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Chapter 7 Summary
Chapter 7
SUMMARY
INTR 0DUCTI 0N
Attempts at tracing the movement of nearshore sediments have continued over the past quarter century. The relatively recent advent of radioactive and fluorescent techniques has stimulated research along these lines and allowed sophisticated analyses to be undertaken. Numerous other materials have been utilized to trace grain motion including pulverized coal, broken brick, magnetic concrete, painted cobbles, and grains dyed non-fluorescent hues. All of the above techniques have exhibited varying degrees of success, however, natural grains tagged radioactively or with a fluorescent dye offer obvious advantages over artificial materials. Furthermore, the use of fluorescent grains holds a number of advantages over the use of radioactive grains; ( I ) natural grains of silt to cobble size are easily, rapidly, and cheaply dyed with readily available fluorescent dyes using simple apparatus, (2) the fluorescent dyes present no serious legal or health hazard, (3) different fluorescent hues can be used to conduct successive tests at a single local or to differentiate between different size fractions, ( 4 ) solubility of binding media can be adjusted, (5) natural grains require no special preparation prior to dyeing, (6) sensitivity of the fluorescent technique is at least one in a million, and (7) dyes do not alter the hydrodynamic properties of natural grains if a wetting agent is employed. A pilot investigation utilizing fluorescent-dyed grains to trace the movement of beach sand was initiated by the writer in 1959. A large-scale sand-tracing program was subsequently initiated in 1961 at five beaches along the coast of southern California. The study was sponsored by the Geophysics Branch of the Office of Naval Research and commenced in February 1961, and was completed in July of 1962. This report describes the results of the above investigation along with some aspects of more recent sediment-tracing investigations. The five beaches selected as semi-permanent test sites were from north to south: Goleta Point, Trancas, Santa Monica, Huntington, and La Jolla (Scripps). Each of the five beaches was within one of the five littoral cells or closed sedimentsystems extant along the southern California coastline. Moreover, the beaches represented a wide spectrum of wave, sediment, and geomorphic characteristics with which tracer movement could be correlated. Various amounts of fluorescent sand were released on each of the five
180
SUMMARY
beaches at month to month-and-one-half intervals. In addition sand movement was traced behind Santa Monica detached breakwater, around a groin, in areas seaward of the breaker zone, in the swash zone, and within rip currents. Movement of different size fractions was analyzed by using grains of contrasting fluorescent hues. The monthly tracer tests allowed sand movement to be delineated in the four principle dynamic zones of the beach environment (Fig. 1 16). Specific emphasis was placed on grain motion beneath the surf zone which comprises the area between the effective limit of backwash and the breaker zone (Fig.116). Previous laboratory investigations of beach-sand transport have invariably taken place on steep-sloped beaches lacking a surf zone. Consequently, the swash or foreshore zone has heretofore been emphasized as the major zone of beach-zone transport. This report offers fresh evidence on this problem in particular.
FIELD A N D LABORATORY PROCEDURES
Realistic response of fluorescent grains under natural conditions was assured by using sand from actual test sites. At low tide from the foreshore-inshore slope of each test beach 100 lb. sand was collected. The sand was subsequently dried and then dyed a fluorescent-red or fluorescent-green hue using a commercial dyeing process; at least five equally elegant non-commercial dyeing techniques are available (Appendix 1). Due to the length of time between sand collection, dyeing, and re-introduction on a beach, the median diameter of tracer sand was not always identical to that of grains covering a beach at the time of a test. The lengthy periods between individual tracer tests and high surf activity at any one beach allowed tracer sand to be completely dispersed between successive tests. Dyed sand was placed in plastic bags with seawater and a wetting agent prior to its release on a beach. The tracer-filled bags were then broken simultaneously at pre-determined locations across the foreshore-inshore slope. Commonly five to six release points were located between the swash and breaker zones; between 3 and 40 Ib. dyed sand were released during an individual test. Arrangement of sampling stations and release points was determined in the field and varied widely in accordance with wave and current conditions. Tracer sand was usually released at the up-drift end of a rectangular sample grid. An ordinate and abscissa arrangement of wooden stakes allowed workers to position themselves in the surf zone. Number of sample stations ranged between 30 and 83. A multitude of techniques have been devised to collect sediment samples. Constant sample volume or area and speed of collection are the primary considerations during a tracer investigation. During this particular study samples of the sand surface were rapidly obtained by pressing 3 x 3 inch vaseline-coated cards onto the beach surface. The cards were numbered and smeared with grease in the
i I
WATER MOTION
DYNAMIC
PROFILE
I I SEDIMENT S I Z E TRENDS
PREDOMINANT SORTING ENERGY
Fig.116. Summary diagram schematically illustrating the effect of the four major dynamic zones in the beach environment. Hatchered areas represent 1963, 1965) indizones of high concentrations of suspended grains. Dispersion of fluorescent sand and electromechanical measurements (SCHIFFMAN, cate that the surf zone is bounded by two high-energy zones; the breaker zone and the transition zone. MLLW = mean lower low water.
182
SUMMARY
field, then attached to clip boards for easy handling in the surf zone. Sampling procedure consisted of one worker carrying a clip board of twenty sample cards into the surf zone while at least two other workers pressed the greased cards to the sand surface. Up to four sets of samples were collected at each sample station after tracer release. After sample cards were brought ashore they were covered with cellophane for transport to the laboratory. Upon return to the laboratory each sand-covered card was viewed under short-wave ultraviolet light and the number of fluorescent grains tabulated. The area of each card covered by sand was also noted allowing a fluorescent grains per square inch value to be obtained for each sample. The absolute tracer concentrations were normalized to an arbitrary elapsed time after tracer release by multiplying the absolute values by the ratio of the arbitrary time to the absolute elapsed time at moment of collection. Normalized values of tracer concentration were then plotted at their respective stations and isopleths representing equal numbers of fluorescent grains per square inch were constructed resulting in contoured patterns of tracer dispersion with time. Oceanographic and sedimentologic information was gathered concurrently as a tracer test proceeded and provided data with which patterns of tracer movement could be correlated. Simple techniques were used to measure breaker height and period, angle of wave incidence, longshore-current velocity, swash and backwash, beach slope, and wind velocity. In addition sand samples were collected for size analysis. Breaker height averaged 3.0 ft. for all tests and velocity of longshore currents averaged about 1.O ft. /sec. Highest longshore-current velocities occurred midway between the swash and breaker zones indicating these currents follow the path of least resistance with drag on their seaward and shoreward edges. Increasing current velocity was correlated with increasing cross-sectional area of the wedge of water overlying the foreshore-inshore slope and consequently with decreasing beach slope. Current velocity also increased with increasing angle of breaker incidence.
