes erosion, and a trend toward a winter limits of flow are defined by the arcs that beach. If the magnitude and duration of in- swing from cusps toward bay centers. The cusp crease is sufficient, large volumes of beach on the right is clearly evident in the picture deposit will be removed, beach elevation will but the cusp to the left centers beyond its be lowered, and the profile will be flattened. edge. Under extreme conditions sand and finer sedi- Cusp growth depends mainly on the fact ments will be carried far enough offshore to that velocities of flow must be higher to reach depths from which they are unlikely to entrain than to carry load. The important be returned, and the coast will recede. Com- factor associated with velocity is the degree of monly, however, the eroded materials are turbulence present. Gross forward movement is scattered about as suspended load or settle in only a secondary consideration. When wave shallow waters, the "lower beach" of Bagnold's surge rises up cusp apices, turbulence decreases, terminology. These gradually shift shoreward and heavier or coarser parts of the entrained later on. Much of the shift occurs in bars that load may be deposited on the horns. The remove toward the step. mainder of the load is carried ahead, around With declining wave energy deposition into bays, and finally back to the step zone. begins promptly. The first layer deposited com- Water flowing down the bays, while possessing monly consists of poorly sorted sand that transportation velocity sufficient to keep its settles from highly turbid near-shore waters. suspended load in motion rarely is capable of The deposit is thin as a rule, but it extends entraining new load across the bay-floor pave- on up to a high level on the beach because ment; this is demonstrated by an absence of limits of wave uprush, although declining, still erosional channels or other scoured depressions. extend across most of the winter beach. The Upon passing over the shore-line convexity coarsest, heaviest element in a beach deposit and reaching the step, however, the turbulence soon arrives and covers the initial deposit. in the moving water is increased abruptly and Its boulders, gravel, heavy-mineral sand, or

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 TOWARD A THEORY OF CUSP ORIGIN 315

other constituents arrive in ways that resemble ground-water temperatures in connection with the transport of bed-load in rivers. Coarse beach-rock investigations. Coarser deposits materials shift toward the beach in rather close were encountered in a large majority of cases proximity to the bottom and become an because the water table commonly lies within extensive layer as a rule as the swash zone is them. The individual layers in the succession wide when they appear. If considerable volumes must not be visualized as having uniform of coarse shell fragments are present, these thickness across the beach. The coarser elements commonly are the next to arrive. Probably constitute a deposit having somewhat the because of their shapes and lower specific shape of the traditional, Gilbertian delta, gravities these fragments are likely to travel thinning in a seaward wedge in which dips of independently, rather than with the gravels individual layers resemble those of rather and heavier materials that are deposited ahead steeply inclined foreset beds. The surface of of them. Presumably they were being tossed the berm may expose their higher parts, and

. sand coarse gravel \ coarse shell coarse sand

fine sand

REWORKING

Figure 4. Beach changes related to increasing and decreasing wave energy

around in highly turbulent waters during much its width depends on the abundance of coarse of the time that the heavier load moved land- materials. Gravel and concentrations of heavy ward close to the bottom. If a distinct shell minerals ordinarily are exposed on the inner layer occurs in a beach deposit, its basal contact side of the berm and may pinch out at in- is ordinarily quite sharp. Later on, the materials creasing depth toward the shore line. Below contributed to the beach become finer-grained, the berm, the slope, if unaffected by sub- until, at length, low-energy waves establish sequent erosion, decreases gradually, producing the tranquility typical before the arrival of the concavity commonly observed in the "up- high-energy conditions. Reworking occurs per beach" of Bagnold's terminology. Along within the swash zone and on the step. The dry beaches the sand is firmest either on the summer beach gradually attains its typical coarse or shelly deposits of the berm or on the large volume and steeper slope toward the finer damp sands close to the shore line. convexity at the step. When cusps form as part of the berm-de- While these depositional events have been positing process, their apices occur where considered irom the standpoint of an idealized, upsurge effects are most concentrated. Al- simple increase in wave energy followed by an though sediments of various sizes reach them, uninterrupted decrease, actual experiences are finer sediments in a turbid load are not likely more complicated. Many minor reversals in to be deposited. If the apex is topped by up- trend interrupt the smooth curve illustrated: surges, water reaching the flat above attains a there are frequent alternations between erosion "dead" period, as elsewhere along the berm, and deposition. The gross stratigraphic suc- and poorly sorted materials accumulate. Most cession just described is based on observations upsurges, however, fail to reach the flats and made in hundreds of pits on beaches most of currents commonly split at apices and continue, which were dug for the purpose of obtaining without halting, into the bays between them,

