Showing papers on "Breaking wave published in 1978"

Energy loss and set-up due to breaking of random waves

Abstract: A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data

A numerical and theoretical study of certain nonlinear wave phenomena

Abstract: An efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations. The method uses a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time. It is combined with theoretical discussions in the study of a variety of problems including solitary wave interactions, wave breaking, the resolution of initial steps and wells, and the development of nonlinear wavetrain instabilities.

A Numerical and Theoretical Study of Certain Nonlinear Wave Phenomena

Abstract: An efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations. The method uses a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time. It is combined with theoretical discussions in the study of a variety of problems including solitary wave interactions, wave breaking, the resolution of initial steps and wells, and the development of nonlinear wavetrain instabilities.

Energy loss and set-up due to breaking random waves

Abstract: A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach. The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth. A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data.

The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics

Abstract: Calculation of the normal-mode perturbation of steep irrotational gravity waves, begun in part I, is here extended to a study of the subharmonic perturbations, namely those having horizontal scales greater than the basic wavelength (2π/k). At small wave amplitudes a , it is found that all perturbations tend to become neutrally stable; but as ak increases the perturbations coalesce in pairs to produce unstable modes. These may be identified with the instabilities analysed by Benjamin & Feir (1967) when ak is small. However, as ak increases beyond about 0.346, these modes become stable again. The maximum growth scale of this type of mode in the unstable range is only about 14 % per wave period, which value occurs at ak ≈0.32. At values of ak near 0.41 a new type of instability appears which has initially zero frequency but a much higher growth rate. It is pointed out that this type might be expected to arise at wave amplitudes for which the first Fourier coefficient in the basic wave is at its maximum value, as a function of the wave height. The corresponding wave steepness was found by Schwartz (1974) to be ak = 0.412. A comparison of the calculated rates of growth are in rather good agreement with those observed by Benjamin (1967) in the range 0.07 ak

Wave characteristics in the surf zone

Abstract: The equations describing conservation of mass, momentum and energy in a turbulent free surface flow are derived for a controle volume extending over the whole depth. The effect of the turbulent surface oscillations are discussed but neglected in the following analysis, where the equations are applied to the energy balance in a surf zone wave motion. This leads to results for the wave height variation and the velocity of propagation. The results cannot be reconciled completely with measurements and the concluding discussion is aimed at revealing how the model can be improved.

Modulational instability of finite-amplitude, circularly polarized Alfven waves

Abstract: The simple theory of the decay instability of Alfven waves is strictly applicable only to a small-amplitude parent wave in a low-beta plasma, but, if the parent wave is circularly polarized, it is possible to analyze the situation without either of these restrictions. Results show that a large-amplitude circularly polarized wave is unstable with respect to decay into three waves, one longitudinal and one transverse wave propagating parallel to the parent wave and one transverse wave propagating antiparallel. The transverse decay products appear at frequencies which are the sum and difference of the frequencies of the parent wave and the longitudinal wave. The decay products are not familiar MHD modes except in the limit of small beta and small amplitude of the parent wave, in which case the decay products are a forward-propagating sound wave and a backward-propagating circularly polarized wave. In this limit the other transverse wave disappears. The effect of finite beta is to reduce the linear growth rate of the instability from the value suggested by the simple theory. Possible applications of these results to the theory of the solar wind are briefly touched upon.

On the numerical modelling of short waves in shallow water

Abstract: A modelling system is described that generates and runs models of short waves of any form (periodic or irregular), with any desired physically realistic current field over any given bathymetry. As this system constitutes the eighth version of the general System 21, “Jupiter”, described in an earlier contribution, it is called the “Mark 8”. The system-generated models are based upon Boussinesq equations, in which the vertical velocity is supposed to increase linearly from zero at the bed to a maximum magnitude at the surface, in two independent (horizontal) space variables and time. The Boussinesq equations are formulated as mass and momentum conservation laws while, by virtue of the high order of accuracy of the difference approximations, there is very little numerical energy falsification. This formulation also appears to provide genuine weak solutions, for correctly simulating breaking waves, and thus assures the correct simulation of wave thrusts, or radiation stresses, and associated longshore current...