GENERAL PATTERNS OF FORESHORE-INSHORE TRACER TRANSPORT
Patterns of tracer dispersion on essentially planar beach surfaces indicated that a significant percentage of the dyed grains were transported obliquely offshore under all wave conditions. Lesser numbers of grains moved alongshore beneath the surf zone and shoreward into the swash zone. When longshore-current velocity was less than 1.0 ft./sec, grain motion was principally perpendicular to shore. As speed of longshore currents increased above 1.0 ft./sec, the major vector of grain movement swung shoreward finally paralleling the shoreline under extremely highvelocity currents of 2.0-4.0 ft./sec. Electro-mechanical measurements have confirmed that a layered flow exists
PATTERNS OF FORESHORE-INSHORE TRACER TRANSPORT
I83
beneath the surf and transition zones (Fig.116). Moreover, the measurements have illustrated that seaward bottom currents often exceed 1.2 ft./sec. Seaward flow on bottom together with gravity aids in the offshore motion of some grain diameters. Once tracer grains reached the breaker zone they traveled alongshore beneath the break point. Tracer movement also indicated that grain motion immediately seaward of the breaker zone was onshore. Thus grains immediately seaward and shoreward of the breaker zone were continually funneled into this most dynamic of all points in the marine environment. Continuous turbulence during wave collapse and residual eddies after collapse allow most grains smaller than 0.150 mm to remain in suspension while larger grains saltate along the bottom. Greatest tracer dispersal occurred at the shoreward and seawardmost release points despite the fact that the highest longshore currents occurred midway across the profiles. This emphasizes the ineffectiveness of longshore currents to initiate grain motion although they are important in moving grains which have been initially disturbed by passing bores (Fig.116). This was in turn demonstrated by the fact that only minor tracer movement occurred in opposite direction to longshore currents Random or irregular grain motion was primarily restricted to periods when aiigle of wave incidence was small and consequently unable to generate strong unidirectional flow. The contours of tracer dispersion on smooth slopes illustrate that the sand grains followed a wide range of vectors or paths during their transport along a beach. Presumably grains possessing similar physical characteristics responded to slope and hydrodynamic conditions in a similar manner. The wide range of transport vectors thus suggest that upon release each grain sought a position of equilibrium on the beach slope. This is in accord with the concepts outlined by sevural previous workers who have pointed out that for any given wave and slope condition there exist grain diameters for which net motion will be zero; an equilibrium fraction. The persistent offshore motion of many tracer grains may well be a reflection of this process in that these grains apparently could not find suitable positions of equilibrium at the time of their release. Further evidence of sorting was found using multi-colored grains. Fluorescent sand was not released directly in the swash zone, however, tracer grains traveled upslope and into the swash zone during almost all tests. Tracer grains released at the seaward edge of the swash zone were dispersed rapidly in relation to grains released farther seaward. Once fluorescent grains reached the swash zone they traveled alongshore although not always in the classic zig-zag pattern. During one test grains released within the swash zone traveled seaward and failed to reappear again within the swash zone. Commonly there was a striking difference between median diameter of grains in the swash and surf zones; moreover, bi-modal size distributions were characteristic of the transition zone at the base of the foreshore slope. Swash velocity was found to be essentially independent of the foreshore slope but dependent upon position of the breaker
184
SUMMARY
zone and thus overall foreshore-inshore slope and tidal phase. Increasing velocity of backwash was related in part to increasing foreshore slope. Swash velocity is principally dependent upon position of the breaker zone and wave period; given a constant wave height swash velocity will increase as the breaker zone moves shoreward during a rising tide and with decreasing wave period. Fluorescent grains consistently moved upslope onto bar crests when these features were present. High-velocity longshore currents active in troughs immediately shoreward of bars deterred offshore movement of the grains, nevertheless, most tracer grains made their way to the bar crest where they continued their travel alongshore beneath the breaker zone. Tracer movement was similarly concentrated under secondary breaker zones even when a bar was absent. Smaller topographic features such as ridges, runnels, and non-active rip channels had limited affect on direction and rate of tracer movement. However, relatively deep water within a runnel did protect an adjacent swash zone from vigorous swash rup-up during low tide. Rip currents represent a response to continual shoreward movement of water against a beach; water trapped shoreward of the breaker zone breaches the breaker zone and rushes seaward at high velocity. Rip currents were commonly present on all test beaches but only rarely within sample grids. One particularly striking test at Santa Monica beach emphasized the well-known role these currents play in carrying sand offshore through the breaker zone. Fluorescent grains released up-drift from the rip current were swept alongshore and then offshore beneath the rip with only rare grains escaping south past the rip zone. Rip currents active on the periphery of several sample grids significantly affected the direction of tracer movement. Wind blew in an onshore direction during almost all tests with velocities ranging from 4 to 13 m.p.h. Theory and model studies have suggested that onshore wind stress on the surface of shallow water may create an offshore counter current on bottom and thus aid seaward motion of sediment. Scatter diagrams illustrated that the amount of tracer sand leaving a sample grid per unit of time increased with increasing onshore wind velocity. In one instance a high-velocity offshore wind locally reversed the direction of longshore current and tracer movement. The process by which grains of different diameter adjust to a given slope and hydrodynamic environment is termed sorting. This process constitutes the most critical process operating on the beach environment and is the most difficult to investigate. For example, grain diameter controls or determines the slope of a beach whereas beach slope in turn affects the point at which a grain will attain a position of equilibrium (in terms of gravity component) under a given surf regime. Considerable descriptive, theoretical, and laboratory evidence indicates sorting of grains takes place in the offshore zone. Areal variations in median grain size also indicate that sorting occurs shoreward of the breaker zone. The multitude of vectors exhibited by fluorescent grains upon their release in the surf zone is
SAND MOVEMENT SEAWARD OF BREAKER ZONE
185
interpreted as a manifestation of this sorting process. Presumably each tracer grain strove to attain a position of equilibrium on the beach surface in accord with the effects of gravity and onshore and offshore water motion. More definitive evidence of sorting beneath the surf zone was provided by tests using grains of different median diameter dyed contrasting fluorescent hues. For example, sand from Trancas Beach was split into two fractions; grains smaller than 0.25 mm and grains larger than 0.25 mm. The coarse fraction was dyed fluorescent green whereas the fine fraction was dyed fluorescent red. Upon release the coarser grains tended to move obliquely offshore to the breaker zone whereas the finer fraction traveled principally alongshore beneath the surf zone. Size analysis indicated the median diameter of grains across the beach slope was smaller than 0.20 mm except beneath the breaker zone. Consequently, the coarser grains were not in equilibrium on the beach surface at the time of the test and were transported offshore to a position of equilibrium beneath the breaker zone. Grains smaller than 0.25 mm found positions of oscillating equilibrium beneath the surf zone and were transported alongshore with the aid of the longshore current. It appears that grains not in equilibrium at any position beneath the surf zone move principally perpendicular to shore. Those grains finding suitable null points or positions of equilibrium with slope and currents beneath the surf zone exhibit strong alongshore vectors of movement; these grains presumably constituted the greatest percentage of sand moving alongshore during a test.
