Changes In Wave Height Research Articles

INDIVIDUAL WAVE ANALYSIS OF IRREGULAR WAVE DEFORMATION IN THE NEARSHORE ZONE

In a field observation, water surface fluctuations were measured at many points on line from the shoreline to just outside the surf zone. The data were analyzed by an individual wave method, where the concept of primary individual wave is introduced in order to investigate irregular wave deformation. Primary individual waves are defined by applying the zero-down crossing method with a suitable band width at the zero level to the high-pass filtered water surface fluctuation. It is shown that a wave thus defined behaves like a regular wave with a fixed period in the nearshore zone. A deterministic model based on wave height change of monochromatic waves on non-uniform beaches is then introduced. The model is found to describe the observed deformation process expressed by the primary individual waves.

Intertidal Sedimentary Structures on Macrotidal Beaches

ABSTRACT A one-month survey of three macrotidal beaches located in south Wales has shown that the distribution of bed forms in the intertidal zone is controlled primarily by wave climate and tidal range. The areas near the high- and low-water marks reflect the predominance of swash-zone action, whereas the middle part of the beach is more likely to contain bed forms formed in either the breaking or shoaling wave zones. Since none of the structures were formed by current action, changes in tidal range affected only the width of the areas, not the type of bed forms produced. The bed forms observed varied directly with changes in wave height; on high wave-energy beaches, the model of Clifton et al. (1971) is valid, whereas on lower energy beaches it must be modified. The rapid response of the bea hes to changes in wave climate makes it unlikely that bed forms will be preserved except possibly during extremely severe storms, when the lowermost part of the bed forms might be preserved as part of a vertical sequence produced by migrating facies.

Strongly Nonlinear Waves

As steep waves have recently come to be described with increasing accuracy, a number of unexpected physical and mathematical phenomena have been revealed. Until ten years ago it had been assumed that accurate solutions for high waves would hold few surprises. Examples of such suppositions are that deep-water solutions would converge for all waves short of the highest, that important integral quantities such as speed, energy, and momentum would increase with wave height until the highest is reached, that the solutions for periodic waves would be unique, and that if one solitary wave overtakes another any change of wave height would be a decrease. It is now known that all these suppositions are false, having been disproved in the last decade. The nonlinearity of the describing equations produces a complexity of solution structure that is only now beginning to be appreciated. This review will deal with effectively exact solutions for nonlinear waves and the phenomena revealed by such solutions. The governing equation within the fluid is taken to be Laplace’s equation, corresponding to irrotational flow of an incompressible fluid. Excluded are the physical effects of viscosity, density gradients, compressibility, and rotation. This model of the flow is the simplest, but one which is an excellent approximation in many cases of wave motion, and is the traditional avenue of approach to most problems of fluid flow. Throughout his review, however, the problems and solutions described are those where the complete nonlinear boundary conditions have been included. It has been the nonlinearity of these conditions which has made the accurate solution of water-wave problems so difficult.

Elevation and velocity measurements of laboratory shoaling waves

Measurements of wave elevation and orbital velocity in the shoaling, breaking, and bore regime of single‐frequency laboratory waves show that third‐order Stokes theory, when energy flux is conserved, predicts the wave height change and harmonic growth in the regime where the Ursell number Ur = (H/ h)/(kh)2 is 0(1) or less. Shoreward of the Stokes region and up to the breakpoint, harmonic amplitudes are well described by the cnoidal theory. It is shown theoretically that a smooth transition regime exists between Stokes and cnoidal regions for waves which eventually break by plunging. The wave profile asymmetry about the vertical plane observed in near‐breaking waves and bores is due to slow changes of phase of the harmonics relative to the primary wave as the wave train shoals. By contrast, only asymmetry about the horizontal plane is possible in the Stokes and cnoidal wave theories, since these classical solutions allow no relative phase shifts between harmonics. Velocity measurements made with hot‐film anemometers show that ‘unorganized’ fluctuations at the bottom under breaking waves are of the order of half the rms amplitude of the wave‐induced ‘organized’ flow. The correlation between surface elevation and bottom velocity under breakers and bores suggests that turbulence contributes more strongly to the unorganized flow at the bottom under plunging than under spilling waves.

