"Of necessity," Pattee writes, "my apparatus had to be scaled to the proportions of my basement. For this reason it cannot duplicate precisely the phenomena that are observed at a natural beach. For example, it generates waves of relatively low energy, whereas waves that break against a typical beach may span a broad range of energy. During periods of calm at a natural beach the surf may develop forces of only a few ounces per square foot-barely enough to destroy a sand castle. On the other hand, violent storms generate waves that often crash against the shore with forces of up to three tons per square foot.

"In addition the small tank that confines my 'sea' functions under certain conditions as a resonant cavity for waves, and the walls of the tank introduce weak reflections that are not present at a natural beach. Doubtless these s spurious effects influence both the manner in which the model beach erodes and the way in which the eroded materials are transported and distributed by the moving water. Even so, the apparatus appears to simulate closely many phenomena of wave action that are observed in nature.

"My experiments have been concerned primarily with shallow waves, which travel in water that does not exceed in depth half the length of a wave. (The length of a wave is the distance from one crest to the next one.) Waves that propagate through water of greater depth are formed by the mass movement of water particles, each of which follows a slightly elliptical path in a vertical plane aligned in the direction in which the wave travels. The particles move upward at the rear of the wave, bend over toward the beach at the top, curve downward at the front and return to their starting point at the bottom. Substantially no net displacement of water occurs in any direction.

"When the wave enters shallow water, however, the natural orbit of the particles is distorted. The velocity and length of the wave decrease and the height in creases. As the wave continues to roll inshore it grows in height. The crest runs ahead of the trough, becomes unstable and eventually breaks. The result is a turbulent mass of water that races toward the beach. Under proper conditions the wave may re-form and break again.

"Shallow waves may be either constructive or destructive in their effect on a beach. Constructive waves are relatively smooth. They break slowly and deposit suspended materials on the beach. Destructive waves are usually generated by storms. They are large and steep; they break violently, eroding beach materials and carrying them out to sea.

"My apparatus generates waves of both types in shallow water and projects them against a model beach. Designed to demonstrate the effects of wave action on sand, the apparatus consists of a slender tank, a supply of sand and a wave generator. The tank is 74 inches long, 12 inches wide and 18 inches deep. The bottom, ends and one side of the tank are made of 3/4-inch marine plywood. The remaining side, cut from a sheet of clear plastic 1/4 inch thick, serves as a window for observing the wave action. The joints were caulked with aquarium cement.

"The waves are generated at one end of the tank by an oscillating paddle that is driven by a motor-actuated crank [Figure 1]. The paddle, together with a pair of brackets, is attached to the bottom of a Hat plate that moves back and forth in a pair of grooves at the upper edges of the tank. The grooves are lubricated with soap.

"The paddle assembly is linked by a rod, a universal joint and a connecting rod to a crank in the form of a disk equipped with a movable wrist pin. The crank is driven through a 40-to-1 reduction gear that is coupled by pulleys and a belt to an induction motor. The motor develops 1/4 horsepower at 1,750 revolutions per minute.

"The period of the water waves is adjusted by altering the speed of the crank. With a pulley 5 1/2 inches in diameter on the motor and a pulley eight inches in diameter on the input shaft of the reduction gear, the crank is operated at 30 revolutions per minute. A 7 1/2-inch pulley on the motor and a 5 1/2-inch one on the reduction gear increase the speed of the crank to 60 revolutions per minute.

"All my experiments so far have been made at these speeds. The longer period generates constructive waves; the shorter, destructive waves. Speeds in excess of 60 revolutions per minute cause excessive splashing in the tank. The height or amplitude of the waves is adjusted by altering the distance of the wrist pin from the center of the disk.

"The beach is composed of white silica sand that occupies the free end of the tank. The slope of the sand is arranged by hand prior to the beginning of each experiment. The particle size of my sand varies considerably. The larger grains are about the size of granulated sugar. Other materials I have used include magnetite sand, granulated lead, granulated zinc and powdered titanium. I was able to get all the materials locally, with the exception of the magnetite sand, which I bought from Ward's Natural Science Establishment, Inc., 3000 Ridge Road, East Rochester, N.Y. 14445.

"To investigate beach erosion, the formation of sandbars and other phenomena that involve the transportation of sand, I first adjust the machine to generate destructive waves. Usually I make a series of three test runs in which the amplitude of the waves is increased from four inches to five inches and finally to 5M inches. The wave period is maintained at one second. The results are photographed at the end of each 15-minute run.

"At the start of each experiment the sand is smoothed and arranged at an angle of approximately 15 degrees. The photographs clearly indicate that the rate at which sand is transported increases with wave amplitude [see bottom illustration at right]. Not as evident are the mechanism of sand transport and the process of bar formation.