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 OJ oh—\

eWn P

to B > O

Figure 5. Sequential stages of turbidity distribution and current flow associated with growing cusps. Three cusps and two bays are outlined by a solid line, the step position by a dashed line.

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. New cusps, West Island, Cocos-Keeling

Figure 2. Gravel cusps, near Precheur, Martinique CUSPS ON FIRM BEACHES, COCOS-KEELING AND MARTINIQUE

RUSSELL AND McINTIRE, PLATE 1 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. Shell cusps, west of Onslow, Western Australia

Figure 2. Flat surface on rounded cusp, Playa del Santiago, Luzon, R. P. JUVENILE CUSPS, WESTERN AUSTRALIA AND REPUBLIC OF THE PHILIPPINES

RUSSELL AND McINTIRE, PLATE 2 Geological Society of America Bulletin, volume 76

Figure 2. Cusps in sand, St. Winifreds, Natal, South Africa WELL-DEVELOPED CUSPS, PUERTO RICO AND SOUTH AFRICA

RUSSELL AND McINTIRE, PLATE 3 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. Cusp erosion. The remnant cusp in the foreground was in part overtopped by a recent wave, as shown by the darker appearance of wet sand, Preston Beach, Western ------

Figure 2. Footprints less than 20 minutes old leading to 3-foot dropoff, same beach CUSP EROSION, PRESTON BEACH, SOUTH OF PERTH, WESTERN AUSTRALIA

RUSSELL AND McINTIRE, PLATE 4 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. Scarp being driven into the stoss side of a cusp that originally extended to the right of the footprints, south of Salt River, Douglas Bay, Dominica

Figure 2. Early stage of cusp attack, Mero, Dominica ASYMMETRICAL EROSION OF CUSPS, DOMINICA

RUSSELL AND McINTIRE, PLATE 5 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. Algal ball (Posidonia filaments), about the size of a baseball, used to identify surface current directions, Myalup, Western Australia

Figure 2. Outflow in bay between cusps, same beach CUSP-ORIGINATING PROCESSES, WESTERN AUSTRALIA

RUSSELL AND McINTIRE, PLATE 6 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 Figure 1. Inflow advances fastest toward cusp apices

Figure 2. Inner limits of flow are indicated by darkened, wet sand which forms two arcs leading to the bay center CURRENT FLOW IN BAYS, WARNBRO SOUND, SOUTH OF SAFETY BAY, WESTERN AUSTRALIA

RUSSELL AND McINTIRE, PLATE 7 Geological Society of America Bulletin, volume 76

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 TOWARD A THEORY OF CUSP ORIGIN 317