PHYSICAL PROCESSES AND SEDIMENT FLUX THROUGH REEF-LAGOON SYSTEMS

Studies of physical processes in reef-lagoon systems continue to emphasize the importance of waves and wave-induced currents at the reef crest as agents of sediment transport to backreef environments. These across-the-reef currents are also largely responsible for driving backreef lagoon circulation. Rapid energy transformations associated with the process of wave breaking at the reef crest are responsible for strong reef-normal surge currents. Estimates of energy loss, as determined by wave height changes caused by wave breaking, can be as high as 70-80%' for discontinuous reefs and >90% for continuous examples. The amount of energy loss is related to depth of water over the reef crest, a function of reef topography and tidal regime. Low-tide conditions promote the greatest incident wave modification and attenuation as a result of increased breaking-wave intensity. Under trade-wind conditions found in the Caribbean, surge currents of 50-80 cm/sec for durations of 2-6 sec are common in a low to moderate wave-energy setting (4-6 sec input waves, 40- 50 cm average heights). Sediments through the sand sizes up to pebbles are easily transported lagoonward by these periodic bursts of energy. Flow in shallow backreef lagoons (generally

Reef-Crest Wave and Current Interactions and Sediment Transport: ABSTRACT

A recent investigation of wave-current processes in a shallow reef-crest environment (eastern Nicaragua) indicates that rapid energy transformations associated with breaking waves are important to sediment transport as well as circulation in the back-reef lagoon. Although these interactions have been considered by other studies, they have not been treated quantitatively. Wave sensors were placed on the seaward and lagoonward sides of the reef crest. Current meters were positioned on the reef crest and in the lee-side moat channel. Energy loss (~67%), calculated from wave-height changes as estimated from wave spectra, are related to depth of water over the reef. At high tide, instantaneous current speeds and wave modifications are minimized even though wave heights are decidedly reduced between fore-reef and back-reef areas. Low-tide conditions favor extreme energy losses resulting from more intense wave breaking. Over-the-crest current velocities are greatest near low tide. Waves in the back reef appear to be solitary in nature, thus favoring greater onshore velocities. Current surges of 50 to 80 cm/sec for durations of a few seconds occurred under the low-wave-energy input conditions of the experiment (4 to 6 sec input waves and average heights of ~45 cm). These periodic currents of short duration are sufficient to drive coarse-grained sediment into the back-reef lagoon. Mean currents are in the range of 10 to 20 cm/sec and therefore do not reflect the true dynamic nature of reef-crest environments. Most currents reverse with tide. On rising tide, moat-current direction indicates lagoon filling, but the reverse is true of falling tide. Representative current speeds of 10 to 20 cm/sec are typical of these exchanges. Data from other areas indicate that reef-crest morphology and lagoon geometry are important to the sediment-transport problem. However, breaking waves drive sediment across the crest by strong surge currents. Water driven across the crest controls circulation and resultant sediment-dispersal patterns in shallow back-reef lagoons. Tidal variations cause periodic fluctuations in the intensity of wave and current interactions at the reef crest. End_of_Article - Last_Page 517------------

Observations of wave height and wave celerity in the surf zone

Observations of wave crest elevation, wave trough elevation, and wave celerity have been made in the surf zone on a natural beach. A series of 22 wave poles having vertical gradations of 7 cm (near shore) and 11 cm (off shore) were placed across the surf zone from outside the break point to the swash zone. Movements of 10 individual waves all having a break point within one wave pole spacing of each other have been photographed, and the data on wave height changes and wave speed changes have been analyzed. Wave celerity within the surf zone, given as a ratio M to solitary wave celerity, shows a systematic increase of wave speeds near the break point to a peak of M ≃ 1.2, thence a decrease farther shoreward to M ≃ 0.8, and finally a second increase where M > 1. Wave height decay after breaking follows the theory of turbulent dissipation recently presented by Sawaragi and Iwata (1974). The wave height to water depth ratio within the surf zone is a function of distance from the break point and ranges from 2.0 to 0.6. The results indicate that the use of linear and nonlinear nonviscous wave theories to quantify surf zone wave characteristics is misleading insofar as quantitative prediction is concerned.