SAND MOVEMENT SEAWARD OF THE BREAKER ZONE
Recent observations by divers and from deep submersibles have emphasized the fact that sediment is in motion across the breadth of the shelf environment. The relative importance of sediment transport seaward of the breaker zone and mechanisms of transport have yet to be delineated. To date most authorities have assumed that the foreshore-inshore zone constitutes the zone of greatest volumetric transport of sediment per unit of time. The dynamic characteristics of deep-water environments have been effectively recreated in model studies and significant information concerning sediment motion seaward of the breaker zone has thus been attained. To date fluorescent sand has seen only limited use in the area seaward of the breaker zone, however, these pilot tests have illustrated the feasibility of using the dyed grains in deep water. An extensive tracer investigation of grain motion in the shelf environment is currently being conducted by J. Vernon at the University of Southern California. The techniques devised for using fluorescent sand in the surf zone have been successfully used in the shelf environment. For example, greased sample cards have been effective in recovering tracer particles from the sea floor at depths ex-
186
SUMMARY
ceeding 100 ft. Divers and wire-line devices have been used to recover the sample cards. Release of dyed sand in deep water has been accomplished by lowering it in containers from ships and by having divers cut tracer-filled bags on bottom. The most critical problem appears to be navigation as close sampling in the vicinity of release points is essential. Use of SCUBA-equipped divers, underwater motion pictures, and diver-manipulated instruments have allowed deep-water tracer investigations to reach a truly sophisticated level. Furthermore, when divers are employed samples can be taken at extremely close intervals with a high degree of accuracy. In addition, a significant advantage of deep-water tracer investigations is that grain motion can be followed over relatively lengthy periods due to lower grain velocities. During the present investigation sand movement was traced with fluorescent sand immediately seaward of the breaker zone. In all cases the majority of tracer grains traveled shoreward into the breaker zone although dispersion occurred in all directions. This pattern is in accord with motion predicted from theory and observed in model studies. Onshore movement can be attributed to the fact that the net horizontal water motion in this zone is consistently higher in the shoreward direction. Grain velocities deducted from tracer dispersion in the offshore area illustrated that average migration speed is very slow when compared with the average speed attained by grains in the surf zone. For example, an average grain velocity of 1.20 ft./min was estimated from the dispersion of sand released 275 ft. seaward of the breaker zone. Pilot tests utilizing fluorescent sand on portions of the inner shelf considerably seaward of the breaker zone illustrated that bottom currents are sometimes adequate enough to move grains in seemingly anomalous directions. Tracer sand released in these areas did not consistently move in the same direction as wave approach. In fact, the limited tests conducted suggest a significant percentage of the marked grains traveled parallel with wave crests rather than parallel with wave orthogonals. Since all offshore bottoms sampled were rippled, it must be assumed that the ripples represented a major factor controlling direction of grain motion. Fluorescent sand offers an obvious tool with which sand movement can be traced down submarine canyons. A large number of canyons intersect the mainland shelf of southern California and provide conduits within which beach sand moves downslope into deep water. Mass movement of sand from canyon heads has been recorded as instantaneous slumps and as slow creep. Sedimentary evidence indicates auto-suspensions or turbidity currents traverse submarine fans and basin floors. Use of fluorescent sand may solve some of the questions concerning mode of transport within canyon axes. Toward this end 1,800 lb. fluorescent sand were released in Scripps Canyon and about 5,300 lb. were released in Dume Canyon. Tracer grains have been recovered downslope from the release point in Scripps Canyon but none have been found at an appreciable distance from the point source in Dume Canyon. Both tests have proven inconclusive in regards to mode of
SAND MOVEMENT AROUND MAN-MADE STRUCTURES
187
transport. It now appears that constant injection of tracer sand into a canyon head coupled with periodic sampling will provide more information on grain motion in canyon axes than a single release of large volume.
SAND MOVEMENT AROUND MAN-MADE STRUCTURES
Coastal-engineering problems have provided a major impetus for research into the dynamics of nearshore sediment transport. Modern sediment-tracing techniques offer the most significant tool yet devised to accomplish this task in the field. During this investigation sand movement was traced around a groin and behind a detached breakwater. The test groin was at near capacity and exhibited the classic features of an accreted up-drift sand-wedge and an eroded zone on the down-drift flank. Tracer sand was released at two positions on the up-drift side of the structure; at a point immediately seaward of the breaker zone and at the base of the foreshore slope. Grains from the offshore point source traveled shoreward into the breaker zone and south past the groin terminus. Grains released in the transition zone moved offshore beneath a rip-like current active along the up-drift flank of the groin. A few grains were recovered in the lee of the groin; these grains were presumably transported into this zone by eddies produced by flow past the obstruction. The test illustrated that sand transport past the groin is currently impeded only when tidal phase allows the breaker zone to be intercepted by the groin. Fluorescent sand was released at two points behind the detached Santa Monica breakwater where a large accumulation of sand extends seaward due to damping of wave action. Coarser tracer grains were buried whereas the finer fraction was transported alongshore past the breakwater. This action pinpoints the mode of formation of the accreted sand wedge. Size analyses of the sand trapped behind the structure since its construction show that coarser grains are dropped from load in the low-energy zone created by the structure. Median diameter of sand behind the breakwater has decreased steadily with time and with seaward advance of the sand wedge into increasingly protected zones.
ANALYSIS OF TRACER DISPERSION
Most sediment-tracing investigations to date have concentrated on the development of field techniques or simply the variation in patterns of tracer dispersal under differing sea states. The present study falls in the latter category, however, a number of investigators are currently attempting to utilize marked grains to measure rates of sand transport.