"The mechanism of sand transport was investigated in another experiment in which destructive waves of 5 1/4-inch amplitude eroded the beach for 15 minutes and were photographed at five minute intervals. (The waves broke approximately 27 inches from the paddle and created a turbulent surf.) The force of the water's impact dislodges particles of sand high on the beach, an turbulence keeps them in suspension for some time. As the surf recedes much of the material is carried seaward by the undertow.

"As the turbulence subsides the water gradually loses its capacity to keep the sand in suspension. It then distributes the sand in one or more well-defined zones on the bottom, thus initiating a sandbar. When the growing bar has decreased the depth of the water sufficiently, the waves break earlier, that is, farther out to sea. Thereafter turbulence attacks the landward side of the bar and eventually shifts it farther from the beach. When the separation between the bar and the beach becomes great enough, surf reforms between the two as a translational wave that usually constructs intermediate bars by the same mechanism [see top illustration at left].

"The seaward movement of bars was observed by having destructive waves act for 45 minutes. Photographs were made at 15-minute intervals. A pair of bars formed within 15 minutes, as in the preceding experiment. During the next 15-minute interval the waves redistributed the sand well out to sea, where it came to rest as a permanent bar, indicating that the system had attained equilibrium. No substantial change was seen during the final 15 minutes.

"Long-term stability is never observed in natural beaches. Tides vary throughout the year, storms periodically generate waves of abnormal destructiveness, coastwise currents shift in response to the ever changing shape of the coastline and geological forces at work in the interior of the earth gradually elevate or lower the land with respect to the level of the sea. Such variables can be controlled in the wave machine, and their effects can be observed one at a time.

"The gently sloping beach that is characteristic during the summer is the product of constructive waves. They are long and relatively flat and do not break violently on the beach. They rebuild beaches eroded by winter storms by removing sand from offshore bars, transporting it landward and depositing it on the face of the beach. Under optimum conditions the process may extend a beach as much as 10 feet per day.

"Constructive waves can be generated in my apparatus by increasing the period and hence the length of the wave, a dimension that is equal to the velocity of the wave divided by its frequency. I determined experimentally that in my machine a period of two seconds quadrupled the deep-water wavelength and simultaneously generated constructive waves approximately equal in amplitude to the destructive waves that were investigated during earlier experiments.

"Starting with a gently sloping beach, destructive waves were generated for 15 minutes. A record was made of the erosion and the sand formations. The apparatus was next adjusted to generate constructive waves for observing how the beach was rebuilt.

"As a crest passed over the first bar the wave would become unstable and break over the interior bars. Turbulence gradually increased during the transit. The growing surf picked up particles of sand along the way and carried them into shallow water, where the waves lost velocity. Part of the sand was scattered as it was carried along and part was deposited on the beach. The process of reconstruction was accelerated as sand accumulated in the trough between the inshore bar and the beach and reduced the depth.

"In the meantime the trough of succeeding waves passed over the bar. The backward movement of water in this lowest part of the wave scoured the sand at the top of the bar, causing it to enter suspension. In that condition it was easily carried forward by the crest of the next wave. Eventually this action leveled the outer bar. The inner bars were then subjected to the full force of the waves and also disappeared. Sand transferred from the bars was deposited on the beach and eventually erased all trace of the previous erosion [see Figure 5].

"A series of experiments that I found particularly interesting was designed to demonstrate how minerals are deposited on the beach and sorted according to the size and specific gravity of the particles. Constructive and destructive waves were used separately and together. Beach materials consisted of silica and magnetite sands and of granular metals that simulated minerals of various specific gravities.

"Destructive waves were first allowed to break for 15 minutes against a beach of silica sand. The apparatus was shut down. Specimens in the form of core samples were removed for examination. The crests of bars were found to be composed chiefly of coarse grains, whereas fine particles had collected in the troughs. Evidently this separation had been produced by differences of turbulence in the two regions.

"Constructive waves were generated for 15 minutes. All signs of erosion disappeared. Both the exposed and the submerged portions of the beach were then examined to learn where sands of particular grain size had been deposited. The coarser particles had formed a ledge at the top of the beach, and another zone of coarse particles was deposited across the bottom. The face of the beach was composed entirely of fine sand.

"I do not know why or how this separation occurs. Perhaps only a little water seeps into the beach during the brief interval when the sand-laden wave rushes up the exposed face. Thereafter, as the water recedes, loses energy and soaks into the sand, the wave loses its lifting power. This combination of events might cause coarse sand to drop out of the water first and form the upper ledge, because maximum force is required to hold the large particles in suspension. The remaining fine particles would then be distributed over the face of the beach. This theory does not account for the distribution of coarse particles across the bottom of the beach, which is a puzzle I am still trying to solve.

"Magnetite sand was selected for another series of sorting experiments because its specific gravity of 7.5 is significantly higher than that of silica sand (2.5) and because the black particles are easily seen. The material is also ferromagnetic and can be recovered easily from silica sand, particularly when the sand is dry, by means of a magnet.