A STUDY ON THE AEOLIAN BED-FORMS IN ENSHUNADA BEACH, SHIZUOKA PREFECTURE, CENTRAL JAPAN-THEIR CONFIGURATIONS AND CRITERIA OF FORMATION

Enshunada beach located in Shizuoka Prefecture, Central Japan, is divided into two similar arcs by the advancement of the delta of River Tenryu (Fig. 1). In this region, the weather is so fine that the surface of beaches is dry in winter. Sand drift occurs by strong westerly to northwesterly wind which is prevailing in winter (Fig. 2). Various aeolian bed-forms are formed on the backshores in this beach (Fig. 3). These aeolian bed-forms are classified into sand ripples (Photo. 1(a)), granule ripples (Photo. 1 (b)), and dunes (Photo. 1 (c) and (d)) according to the wave-length. Regardless of size of the wave-length, aeolian bed-forms have two characteristics. One is that they have transverse ridges against the wind direction, and the other is that they have a gentle slope in the windward and a steeper slope in the leeward (Fig. 4). In dunes, two kinds of the bed-forms are observed; one has the smooth curve all over a dune from windward slope to leeward slope (Photo. 1 (c)), and the other has the straight and steeper slope, which is called “slip face” in the leeward (Photo. 1 (d)). The former is named “wavy dune”, and the latter is named “dune with slip face” by the author. In addition to ripples and dunes, two plane forms are observed. They are “flat bed” which involve large amount of sand drift, and “plane bed” which involve the least amount of sand drift. Bed-fours observed in this region are classified into following six types by their wave-lengths and the characteristics of configulations: “plane bed”, “sand ripples”, “granule ripples”, “wavy dunes”, “dunes with slip face”, and “flat bed”. Sand ripples are generally formed everywhere in these beaches and granule ripples are observed on backshores of Nakatajima where bed materials contain granule and coarse sand (Table 2). In many cases, dunes are formed on the backshores of eastern districts in both arcs. For the formation of the dunes, a long fetch of wind and a supply of sand are neccessary. In the eastern districts, the direction of prevailling wind is parallel with the strike of beach lines (Table 1). Because the mean diameter of bed materials varies from place to place, there are some differences in wind velocity (V1.0), which corresponds to the formation of sand ripples. As the mean diameter is larger, V1.0 is slightly larger in Nakatajima than in any other places. The transformation of the dune profiles were measured by leveling on Dec. 6, 8, and 14, 1974 in Chihama (Fig. 6 and Table 3). The wave-length change is generally small. The wave-height change is clearly recongnized and it is classified into following three types: Type 1 There is no distinct change of wave-height, Type 2 Wave-heights increase markedly, and Type 3 Wave-heights decrease prominently. There is a good correlation among these three types of changing dune profile, the wind velocity (V1, 0), and the condition of formation or disappearance of ripples (Table 4). When the wind velocity is small, the dune profile change becomes the type 1 and the ripples are formed clearly. When the wind velocity is medium, the dune profile change becomes the type 2 and the ripples disappeare. When the wind velocity is large, the dune profile change becomes type 3 and the ripples completely disappeare. Thus it seems that the types 1, 2, and 3 correspond to the cases of ripple formation, dune formation, and flat bed formation respectively. Aeolian bed-forms are the results of processes occuring at the interface between the sand bed and air flow.

The reduction mechanism of cytochrome c and methemoglobin on the mercury electrode

Using AC polarography on a stationary mercury electrode and transferring the electrode covered with an adsorbed protein into another protein solution possessing a greater electrochemical activity, we established that the exchange of the protein from the first layer does not occur and that the same monolayer of flattened protein develops both at large and small concentrations. Using the same technique of layer—by—layer adsorption of two different proteins, but enlarging the mercury drop size in the buffer, we studied adsorption in the second layer. The mercury drop enlargment permits the second layer to move over onto the electrode surface, so that it becomes visible. It was found that adsorption in the second layer is reversible and that no denaturating processes occur in it. The data obtained about the nature of the protein adsorption were used to analyse the reduction mechanism of cytochrome, methemoglobin and other heme—containing proteins. It was shown that the reduction current of oxidized cytochrome and methemoglobin depends linearly on protein concentration up to 7–10 mg/cm 3. Ten—fold excess of BSA, globulin or ribonuclease at the total concentration of 40 mg/cm 3 does not lead to any change in the cytochrome wave height. The data obtained made it possible to formulate a hypothesis explaining the protein reduction mechanism. The first portions of protein denaturate irreversibly on the electrode surface, forming a monolayer of flattened protein. In the pores of the monolayer reduction of native molecules capable of desorption takes place. This mechanism may be extrapolated to all electrochemical processes occurring both during the reduction of heme—groups and of other electron—active groups in proteins. In a number of cases no polarographic wave was observed due to the strongly irreversible process, as is the csae with the reduction of sulfide groups.