The Deformation of Steep Surface Waves on Water. II. Growth of Normal-Mode Instabilities

Abstract: Studies of the normal-mode perturbations of steep gravity waves (Longuet-Higgins 1978 b , c ) have suggested two distinct types of instability: at low wave steepnesses we find subharmonic instabilities with fairly low rates of growth, and at higher wave steepnesses there are apparently local (‘superharmonic’) instabilities leading directly to wave breaking. Between these two types of instability is an intermediate range of wave steepnesses where the unperturbed wave train is neutrally stable. In the present paper we employ the time-stepping method of an earlier paper (Longuet-Higgins & Cokelet 1976) to test the rate of growth of each type of instability. For the initial linear stages of each instability, the computed rates of growth are accurately confirmed, and it is verified that the local instability does indeed lead to breaking. The later nonlinear stages of the subharmonic instabilities are further investigated. In the two examples so far computed it is found that the gradual rates of growth of the subharmonic instabilities are maintained, and that ultimately every alternate crest develops a fast-growing local instability which quickly leads to breaking.

Edge waves and surf beat

Abstract: Surf beat, wave motion at relatively low frequency (periods of 30–200 s), is often observed on beaches. However, even with modern instrumentation it is difficult to describe the spatial variation of the low-frequency motion; consequently, the relative importance of a number of suggestions which, at least in theory, provide mechanisms for the generation of low-frequency energy has never been established. Recent observations (e.g., Huntley, 1976) have reinforced the idea that edge waves, the free wave modes trapped at the shoreline, are a major component of low-frequency energy. One of the most interesting explanations of surf beat suggests that the beating between particular pairs of incoming waves leads to resonant growth of edge wave modes, which may then dominate the low-frequency spectrum (Gallagher, 1971). Empirical evidence is essential, as any theoretical development breaks down when the incoming waves break, a fundamental problem with Gallagher's (1971) model. To investigate the importance of this resonant interaction, the general interaction conditions were therefore used to design laboratory experiments in which both resonant and nonresonant conditions were expected. The experimental results show that the response at the beat frequency is stronger when the resonance conditions for edge wave growth are satisfied and that the response is in the form of the theoretically predicted edge wave mode, even when the incident waves are breaking. These results strongly suggest that surf beat is predominantly an edge wave phenomenon.

Measurements and models of fine structure, internal gravity waves, and wave breaking in the deep Ocean

Abstract: Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences.

On the shape and breaking of finite amplitude internal gravity waves in a shear flow

Abstract: This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.

Nonlinear Investigation of the Spatial Resonance Effect in the Nighttime Equatorial F Region

Abstract: In the nighttime equatorial F region, zonal neutral air winds and gravity waves propagating across the magnetic field tend to drive the ionization as if there were no field. When the phase trace speed of a gravity wave equals the drift speed of the ionization, strong ionization perturbations may occur (Whitehead's spatial resonance effect). The resonance effect is described by a parametric differential equation. Without diffusion, it yields perturbations in the form of periodic δ functions. Therefore a coefficient of turbulent diffusion is introduced to limit the perturbation amplitude. Then the equation can be solved in terms of partial Fourier sums. Numerical calculations with reasonable F region parameters indicate that under spatial resonance conditions, gravity waves cause considerable secondary flows of ionization as a result of nonlinear effects. The contours of constant ionization density show steep or even breaking wave fronts similar to those observed by HF radar and radio propagation experiments in the large-scale structure of the equatorial spread F. The spatial resonance mechanism produces field-aligned tubes of decreased ionization density which may be the primary cause of ‘plasma bubbles’ detected by satellite and rocket probes.

Breaking invariants in shoaling waves

Abstract: The inability of present theory to describe correctly the shoaling transformation of surface gravity waves is well recognized. It owes, at least in part, to the lack of experimental information on internal flow fields. This paper describes a portion of the results from laboratory experiments in which the time histories of surface elevation, crest speed, and horizontal subsurface flow velocities in trains of uniform waves were measured at a plurality of stations before and after breaking, as functions of (uniform) beach slope and wave frequency. It was found that over gentle slopes, wave breaking is characterized by invariancy of crest profiles and kinematics and that most important breaking parameters can be expressed in terms of period and breaker height, the latter of which appears to be related simply to deepwater height and steepness.