"To do the sorting experiment, I first made a standard beach of white sand. The beach sloped at an angle of 15 degrees. Next I released a stream of magnetite into surf produced by a series of destructive waves. The magnetite spread across the beach but did not move out to sea in significant quantity. Thereafter the size of the patch did not change appreciably, apparently because the particles could not be lifted by the water. Sandbars formed as usual.

"Several constructive waves were then launched. They returned sand to the beach, completely covering the magnetite. After the magnetite was buried destructive waves were generated for the same interval of time as before. This action laid the beach bare to the level of the magnetite. The beach was then reconstructed by wave action and again exposed to destructive waves while additional magnetite was added to the surf. Wave action again eroded the beach to the previous level and combined the added magnetite with the original layer [see Figure 6].

"The experiments demonstrated interesting features of the deposit on beaches of minerals that are too heavy to be lifted and carried by waves. Such minerals are transported to the beach by rivers or by the weathering of rocks along the shore. If the minerals arrive during a period of beach construction, they will be buried by sand. During the next period of destructive waves the beach will be eroded and the minerals will be exposed. Eventually the heavy materials mix with those deposited by earlier storms to form a mineral layer at a depth determined by the maximum erosion of the beach. Should the beach then be lifted above sea level by some geological disturbance the layer can be exposed as a valuable mineral deposit.

"Experiments were also made to observe the sorting and deposition of minerals heavier than silica sand. Magnetite was mixed with granulated zinc and lead. The specific gravities of the three are 7.5, 7 and 11.5 respectively. The mixture was deposited on the beach and covered and uncovered by wave action as in the preceding experiments. Little sorting took place. The larger particles of lead remained in place. Zinc particles and the smaller particles of lead moved about slightly, but little if any separation occurred. Next I rebuilt the beach with clean sand.

"A mixture of magnetite and titanium was then tried. The density of titanium is 4.5, not quite twice that of silica sand. The mixture was poured on the beach at the waterline and subjected to a series of destructive waves. The magnetite behaved as in the earlier experiments: it spread slowly across the beach but did not move seaward.

"The titanium behaved quite differently. It disappeared even before the distribution of the magnetite was completed. Only a few particles remained on the slope of the beach. Most of the material was carried out to sea.

"Specimens were taken from the sandbars. They were saturated with titanium but contained only a few grains of magnetite. A series of constructive waves was launched to rebuild the beach. The magnetite was buried as usual, but a search of the rebuilt beach disclosed little titanium. Several small ripples of sand marked the former location of the sandbars. Most of the titanium was recovered from these remnants.

"Other consequences of wave action include characteristic-markings, such as cusps and ripples, that often appear in the sand. In nature cusps frequently are seen in a regularly spaced pattern along the beach. In the wave tank two pairs of cusps similarly form, one pair on the exposed portion of the beach and an identical pair just below the waterline. A mirror image of the first two cusps also appears farther out to sea.

"Ripple marks are roughly parallel sets of wave-shaped ridges and troughs. They form on the beach chiefly during constructive-wave experiments. The few that are developed by destructive waves are usually found in sand deposited between the offshore bar and the next inshore bar.

"Although I have had a lot of fun with my present apparatus, I look forward to enlarging it so that other aspects of wave action can be demonstrated. Some actions are known to exert a major influence on the rate of sand transport, on beach erosion and on bar formation. One factor is the steepness of the beach. Steep beaches erode more rapidly than those of gentle slope, although more bars and ripples form on a flat beach. My apparatus is too short for demonstrating wave action on a fiat beach.

"The apparatus is also much too narrow for investigating currents that move along the shore. These currents develop when waves advance against the beach at an acute angle. Such a wave may create a breaker that travels along the beach. For example, a wave might approach the observer from the left and sweep along the waterline to the right, followed by a succession of similarly directed waves.

"This action causes water near the edge of the beach to oscillate as a pattern of scallops that constitute a net flow to the right. The flow is capable of transporting beach materials. Longshore currents shift enough sand to fill harbors, seal off bays, create lagoons and even construct bars that link offshore islands to the mainland. A square or rectangular tank with a movable wave generator on one of the long sides should be capable of demonstrating longshore currents, and I look forward to making such a wave machine.

Bibliography

BORES, BREAKERS, WAVES AND WAKES: AN INTRODUCTION TO THE STUDY OF WAVES ON WATER. R. A. R. Tricker. American Elsevier Publishing Company, Inc., 1965.

ESTUARY AND COASTLINE HYDRODYNAMICS. Edited by Arthur Ippen. McGraw-Hill Book Company, 1966.

THE EVER-CHANGING SEA. David B. Ericson and Goesta Wollin. Alfred A. Knopf, 1967.

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