TRANSFORMATION OF IRREGULAR WAVES IN SHOALING WATER

In the numerical method of prediction of wind waves in deep water, Hasselmann's nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks. It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamada's theory of nonlinear interaction in uniform depth.

Analysis of Water-Level-Rise Effects on Littoral Transport: ABSTRACT

A computer project has included evaluation of the effects of changes in wave height, wave period, wave-approach angle, bottom slope, and water depth on beach erosion. This work is primarily applicable to large lakes where long-term changes in water level may be as much as one or two m. The change in potential erosion is expressed as a ratio of littoral power values. The most important independent variable entering into this ratio is the change in water level. An increase in level of one or two m can give ratios in the range of 100 to 250 and even higher. A ratio of 100 means that, after the rise in level, the littoral component of power, and hence the amount of sand eroded and transported, is initially 100 times as great as prior to the rise. End_of_Article - Last_Page 2207------------

Analysis of Peak Mooring Forces Caused by Slow Vessel Drift Oscillations in Random Seas

Abstract A procedure for calculation of peak mooring force caused by the long-period vessel drift oscillation is described. The long-period drift oscillation is induced by the action of groups of high waves in random seas. The procedure is developed from consideration of momentum flux change in ocean waves. Introduction The demand on the offshore petroleum industry for mooring under trying conditions has created the need for a clearer understanding of the physical phenomena involved in mooring large vessels under phenomena involved in mooring large vessels under severe conditions in the open ocean. The offshore industry has experienced major difficulties in mooring under storm conditions and has suffered extensive financial loss. Over the years, attempts have been made to solve offshore mooring problems, utilizing a variety of vessels and mooring techniques. Results of experience and practice offer conflicting indications of the relative merits of various mooring systems. Various engineering and scientific studies have contributed toward an understanding of many factors influencing forces; however, it appears that previous studies have, for the most part, ignored an important phenomenon, which under certain situations is the governing factor to be considered in design of mooring systems. Specifically, there has been little attention devoted to the effects of slow vessel drift oscillations in random or irregular seas. It is this phenomenon that is the prime subject of the present phenomenon that is the prime subject of the present paper. paper. Fig. 1 illustrates results obtained from model tests of a moored vessel in irregular waves. Shown in the figure, as a function of time, are the variations of wave height and period, the surge or drift position of the vessel, and the tension in the primary mooring line. It will be noted that the surge primary mooring line. It will be noted that the surge motion of the vessel involves both a direct wave-induced short-period surge and a gradual long-period drift oscillation taking place over a period of 1 minute or more in prototype time. This type of drift motion is also found in the motion records of moored ships in an actual ocean storm environment. Moreover, the basic behavior of slow oscillations is not unique to moored vessels. For instance, such behavior has been observed in tests involving vessels towed through irregular waves with a constant towing force. In such case, it has been observed that the vessel velocity exhibits slow oscillations with periods in the range of 1 to 2 minutes. When an ocean wave is propagated toward a moored vessel, part of the wave is reflected, the remainder being transmitted on beyond the vessel The conservation of wave momentum results in a net force applied to the vessel for each wave. For regular waves the consequence is a steady drift force resulting in a static shift of the average position of the moored vessel. For irregular waves, position of the moored vessel. For irregular waves, on the other hand, a varying sequence of drift forces arises in correspondence to changes in wave height and period. Investigations leading to this paper show that the ensuing long period drift oscillation of the vessel can, for many cases, be the completely dominating influence in determining maximum mooring line tension.