dropping only some of their coarse load, if the turbid vortices ordinarily had drifted into anything. positions where their suspended materials were The observations of Boye (1954) apparently available for transport shoreward and con- relate to processes associated with this kind of centration on cusp horns. Coarser parts of the current activity. The horns appear to exhibit load were there subjected to the possibility of "sea-sorted" deposits because they are the being deposited. The return currents of flow direct products of swash activities. On the are emphasized in stage E, as well as in Plates other hand, while the floors of bays are also 6 and 7. As the water swirled into the bays to marine deposits, they are subjected to winnow- pile up against streams from cusps on their ing such as occurs along stream beds, and opposite sides and flowed down central parts of hence develop "fluviomarine" characteristics. the bays, little sediment appeared to be drop- In 1963 we had the rare fortune of being ped or entrained. The waning stage of sea- able to witness intense cusp development taking ward flow is emphasized in F. By that time place along the shores of Warnbro Sound about the turbulence was greatly intensified at the 20 miles south of Perth, W.A. On one beach step, and a new patch of turbid water ap- possibly a hundred cusps were forming, and peared. A return to stage A was evident, and a we watched the process for about 2 hours, new cycle was initiated. during which there was no slackening of The coarse materials characteristic of cusp activity, but only repetitions of rhythmic horns are derived mainly from the step zone. events occurring as the cusps grew seaward. One commonly finds coarser sediments there We may discuss the process in terms of six than on the beach above or on the lower beach stages each of which occurred nearly simultane- farther out in the water. ously on cusps in proximity to each other. While we are confident of our conclusions, These are illustrated in Figure 5. it is apparent that we have not been able to During stage A, highly turbid water was explain something vital to a complete theory of evident in small patches just seaward from cusp origin, the reasons for cusp-width uni- the step, in front of each bay. These areas formity. That it is characteristic is demon- grew, and after attaining diameters of about strated in Appendix 2. 30 feet became almost perfectly circular and The widths of cusps in some way depend on formed mildly rotating vortices, circulating in wave dimension, in all probability height or clockwise directions. This effect presumably steepness. This is indicated by the broader resulted from slow longshore drift. Each spacing on higher berms and also along more vortex moved along the shore in directions exposed coasts. Something resembling cellular suggested by the heavy arrows in stage B. flow patterns must be present when juvenile During stage C, or about the time when the cusps appear and the regularity of the circu- vortices had come to positions opposite cusps, lation becomes pronounced later on, when the we observed trends of wave fronts and con- flow returns in distinct columns, as was ob- sidered their associated orthogonal lines. The served by Palmer. By the time cusps are well fronts are illustrated as wavy lines and the developed these circulation patterns are ac- orthogonals as heavy lines, many of which con- centuated and follow directions such as are verge toward cusp horns. During stages A, B, indicated in Figure 5. and C, waves had been breaking along the step, The initial cellular flow patterns suggest approximately along the dashed line shown in those along coasts where definite rip currents A. Their upsurges advanced small or moderate lead seaward at various places. Relationships to distances up apices and into bays but had slight irregularities in bar configuration are well effect on morphology or the accumulation of known and it may well be that future investi- sediment. Occasionally a larger wave arrived, gation will find that the key to initial cusp or possibly two in succession. These "king spacing will be found a short distance offshore waves," as they are called in Australian termi- from the step, in a zone where bars form and nology, were the ones that brought real changes. undergo many changes. Until such relationships Streamlines of current flow associated with are established any theory of cusp origin re- the arrival of larger waves are illustrated in mains incomplete. stage D. At the time they became meaningful

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 318 RUSSELL AND McINTIRE—BEACH CUSPS

REFERENCES CITED Bagnold, R. A., 1940, Beach formation by waves; some model-experiments in a wave tank: Jour. Inst. Civil Engineers, v. 15, p. 27-52 Boye, M., 1954, Solution granulometrique au probleme des croissants de plage (beach cusps): Rev. Geomorphol. Dynamique, v. 5, p. 241-271 Guilcher, A., 1949, Observations sur le croissants de plage: Soc. Geol. France, (5), v. 19, p. 15-30 Kuenen, Ph. H., 1948, The formation of beach cusps: Jour. Geology, v. 56, p. 34-40 Palmer, H. R., 1834, Observations on the motions of shingle beaches: Royal Soc. London, Philos. Trans., v. 124, p. 567-576 Shepard, F. P., 1963, Submarine geology: New York, Harper and Row, 557 p.

MANUSCRIPT RECEIVED BY THE SOCIETY MAY 11, 1964 COASTAL STUDIES INSTITUTE, LOUISIANA STATE UNIVERSITY, BATON ROUGE, LA.