188
SUMMARY
The most successful investigation to date utilizing fluorescent grains to establish rates of particle movement was carried out on shingle beaches by workers at the Hydraulics Research Station, Wallingford, Great Britain. The method has been termed the Russell-Abbott concentration or constant-injection technique. The procedure consisted of theoretically and empirically establishing ratios of fluorescent to non-fluorescent particles after their release at a constant rate at a point on a beach. Fluorescent, cobble-sized particles were next released on a natural shingle beach at a constant rate. Surface concentrations of the fluorescent cobbles were recorded at varying distances from the release position and over varying elapsed times. The distribution of tracer concentrations on the beach surface was matched with surface-distribution curves derived by theory. The corresponding tracer concentration was used to compute a drift rate. Drift rates deduced by this method were corroborated by measurements of accretion behind a breakwater. The experimentors feel the technique is limited to shingle beaches, however, Russian investigators are attempting to use this method on sand beaches. During the present investigation an attempt was made to deduce the rate of tracer flux out of sample grids and in turn estimate grain velocities. Although this problem may eventually be solved using the mathematical principles of diffusion or statistical physics, a more elementary approach was used during this study. In order to utilize the tracer data quantitatively, several assumptions were necessary: ( I ) that isopleths of tracer concentration were accurate; (2) that only a small percentage of tracer grains were unaccounted for due to burial; and (3) that most nearshore sand transport occurs in the foreshore-inshore zone. Initially depletion rates (amount of fluorescent sand leaving a sample grid per unit of time) were established by using a planimeter to measure the area within each isopleth of tracer concentration on each dispersal map. These values were in turn used to estimate the number of tracer grains remaining within a sample grid at the elapsed times represented by the maps. Depletion curves were constructed for each of the 45 tests depicting the percentage of total tracer sand remaining within a sample grid at any moment after release. Each curve was characterized by an abrupt inflection point. The persistent inflection or change in rate of tracer flux was interpreted as a reflection of the difference between paths of grains in equilibrium and those lacking a null point beneath the surf zone. Grains moving perpendicular to shore and out of equilibrium left sample grids in a much shorter time than those grains traveling alongshore within a zone of oscillating equilibrium. Knowing the average distance of grain travel and the average rate of tracer flux below an inflection point, the amount of time necessary for half the total grains released to escape a sample grid was computed. Determination of time and distance enabled an estimate to be made of the average velocity of sand grains traveling beneath the surf zone during each test. Computed average grain velocities ranged between 3.6 and 22.7 ft./min and exhibited a fairly normal frequency distribution. Mean velocity for all 45 tests was
ANALYSIS OF TRACER DISPERSION
189
about 10 ft./min. This value is about 1/ 6 the average velocity of longshore currents active during the test and reflects the inefficient nature of the surf system. Scatter diagrams were used to correlate grain velocities with various wave and current parameters. It was found that average grain velocity generally increased with increasing kinetic wave energy, relative wave energy (breaker height), and velocity of longshore currents. However, the best straight-line correlation was obtained with increasing values of the alongshore component of wave power or energy; a parameter which includes a consideration for both breaker height and angle of wave incidence. Further, grain velocity was found to increase markedly as cross-sectional area of the water overlying the foreshore-inshore zone increased. This correlation pinpoints the "feedback" mechanisms involved in the transportation of beach sand and the morphology of beaches. The cross-sectional area of water within the surf zone (Fig.116) is a function of the position of the breaker zone, tidal phase, and beach slope. In turn, beach slope is a direct function of grain diameter and grain diameter directly affects grain velocity. Moreover, the prevailing beach slope together with the velocity-energy gradient across the slope determine which diameters will be in transport beneath the surf zone and which diameters will leave the beach via deposition in the swash zone, diffusion to the offshore zone, or transport beneath the breaker zone. In order to arrive at rates of sand transport depth of the mobile or active bed layer had to be established. The average annual rate of accretion of sand behind three southern California breakwaters provided known rates of drift at three of the test beaches (Goleta Point, Santa Monica, and La Jolla). Using the known transport rates at the three beaches together with ( I ) the average annual unit of sand transport (average width between breaker zone and swash zone multiplied by a constant beach length of 1.O ft.) and (2) the average annual grain velocity at each beach, the depth of mobile bed necessary to account for the known annual volume of sand transport was calculated. Since Einstein has shown that depth of the mobile bed layer is primarily a function of grain diameter, these values were plotted against corresponding average annual grain diameters at the three beaches. The resulting straight-line relationship allowed depth of the mobile bed layer to be estimated for all tests using the median diameter of grains across the foreshore-inshore slope. Next, a unit volume of sand transport was calculated for each tracer test using width of the foreshore-inshore zone, depth of the mobile bed, and a constant beach length of 1.0 ft. Multiplying the unit volume of sand transport by the average grain diameter resulted in a wide range of transport rates corresponding to the wide spectrum of surf conditions prevailing during the tests. Frequency of the drift rates was bimodal and squewed heavily toward low values, emphasizing the fact that the greatest volume of sand transport takes place under relatively low-energy conditions. High rates of transport occuring during storm conditions accounted for a relatively small portion of the total annual load at any beach. The average rate of sand transport for all tests was about 400 cubic yards/ day; the maximum
190
SUMMARY
and minimum rates calculated were 2,875 and 74 cubic yards/ day, respectively. Rates of alongshore sand transport exhibited a wide but general increase with increasing angle of breaker incidence, increasing longshore-current velocity, and increasing alongshore component of wave energy or power. Greatest rates of sand transport occurred when deep-water wave steepness varied between 0.003 and 0.0045. Following the relationship established between depth of the mobile bed layer and grain-diameter values of the average median diameter across each foreshore-inshore slope were plotted at the coordinates of corresponding values of wave energy and rate of sand transport. Drawing best-fit lines of equal grain diameter through the scatter of median diameters resulted in a log-log nomograph relating wave energy, average median grain size, and rate of alongshore sand transport. The nomograph illustrates that the rate of sand transport increases with increasing energy for any given average median diameter between 0.140 and 0.280 mm. By using simple measurements of breaker characteristics to obtain a value of alongshore energy and size analysis to obtain a value of the average median grain diameter across a beach, a corresponding value of sand transport (cubic yards per day) can be picked from the nomograph. Further, variation in distance between the lines of equal grain diameter suggests that increasing units of wave energy are necessary to sustain a constant rate of sand transport when diameter is smaller than 0.180-0.200 mm. Decreasing values of wave energy will sustain the same rate of transport when diameter is between 0.200 and 0.280 mm. These trends are interpreted as a manifestation of the well-known relationship between grain diameter, settling velocity, threshold drag velocity, and bed roughness. As grain diameter becomes smaller than 0.180 mm, the bed presents an increasingly smooth surface to the fluid traveling across it. Consequently, increasing velocities are necessary to initiate motion of grains as grain diameter falls below this critical diameter. Because of the oscillatory nature of the beach environment, grain motion is continually reversed and reinitiated. It appears the empirical relationship established between wave energy, grain diameter, and rate of sand transport represents a portion of a parabolic relationship between these variables. In fact, future measurements of sand transport with the aid of tracers should allow an energy-sediment-transport envelope to be constructed for the beach environment. Medium to coarse sand-size material will exhibit ever-increasing rates of transport with increasing values of alongshore wave energy whereas it will theoretically take increasing units of energy to sustain a given rate of transport for coarser or finer material. Since it has been established that grains smaller than 0.150 mm form suspensates on open coast beaches, a lower limit to this relationship exists in terms of available grain diameters. An upper limit has yet to be estatAished. Available information suggests that increasingly greater units of alongshore energy are necessary to sustain a given rate of transport when grain diameter exceeds 1.00 mm.