The Slow Drift Oscillations of a Moored Object in Random Seas

Abstract The phenomenon of the slowly varying drifting force on a mowed object in a random sea is explained and illustrated from the results of several model tests with a rectangular barge. These tests, conducted at the Netherlands Ship Model Basin, were an extension of an object executed program. Using the results of measured or calculated drifting forces on an object moored in regular waves, a prediction can be Made of the drifting forces induced by wave trains consisting of regular wave groups. Also, for an irregular wave train the drifting force on the barge can be computed as a function of time, which makes it possible to calculate the surge motion of the barge. The results of tests and calculations show a reasonable agreement. Introduction In the last few years the problems concerning the mooring of objects in random seas have gained much attention as a result of the necessity to load and discharge big tankers in open sea, or because the sea bottom has to be explored and exploited by vessels operating from the water surface. Generally a floating object moored in waves will be subjected to forces causing horizontal and vertical motions and to moments causing angular motions about the horizontal and vertical axes. Here we will deal with the horizontal surge motion of a rectangular barge moored by means of linear springs in head waves. The surge motion can be split up into a mean excursion, a slowly varying motion, and a higher frequency oscillation around the slowly varying position. The period of the higher frequency oscillation is equal to that of the wave motion; and since a considerable amount of literature is available concerning this part of the motion, it will not be treated in this paper. From the results of model tests in regular waves the mean drifting force on the barge could be determined as a function of the wave frequency. Using these data, the long-periodical surge motion of the barge was calculated for different stiffnesses of the mooring system for the condition in which the barge was moored in a wave train consisting of regular wave groups. The results of these calculations are compared with model test results. From these and earlier executed tests it is clear that resonance phenomena may occur when the period with which the wave groups encounter the barge equals the natural period of the surge motion of the moored barge. period of the surge motion of the moored barge. It also appears to be possible to calculate the drifting force induced by regular wave groups when such a wave train is taken to consist of two regular waves with a small difference in frequency. The regular wave groups, used for a clear demonstration of certain long-periodical phenomena, have mainly educational value. Regular wave groups will seldom occur. Generally the wave height changes irregularly. To estimate the drifting forces exerted on an object in a particular irregular wave train as a function of time, a method exists which produces reasonable results. This method, based on the principle of known drifting force in regular waves, principle of known drifting force in regular waves, will be dealt with. Starting from the obtained drifting force, the surge motion of the object moored in this particular wave train can be calculated. This is illustrated by comparison of some calculated surge motion records with those of measured ones.

SHOALING OF FINITE AMPLITUDE LONG WAVES ON A BEACH OF CONSTANT SLOPE

A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions. The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories. On the other hand, the experiments are conducted with respect to the transformation of waves progressing on beaches of three kinds of slopes ( 1/30, 1/2.0 and 1/10 ) . The experimental results are compared with the theoretical curves to confirm the validity of the theory.

Laboratory Experiments On The Hydrodynamics Of Waves On AdverseCurrents

A series of laboratory experiments on waves on adverse currents were conducted. The transformation of regular and irregular waves on a sloping bed was studied with and without currents. Effects of the currents on the waves transformations are reported. Concerning regular waves, wave height and wave length changes were measured. The analysis of data shows an increase of the former and decrease of the latter. Wave steepness increment, related to the case without currents, shows a clear trend proportional to the ratio between the mean current velocity and the wave celerity. For what concerns irregular waves, spectral transformation was noticed. Results show drastic changes for higher frequencies compared to the lower ones. Due to adverse currents, the frequencies higher than the peak frequency increase energy before breaking. Such transfer of energy increases when the mean current velocity increases. For adverse flow that are strong enough, waves breaking occurs and energy dissipation is concentrated on higher frequencies. Zero moment wave height changes according to the spectral transformations.

Third Order Solution Wave Motion Under IceSheet

A third order solution of wave motion under the ice sheet was derived. The energy flux method was employed to calculate the wave height change at the ice sheet edge. According to the theory of elastic bending, the wave conditions for the ice sheet fracture were examined. Main discussion in this paper was focused on the effect of nonlinearity.