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 APPENDIX 1 319

APPENDIX 1. RELATIONSHIP BETWEEN APEX AND BAY SLOPES (FIGURE 2) Dr. John C. Perm, assisted by Mr. Robert Ehrlich, provided the following analysis of data. Mr. Rodney Adams performed the calculations. The inclination of beach surface on cusp apices and adjacent bays were set in a table with slopes divided at the median of about 10° for apices and about 5° for bays.

BAYS < 5° > 6° APICES < 10° 4 6 10 > 11° 4 6 10 8 12 20 Since the data indicate absolutely no relationship between apex and bay slopes, analysis was not continued.

APPENDIX 2. RELATIONSHIP OF CUSP LENGTH TO DEGREE OF EXPOSURE As an initial test, data pertaining to the relationship of cusp length to degree of exposure were cast in the form of a table with major divisions at the median cusp length (about 18 paces) and degree of exposure (good, better intermediate, and poorer intermediate). These latter categories were further subdivided as to specific beaches in order to estimate variation in cusp length within exposure type.

Good exposure Better intermediate exposure Poorer intermediate exposure Myalup Myalup Spirits Laai- 1961 1963 Preston Bay plek Cluny Vigie Mero Torquav > 18 paces 8 13 6 6 6 7 5 1 2 54 ^18 paces 0 0 0 0 0 0 41 8 4 53 8 13 6 6 6 7 46 9 6 107 Location of beaches: Myalup and Preston, north of Bunbury, Western Australia (exposed to full Indian Ocean swell and waves) Spirits Bay, northern end, North Island, New Zealand (somewhat sheltered by capes on either side) Laaiplek, north of Cape Town, South Africa, on east-west coast (somewhat sheltered from direct Atlantic swell and waves) Cluny, north end of Basse Terre, Guadeloupe (somewhat sheltered by wide shoal areas) Vigic (St. Lucia) and Mero (Dominica) are Caribbean beaches on leeward side of islands. Torquay, Queensland, is protected by the Barrier Reef and shoal areas from Pacific swells and waves.

Chi square tests for the data in this form are as follows:

Source of variation: Degree of Freedom X2* X2 at 0.1 Between degrees of exposure 2 57.82 9.2 Between beaches within degree of exposure 6 15.05 16.8 Total 8 72.87 20.01

* Yates correction applied because of small expected frequencies This analysis yields an expected result. First, the probability that the observed cusp lengths are distributed through beaches and kinds of exposure in pure chance fashion is much less than 1 in 100. Furthermore, the amount of variation in cusp length within an exposure type is (1) not highly significant, and (2) is less than cusp length variation between kinds of exposure.

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021 320 RUSSELL AND McINTIRE—BEACH CUSPS

APPENDIX 2. (continued) In order to examine cusp length and exposure in a somewhat more rigorous fashion, the data were set in the form of an hierarchical analysis of variance. The results are:

Source of variation: Degree of Freedom S.S. M.S. F. Between kinds of exposure 2 1,848.74 924.37 18.25* Between beaches within kinds of exposure 6 303.90 50.65 He Between beaches within kinds of exposure 6 2,148.25 358.0 20.69t Within beaches 98 1,703.47 17.3 Total 106

* Significant at this level because of very unequal numbers of items at the lowest level, the actual analysis is broken at this point and on this table the nonrelevant details are not shown, t Significant at the 1-per cent level of probability As in the Chi square test, variations within kinds of exposure is clearly less than between kinds. In addition the amount of variation within beaches is significantly less than between beaches. From the available data, the length of beach cusps seems to be clearly related to the degree of exposure to open sea; smaller cusps are associated with poorer exposure. Should studies of this type continue, wave properties associated with "exposure" could be measured, and more precise relationships governing cusp properties might be determined.

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/76/3/307/3427659/i0016-7606-76-3-307.pdf by guest on 25 September 2021