SUMMARY
INTR 0DUCTI 0N
Attempts at tracing the movement of nearshore sediments have continued over the past quarter century. The relatively recent advent of radioactive and fluorescent techniques has stimulated research along these lines and allowed sophisticated analyses to be undertaken. Numerous other materials have been utilized to trace grain motion including pulverized coal, broken brick, magnetic concrete, painted cobbles, and grains dyed non-fluorescent hues. All of the above techniques have exhibited varying degrees of success, however, natural grains tagged radioactively or with a fluorescent dye offer obvious advantages over artificial materials. Furthermore, the use of fluorescent grains holds a number of advantages over the use of radioactive grains; ( I ) natural grains of silt to cobble size are easily, rapidly, and cheaply dyed with readily available fluorescent dyes using simple apparatus, (2) the fluorescent dyes present no serious legal or health hazard, (3) different fluorescent hues can be used to conduct successive tests at a single local or to differentiate between different size fractions, ( 4 ) solubility of binding media can be adjusted, (5) natural grains require no special preparation prior to dyeing, (6) sensitivity of the fluorescent technique is at least one in a million, and (7) dyes do not alter the hydrodynamic properties of natural grains if a wetting agent is employed. A pilot investigation utilizing fluorescent-dyed grains to trace the movement of beach sand was initiated by the writer in 1959. A large-scale sand-tracing program was subsequently initiated in 1961 at five beaches along the coast of southern California. The study was sponsored by the Geophysics Branch of the Office of Naval Research and commenced in February 1961, and was completed in July of 1962. This report describes the results of the above investigation along with some aspects of more recent sediment-tracing investigations. The five beaches selected as semi-permanent test sites were from north to south: Goleta Point, Trancas, Santa Monica, Huntington, and La Jolla (Scripps). Each of the five beaches was within one of the five littoral cells or closed sedimentsystems extant along the southern California coastline. Moreover, the beaches represented a wide spectrum of wave, sediment, and geomorphic characteristics with which tracer movement could be correlated. Various amounts of fluorescent sand were released on each of the five
180
SUMMARY
beaches at month to month-and-one-half intervals. In addition sand movement was traced behind Santa Monica detached breakwater, around a groin, in areas seaward of the breaker zone, in the swash zone, and within rip currents. Movement of different size fractions was analyzed by using grains of contrasting fluorescent hues. The monthly tracer tests allowed sand movement to be delineated in the four principle dynamic zones of the beach environment (Fig. 1 16). Specific emphasis was placed on grain motion beneath the surf zone which comprises the area between the effective limit of backwash and the breaker zone (Fig.116). Previous laboratory investigations of beach-sand transport have invariably taken place on steep-sloped beaches lacking a surf zone. Consequently, the swash or foreshore zone has heretofore been emphasized as the major zone of beach-zone transport. This report offers fresh evidence on this problem in particular.
FIELD A N D LABORATORY PROCEDURES
Realistic response of fluorescent grains under natural conditions was assured by using sand from actual test sites. At low tide from the foreshore-inshore slope of each test beach 100 lb. sand was collected. The sand was subsequently dried and then dyed a fluorescent-red or fluorescent-green hue using a commercial dyeing process; at least five equally elegant non-commercial dyeing techniques are available (Appendix 1). Due to the length of time between sand collection, dyeing, and re-introduction on a beach, the median diameter of tracer sand was not always identical to that of grains covering a beach at the time of a test. The lengthy periods between individual tracer tests and high surf activity at any one beach allowed tracer sand to be completely dispersed between successive tests. Dyed sand was placed in plastic bags with seawater and a wetting agent prior to its release on a beach. The tracer-filled bags were then broken simultaneously at pre-determined locations across the foreshore-inshore slope. Commonly five to six release points were located between the swash and breaker zones; between 3 and 40 Ib. dyed sand were released during an individual test. Arrangement of sampling stations and release points was determined in the field and varied widely in accordance with wave and current conditions. Tracer sand was usually released at the up-drift end of a rectangular sample grid. An ordinate and abscissa arrangement of wooden stakes allowed workers to position themselves in the surf zone. Number of sample stations ranged between 30 and 83. A multitude of techniques have been devised to collect sediment samples. Constant sample volume or area and speed of collection are the primary considerations during a tracer investigation. During this particular study samples of the sand surface were rapidly obtained by pressing 3 x 3 inch vaseline-coated cards onto the beach surface. The cards were numbered and smeared with grease in the
i I
WATER MOTION
DYNAMIC
PROFILE
I I SEDIMENT S I Z E TRENDS
PREDOMINANT SORTING ENERGY
Fig.116. Summary diagram schematically illustrating the effect of the four major dynamic zones in the beach environment. Hatchered areas represent 1963, 1965) indizones of high concentrations of suspended grains. Dispersion of fluorescent sand and electromechanical measurements (SCHIFFMAN, cate that the surf zone is bounded by two high-energy zones; the breaker zone and the transition zone. MLLW = mean lower low water.
182
SUMMARY
field, then attached to clip boards for easy handling in the surf zone. Sampling procedure consisted of one worker carrying a clip board of twenty sample cards into the surf zone while at least two other workers pressed the greased cards to the sand surface. Up to four sets of samples were collected at each sample station after tracer release. After sample cards were brought ashore they were covered with cellophane for transport to the laboratory. Upon return to the laboratory each sand-covered card was viewed under short-wave ultraviolet light and the number of fluorescent grains tabulated. The area of each card covered by sand was also noted allowing a fluorescent grains per square inch value to be obtained for each sample. The absolute tracer concentrations were normalized to an arbitrary elapsed time after tracer release by multiplying the absolute values by the ratio of the arbitrary time to the absolute elapsed time at moment of collection. Normalized values of tracer concentration were then plotted at their respective stations and isopleths representing equal numbers of fluorescent grains per square inch were constructed resulting in contoured patterns of tracer dispersion with time. Oceanographic and sedimentologic information was gathered concurrently as a tracer test proceeded and provided data with which patterns of tracer movement could be correlated. Simple techniques were used to measure breaker height and period, angle of wave incidence, longshore-current velocity, swash and backwash, beach slope, and wind velocity. In addition sand samples were collected for size analysis. Breaker height averaged 3.0 ft. for all tests and velocity of longshore currents averaged about 1.O ft. /sec. Highest longshore-current velocities occurred midway between the swash and breaker zones indicating these currents follow the path of least resistance with drag on their seaward and shoreward edges. Increasing current velocity was correlated with increasing cross-sectional area of the wedge of water overlying the foreshore-inshore slope and consequently with decreasing beach slope. Current velocity also increased with increasing angle of breaker incidence.