EXPERIMENTAL DATA ON THE OVERTOPPING OF SEAWALLS BY WAVES

In the past it has been found that serious damage and breaching of seawalls is most frequently caused by overtopping. Hence for the design of seawalls data must be available about the overtopping by waves of the different profiles that might be possible. Naturally the conditions under which damage is caused to the seawall also depend on the type of construction and the materials used, for example: the stability of grass covered dikes can be endangered seriously by water flowing over the inner slope. In many designs the necessary height of a seawall has been defined such that not more than 2% of the waves overtop the crest, under chosen design conditions. This criterion has been determined on the assumption that the overtopping must remain very small. Some overtopping has to be accepted because no maximum value for wave height and wave run-up can be given, unless of course the wave height is limited by fore-shore conditions. Unfortunately this criterion gives no information about the volume and concentration of water overtopping the crest in each instance. Moreover it is of interest to know how this overtopping varies with other conditions, such as changes in the significant wave height. Information about the overtopping by waves was obtained from model investigations on simple plane slopes w^th inclinations varying from 1 : 8 to 1 : 2. The experiments were made in a windflume where wind generated waves as well as regular waves were employed. Using wind generated waves, conditions from nature regarding the distribution of wave heights could be reproduced. It appeared that the overtopping depends on the irregularity of the waves and that the same effects cannot be reproduced using regular paddle generated waves. In this paper a description of the model and the results of these tests are given. Investigations are m progress on composite slopes, including the reproduction of conditions for a seawall which suffered much overtopping but remained practically undamaged during the flood of 1953.

Applications of Square Wave Polarograph in Non-Ferrous Metal Analysis

Scope and limitation of square wave (S.w.) polarogaphic method of analysis, in constrast with those of d.c. and a.c. polarographic methods, have been investigated. Procedures for the analysis of metallic impurities in non-ferrous metals by s.w. polarographic method have been developed. The procedures have been applied in practice. The results and some comments on the method were given. By s.w. polarographic method Bi(lll), Sb(lll), Cu(ll), Pb(ll) + Sn(ll, lV) and Cd(ll) gave separated waves, repectively, from 1 N HCL base solution (each 30γ mg/100 ml), while the d.c. polarographic waves of Bi, Sb and Cu and a.c. polarographic waves of Bi and Sb overlapped each other. (each 0.2mg/100m1) The lowest concentration levels for the quantitative analysis of the metals from the state base solution were 50γ/100ml, 30-50γ/100rnl and 20 to 10γ or less/100ml by d.c., a.c., and s.w. polarographic method, respectively. The lowest relative cocentration levels for the determination of Zn in the presence of Cd were ca. 2%, 0.025% and 0.002% relative by d.c., a.c., and s.w. polarographic method, respectively. The change of wave height of s.w. polarograms of Cu and Zn from 0.45 N HCLO (50r/100ml) with the change of the distance between d.m.e. and anode (5-20 mm) was negligibly small. The temperature coefficients of the wave height were generally smaller or even negative. Best results were generally obtained when the dissolved oxygen was removed before electrloysis. The wave heights were very sensitive to the change of droptime. The determination procedures of Pb and Cu (0.0018-0.0027%) in electrolytic tin, Pb and Cu (0.0004-0.0009%) in high pure selenium, and Bi and Pd (0.0001-0.0006%) in electrolytic silber were established. The results obtained by these methods showed a good agreement with those by the dithizone method and d.c. polarographic method. The s.w. polarographic method has several advantages, i.e., it requires less skill in comparison with the dithizone method and smaller amount of the sample, ease of chemical pre-treatment, and shorter time for analysis in comparison with the d.c. polarographic method.

Refraction of Ocean Waves: A Process Linking Underwater Topography to Beach Erosion

Waves out at sea, though usually forming a complex pattern, have essentially the same characteristics over large distances. Upon entering shallow water, these waves are transformed under the influence of bottom features, and such transformations may be so marked that breaker heights may vary greatly over short distances along the shore. The effect of bottom features upon waves can largely be interpreted in terms of a simple physical process-wave refraction. In turn, wave refraction may be responsible for alteration of the bottom features by accumulation or removal of sediments and, in this manner, be an important factor in beach erosion. In this report the role of wave refraction is first reviewed in the light of other processes affecting the transformation of waves in shallow water. The mechanism of refraction is illustrated by means of a few idealized examples, such as the refraction pattern along a straight uniformly sloping beach, over a submarine canyon and ridge, and around a headland. Next it is shown that extreme variations in breaker height along the beach north of La Jolla, California, can be computed for typical swell conditions, taking the complex local bottom topography and the orientation of the coastline into consideration. These changes are computed from refraction diagrams for typical swell conditions, and they compare favorably with observed changes in wave height, thus indicating that wave refraction is the primary mechanism controlling changes in wave height along a beach, and that friction, diffraction, and other processes can be of secondary importance only. Finally, it is noted that the transportation of sediments is dependent upon longshore currents, rip currents, and horizontal diffusion and that all these factors are greatly influenced by the existing refraction pattern.