GENERAL PATTERNS OF FORESHORE-INSHORE TRACER TRANSPORT
Patterns of tracer dispersion on essentially planar beach surfaces indicated that a significant percentage of the dyed grains were transported obliquely offshore under all wave conditions. Lesser numbers of grains moved alongshore beneath the surf zone and shoreward into the swash zone. When longshore-current velocity was less than 1.0 ft./sec, grain motion was principally perpendicular to shore. As speed of longshore currents increased above 1.0 ft./sec, the major vector of grain movement swung shoreward finally paralleling the shoreline under extremely highvelocity currents of 2.0-4.0 ft./sec. Electro-mechanical measurements have confirmed that a layered flow exists
PATTERNS OF FORESHORE-INSHORE TRACER TRANSPORT
I83
beneath the surf and transition zones (Fig.116). Moreover, the measurements have illustrated that seaward bottom currents often exceed 1.2 ft./sec. Seaward flow on bottom together with gravity aids in the offshore motion of some grain diameters. Once tracer grains reached the breaker zone they traveled alongshore beneath the break point. Tracer movement also indicated that grain motion immediately seaward of the breaker zone was onshore. Thus grains immediately seaward and shoreward of the breaker zone were continually funneled into this most dynamic of all points in the marine environment. Continuous turbulence during wave collapse and residual eddies after collapse allow most grains smaller than 0.150 mm to remain in suspension while larger grains saltate along the bottom. Greatest tracer dispersal occurred at the shoreward and seawardmost release points despite the fact that the highest longshore currents occurred midway across the profiles. This emphasizes the ineffectiveness of longshore currents to initiate grain motion although they are important in moving grains which have been initially disturbed by passing bores (Fig.116). This was in turn demonstrated by the fact that only minor tracer movement occurred in opposite direction to longshore currents Random or irregular grain motion was primarily restricted to periods when aiigle of wave incidence was small and consequently unable to generate strong unidirectional flow. The contours of tracer dispersion on smooth slopes illustrate that the sand grains followed a wide range of vectors or paths during their transport along a beach. Presumably grains possessing similar physical characteristics responded to slope and hydrodynamic conditions in a similar manner. The wide range of transport vectors thus suggest that upon release each grain sought a position of equilibrium on the beach slope. This is in accord with the concepts outlined by sevural previous workers who have pointed out that for any given wave and slope condition there exist grain diameters for which net motion will be zero; an equilibrium fraction. The persistent offshore motion of many tracer grains may well be a reflection of this process in that these grains apparently could not find suitable positions of equilibrium at the time of their release. Further evidence of sorting was found using multi-colored grains. Fluorescent sand was not released directly in the swash zone, however, tracer grains traveled upslope and into the swash zone during almost all tests. Tracer grains released at the seaward edge of the swash zone were dispersed rapidly in relation to grains released farther seaward. Once fluorescent grains reached the swash zone they traveled alongshore although not always in the classic zig-zag pattern. During one test grains released within the swash zone traveled seaward and failed to reappear again within the swash zone. Commonly there was a striking difference between median diameter of grains in the swash and surf zones; moreover, bi-modal size distributions were characteristic of the transition zone at the base of the foreshore slope. Swash velocity was found to be essentially independent of the foreshore slope but dependent upon position of the breaker
184
SUMMARY
zone and thus overall foreshore-inshore slope and tidal phase. Increasing velocity of backwash was related in part to increasing foreshore slope. Swash velocity is principally dependent upon position of the breaker zone and wave period; given a constant wave height swash velocity will increase as the breaker zone moves shoreward during a rising tide and with decreasing wave period. Fluorescent grains consistently moved upslope onto bar crests when these features were present. High-velocity longshore currents active in troughs immediately shoreward of bars deterred offshore movement of the grains, nevertheless, most tracer grains made their way to the bar crest where they continued their travel alongshore beneath the breaker zone. Tracer movement was similarly concentrated under secondary breaker zones even when a bar was absent. Smaller topographic features such as ridges, runnels, and non-active rip channels had limited affect on direction and rate of tracer movement. However, relatively deep water within a runnel did protect an adjacent swash zone from vigorous swash rup-up during low tide. Rip currents represent a response to continual shoreward movement of water against a beach; water trapped shoreward of the breaker zone breaches the breaker zone and rushes seaward at high velocity. Rip currents were commonly present on all test beaches but only rarely within sample grids. One particularly striking test at Santa Monica beach emphasized the well-known role these currents play in carrying sand offshore through the breaker zone. Fluorescent grains released up-drift from the rip current were swept alongshore and then offshore beneath the rip with only rare grains escaping south past the rip zone. Rip currents active on the periphery of several sample grids significantly affected the direction of tracer movement. Wind blew in an onshore direction during almost all tests with velocities ranging from 4 to 13 m.p.h. Theory and model studies have suggested that onshore wind stress on the surface of shallow water may create an offshore counter current on bottom and thus aid seaward motion of sediment. Scatter diagrams illustrated that the amount of tracer sand leaving a sample grid per unit of time increased with increasing onshore wind velocity. In one instance a high-velocity offshore wind locally reversed the direction of longshore current and tracer movement. The process by which grains of different diameter adjust to a given slope and hydrodynamic environment is termed sorting. This process constitutes the most critical process operating on the beach environment and is the most difficult to investigate. For example, grain diameter controls or determines the slope of a beach whereas beach slope in turn affects the point at which a grain will attain a position of equilibrium (in terms of gravity component) under a given surf regime. Considerable descriptive, theoretical, and laboratory evidence indicates sorting of grains takes place in the offshore zone. Areal variations in median grain size also indicate that sorting occurs shoreward of the breaker zone. The multitude of vectors exhibited by fluorescent grains upon their release in the surf zone is
SAND MOVEMENT SEAWARD OF BREAKER ZONE
185
interpreted as a manifestation of this sorting process. Presumably each tracer grain strove to attain a position of equilibrium on the beach surface in accord with the effects of gravity and onshore and offshore water motion. More definitive evidence of sorting beneath the surf zone was provided by tests using grains of different median diameter dyed contrasting fluorescent hues. For example, sand from Trancas Beach was split into two fractions; grains smaller than 0.25 mm and grains larger than 0.25 mm. The coarse fraction was dyed fluorescent green whereas the fine fraction was dyed fluorescent red. Upon release the coarser grains tended to move obliquely offshore to the breaker zone whereas the finer fraction traveled principally alongshore beneath the surf zone. Size analysis indicated the median diameter of grains across the beach slope was smaller than 0.20 mm except beneath the breaker zone. Consequently, the coarser grains were not in equilibrium on the beach surface at the time of the test and were transported offshore to a position of equilibrium beneath the breaker zone. Grains smaller than 0.25 mm found positions of oscillating equilibrium beneath the surf zone and were transported alongshore with the aid of the longshore current. It appears that grains not in equilibrium at any position beneath the surf zone move principally perpendicular to shore. Those grains finding suitable null points or positions of equilibrium with slope and currents beneath the surf zone exhibit strong alongshore vectors of movement; these grains presumably constituted the greatest percentage of sand moving alongshore during a test.
SAND MOVEMENT SEAWARD OF THE BREAKER ZONE
Recent observations by divers and from deep submersibles have emphasized the fact that sediment is in motion across the breadth of the shelf environment. The relative importance of sediment transport seaward of the breaker zone and mechanisms of transport have yet to be delineated. To date most authorities have assumed that the foreshore-inshore zone constitutes the zone of greatest volumetric transport of sediment per unit of time. The dynamic characteristics of deep-water environments have been effectively recreated in model studies and significant information concerning sediment motion seaward of the breaker zone has thus been attained. To date fluorescent sand has seen only limited use in the area seaward of the breaker zone, however, these pilot tests have illustrated the feasibility of using the dyed grains in deep water. An extensive tracer investigation of grain motion in the shelf environment is currently being conducted by J. Vernon at the University of Southern California. The techniques devised for using fluorescent sand in the surf zone have been successfully used in the shelf environment. For example, greased sample cards have been effective in recovering tracer particles from the sea floor at depths ex-
186
SUMMARY
ceeding 100 ft. Divers and wire-line devices have been used to recover the sample cards. Release of dyed sand in deep water has been accomplished by lowering it in containers from ships and by having divers cut tracer-filled bags on bottom. The most critical problem appears to be navigation as close sampling in the vicinity of release points is essential. Use of SCUBA-equipped divers, underwater motion pictures, and diver-manipulated instruments have allowed deep-water tracer investigations to reach a truly sophisticated level. Furthermore, when divers are employed samples can be taken at extremely close intervals with a high degree of accuracy. In addition, a significant advantage of deep-water tracer investigations is that grain motion can be followed over relatively lengthy periods due to lower grain velocities. During the present investigation sand movement was traced with fluorescent sand immediately seaward of the breaker zone. In all cases the majority of tracer grains traveled shoreward into the breaker zone although dispersion occurred in all directions. This pattern is in accord with motion predicted from theory and observed in model studies. Onshore movement can be attributed to the fact that the net horizontal water motion in this zone is consistently higher in the shoreward direction. Grain velocities deducted from tracer dispersion in the offshore area illustrated that average migration speed is very slow when compared with the average speed attained by grains in the surf zone. For example, an average grain velocity of 1.20 ft./min was estimated from the dispersion of sand released 275 ft. seaward of the breaker zone. Pilot tests utilizing fluorescent sand on portions of the inner shelf considerably seaward of the breaker zone illustrated that bottom currents are sometimes adequate enough to move grains in seemingly anomalous directions. Tracer sand released in these areas did not consistently move in the same direction as wave approach. In fact, the limited tests conducted suggest a significant percentage of the marked grains traveled parallel with wave crests rather than parallel with wave orthogonals. Since all offshore bottoms sampled were rippled, it must be assumed that the ripples represented a major factor controlling direction of grain motion. Fluorescent sand offers an obvious tool with which sand movement can be traced down submarine canyons. A large number of canyons intersect the mainland shelf of southern California and provide conduits within which beach sand moves downslope into deep water. Mass movement of sand from canyon heads has been recorded as instantaneous slumps and as slow creep. Sedimentary evidence indicates auto-suspensions or turbidity currents traverse submarine fans and basin floors. Use of fluorescent sand may solve some of the questions concerning mode of transport within canyon axes. Toward this end 1,800 lb. fluorescent sand were released in Scripps Canyon and about 5,300 lb. were released in Dume Canyon. Tracer grains have been recovered downslope from the release point in Scripps Canyon but none have been found at an appreciable distance from the point source in Dume Canyon. Both tests have proven inconclusive in regards to mode of
SAND MOVEMENT AROUND MAN-MADE STRUCTURES
187
transport. It now appears that constant injection of tracer sand into a canyon head coupled with periodic sampling will provide more information on grain motion in canyon axes than a single release of large volume.
SAND MOVEMENT AROUND MAN-MADE STRUCTURES
Coastal-engineering problems have provided a major impetus for research into the dynamics of nearshore sediment transport. Modern sediment-tracing techniques offer the most significant tool yet devised to accomplish this task in the field. During this investigation sand movement was traced around a groin and behind a detached breakwater. The test groin was at near capacity and exhibited the classic features of an accreted up-drift sand-wedge and an eroded zone on the down-drift flank. Tracer sand was released at two positions on the up-drift side of the structure; at a point immediately seaward of the breaker zone and at the base of the foreshore slope. Grains from the offshore point source traveled shoreward into the breaker zone and south past the groin terminus. Grains released in the transition zone moved offshore beneath a rip-like current active along the up-drift flank of the groin. A few grains were recovered in the lee of the groin; these grains were presumably transported into this zone by eddies produced by flow past the obstruction. The test illustrated that sand transport past the groin is currently impeded only when tidal phase allows the breaker zone to be intercepted by the groin. Fluorescent sand was released at two points behind the detached Santa Monica breakwater where a large accumulation of sand extends seaward due to damping of wave action. Coarser tracer grains were buried whereas the finer fraction was transported alongshore past the breakwater. This action pinpoints the mode of formation of the accreted sand wedge. Size analyses of the sand trapped behind the structure since its construction show that coarser grains are dropped from load in the low-energy zone created by the structure. Median diameter of sand behind the breakwater has decreased steadily with time and with seaward advance of the sand wedge into increasingly protected zones.
ANALYSIS OF TRACER DISPERSION
Most sediment-tracing investigations to date have concentrated on the development of field techniques or simply the variation in patterns of tracer dispersal under differing sea states. The present study falls in the latter category, however, a number of investigators are currently attempting to utilize marked grains to measure rates of sand transport.
188
SUMMARY
The most successful investigation to date utilizing fluorescent grains to establish rates of particle movement was carried out on shingle beaches by workers at the Hydraulics Research Station, Wallingford, Great Britain. The method has been termed the Russell-Abbott concentration or constant-injection technique. The procedure consisted of theoretically and empirically establishing ratios of fluorescent to non-fluorescent particles after their release at a constant rate at a point on a beach. Fluorescent, cobble-sized particles were next released on a natural shingle beach at a constant rate. Surface concentrations of the fluorescent cobbles were recorded at varying distances from the release position and over varying elapsed times. The distribution of tracer concentrations on the beach surface was matched with surface-distribution curves derived by theory. The corresponding tracer concentration was used to compute a drift rate. Drift rates deduced by this method were corroborated by measurements of accretion behind a breakwater. The experimentors feel the technique is limited to shingle beaches, however, Russian investigators are attempting to use this method on sand beaches. During the present investigation an attempt was made to deduce the rate of tracer flux out of sample grids and in turn estimate grain velocities. Although this problem may eventually be solved using the mathematical principles of diffusion or statistical physics, a more elementary approach was used during this study. In order to utilize the tracer data quantitatively, several assumptions were necessary: ( I ) that isopleths of tracer concentration were accurate; (2) that only a small percentage of tracer grains were unaccounted for due to burial; and (3) that most nearshore sand transport occurs in the foreshore-inshore zone. Initially depletion rates (amount of fluorescent sand leaving a sample grid per unit of time) were established by using a planimeter to measure the area within each isopleth of tracer concentration on each dispersal map. These values were in turn used to estimate the number of tracer grains remaining within a sample grid at the elapsed times represented by the maps. Depletion curves were constructed for each of the 45 tests depicting the percentage of total tracer sand remaining within a sample grid at any moment after release. Each curve was characterized by an abrupt inflection point. The persistent inflection or change in rate of tracer flux was interpreted as a reflection of the difference between paths of grains in equilibrium and those lacking a null point beneath the surf zone. Grains moving perpendicular to shore and out of equilibrium left sample grids in a much shorter time than those grains traveling alongshore within a zone of oscillating equilibrium. Knowing the average distance of grain travel and the average rate of tracer flux below an inflection point, the amount of time necessary for half the total grains released to escape a sample grid was computed. Determination of time and distance enabled an estimate to be made of the average velocity of sand grains traveling beneath the surf zone during each test. Computed average grain velocities ranged between 3.6 and 22.7 ft./min and exhibited a fairly normal frequency distribution. Mean velocity for all 45 tests was
ANALYSIS OF TRACER DISPERSION
189
about 10 ft./min. This value is about 1/ 6 the average velocity of longshore currents active during the test and reflects the inefficient nature of the surf system. Scatter diagrams were used to correlate grain velocities with various wave and current parameters. It was found that average grain velocity generally increased with increasing kinetic wave energy, relative wave energy (breaker height), and velocity of longshore currents. However, the best straight-line correlation was obtained with increasing values of the alongshore component of wave power or energy; a parameter which includes a consideration for both breaker height and angle of wave incidence. Further, grain velocity was found to increase markedly as cross-sectional area of the water overlying the foreshore-inshore zone increased. This correlation pinpoints the "feedback" mechanisms involved in the transportation of beach sand and the morphology of beaches. The cross-sectional area of water within the surf zone (Fig.116) is a function of the position of the breaker zone, tidal phase, and beach slope. In turn, beach slope is a direct function of grain diameter and grain diameter directly affects grain velocity. Moreover, the prevailing beach slope together with the velocity-energy gradient across the slope determine which diameters will be in transport beneath the surf zone and which diameters will leave the beach via deposition in the swash zone, diffusion to the offshore zone, or transport beneath the breaker zone. In order to arrive at rates of sand transport depth of the mobile or active bed layer had to be established. The average annual rate of accretion of sand behind three southern California breakwaters provided known rates of drift at three of the test beaches (Goleta Point, Santa Monica, and La Jolla). Using the known transport rates at the three beaches together with ( I ) the average annual unit of sand transport (average width between breaker zone and swash zone multiplied by a constant beach length of 1.O ft.) and (2) the average annual grain velocity at each beach, the depth of mobile bed necessary to account for the known annual volume of sand transport was calculated. Since Einstein has shown that depth of the mobile bed layer is primarily a function of grain diameter, these values were plotted against corresponding average annual grain diameters at the three beaches. The resulting straight-line relationship allowed depth of the mobile bed layer to be estimated for all tests using the median diameter of grains across the foreshore-inshore slope. Next, a unit volume of sand transport was calculated for each tracer test using width of the foreshore-inshore zone, depth of the mobile bed, and a constant beach length of 1.0 ft. Multiplying the unit volume of sand transport by the average grain diameter resulted in a wide range of transport rates corresponding to the wide spectrum of surf conditions prevailing during the tests. Frequency of the drift rates was bimodal and squewed heavily toward low values, emphasizing the fact that the greatest volume of sand transport takes place under relatively low-energy conditions. High rates of transport occuring during storm conditions accounted for a relatively small portion of the total annual load at any beach. The average rate of sand transport for all tests was about 400 cubic yards/ day; the maximum
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SUMMARY
and minimum rates calculated were 2,875 and 74 cubic yards/ day, respectively. Rates of alongshore sand transport exhibited a wide but general increase with increasing angle of breaker incidence, increasing longshore-current velocity, and increasing alongshore component of wave energy or power. Greatest rates of sand transport occurred when deep-water wave steepness varied between 0.003 and 0.0045. Following the relationship established between depth of the mobile bed layer and grain-diameter values of the average median diameter across each foreshore-inshore slope were plotted at the coordinates of corresponding values of wave energy and rate of sand transport. Drawing best-fit lines of equal grain diameter through the scatter of median diameters resulted in a log-log nomograph relating wave energy, average median grain size, and rate of alongshore sand transport. The nomograph illustrates that the rate of sand transport increases with increasing energy for any given average median diameter between 0.140 and 0.280 mm. By using simple measurements of breaker characteristics to obtain a value of alongshore energy and size analysis to obtain a value of the average median grain diameter across a beach, a corresponding value of sand transport (cubic yards per day) can be picked from the nomograph. Further, variation in distance between the lines of equal grain diameter suggests that increasing units of wave energy are necessary to sustain a constant rate of sand transport when diameter is smaller than 0.180-0.200 mm. Decreasing values of wave energy will sustain the same rate of transport when diameter is between 0.200 and 0.280 mm. These trends are interpreted as a manifestation of the well-known relationship between grain diameter, settling velocity, threshold drag velocity, and bed roughness. As grain diameter becomes smaller than 0.180 mm, the bed presents an increasingly smooth surface to the fluid traveling across it. Consequently, increasing velocities are necessary to initiate motion of grains as grain diameter falls below this critical diameter. Because of the oscillatory nature of the beach environment, grain motion is continually reversed and reinitiated. It appears the empirical relationship established between wave energy, grain diameter, and rate of sand transport represents a portion of a parabolic relationship between these variables. In fact, future measurements of sand transport with the aid of tracers should allow an energy-sediment-transport envelope to be constructed for the beach environment. Medium to coarse sand-size material will exhibit ever-increasing rates of transport with increasing values of alongshore wave energy whereas it will theoretically take increasing units of energy to sustain a given rate of transport for coarser or finer material. Since it has been established that grains smaller than 0.150 mm form suspensates on open coast beaches, a lower limit to this relationship exists in terms of available grain diameters. An upper limit has yet to be estatAished. Available information suggests that increasingly greater units of alongshore energy are necessary to sustain a given rate of transport when grain diameter exceeds 1.00 mm.