Wave action and set-down for waves on a shear current

Abstract: This paper considers steady, slowly varying water waves propagating over a gently sloping bed on a steady current. The current varies linearly with depth, and so has constant vorticity ω. The analysis is two-dimensional and dissipation is neglected. Definitions, and expressions correct to second order in the amplitude, are given for the radiation stress, wave energy density E and total energy flux. An average La-grangian [Lscr ], obtained by heuristic arguments from Clebsch potentials, leads to the result that for this particular problem E equals the wave action [Lscr ]ω times the angular frequency ωrm relative to a frame of reference moving with the average-over-depth current velocity Um. This determines the variation of the amplitude with distance explicitly. An analytical expression for the height of the mean water surface is found by a heuristic argument which compares the conservation equations for total energy and wave action. All the results have been checked directly by substitution back into the basic equations. Graphs illustrate the effect of the vorticity ω on the wavelength, amplitude and set-down.

Surf zone measurements of suspended sediment

Abstract: Suspended sediment concentration was measured in approximately 250 breaking waves on undeveloped beaches near Price Inlet, South Carolina, U.S.A., using portable in situ bulk water samplers. As many as 10 instantaneous 2-liter water volumes were obtained in each wave for a total of 1500 samples. Concentrations of suspended sediment were determined at fixed intervals of 10, 30, 60 and 100 cm above the bed for various surf zone positions relative to the breakpoint. The majority of waves sampled during 22 days in June and July, 1977 were relatively long crested, smooth, spilling to plunging in form, with breaker heights ranging from 20 to 150 cm. Surf zone process variables measured included breaker height and depth, breaker type, wave period, surface longshore current velocity, wind velocity and direction. Scatter plots of mean concentration against various process parameters indicate the amount of sediment entrained in breaking waves is primarily a function of elevation above the bed, breaker type, breaker height and distance from the breakpoint. Concentration ranged over 3 orders of magnitude up to 10 gm/1, but varied less than 1 order for samples collected under similar conditions with regard to elevation and breaker type. Plunging breakers generally entrain 1 order more sediment than spilling breakers equal in height. Despite considerable scatter, these data indicate concentration decreases with increasing wave height for waves 50 to 150 cm high, suggesting that small waves can be important in the transport of sand on gently-sloping open coasts.

Field study of breaking wave characteristics

Abstract: This study focuses upon four elements of breaking wave behavior: 1) Relative breaking depth criteria 2) Breaking wave classification 3) Evaluation of the plunge distance 4) Breaking wave height prediction The data set is 116 waves filmed at Virginia Beach, Va., on the Atlantic U.S. coast. The cine-photographic observation technique permitted the viewer to freeze the free surface profile at successive time steps as the waves passed an upright plane grid placed perpendicular to the beach. The results indicate that: 1) While the average value of %/d^ - 0.78, there was a significant difference between plunging and nonplunging waves. 2) Neither the breaker classification of Galvin nor that of Battjes successfully discriminated between plunging and spilling breakers. 3) The distance travelled by the foreface of a plunging wave was found to be underestimated by the free fall trajectory model advanced by Galvin. The field observations show the weakness to be in the plunge time arising from neglect of the vertical velocity component. 4) The breaking wave height prediction formulation advanced by Komar and Gaughan adequately predicts the breaking wave height within the constraints of calculating deep water wave characteristics, neglecting wave refraction and frictional effects. The combined data set covers the breaker wave height between laboratory scale observations to greater than 3 m.

Energy flux and wave action in gravity waves propagating on a current

Abstract: The total energy flux with the mean energy level as a datum is shown to be proportional to the wave action flux for waves on steady irrotational currents. This leads directly to the wave action conservation principle. The set-down of the mean water surface is calculated in a new and simple way. In addition the mean Eulerian current velocity profile is discussed, and the myth of a non-zero mass transport in a pure wave motion is reconsidered. Dissipative effects are neglected.

Mixing in an Arctic Fjord

Abstract: Measurements made in Cambridge Bay, N.W.T., during the winter show that the breaking of internal waves on the shore influences downward salt transport from the homogeneous surface layer produced by saline convection beneath sea ice during growth. Denser water from the shallows, where the depth of this convective layer is limited by the sea bed, flows down the slope to the layer interface contour where the breaking waves introduce turbulence aiding mixing of the convecting water into the lower layer. Away from the boundaries entrainment of salt from the lower to the upper mixed layer is aided by the internal waves on the interface. These two salt transports, downward at the boundaries upward over the basin, produce horizontal salinity gradients which overall make water in the shallows less saline than the surface layer of the basin. The energies available for these mixing processes are estimated.

On the Spectral Evolution of Strongly Interacting Waves

Abstract: Spectral evolution of small amplitude waves can be predicted by the resonant interaction (RI) formalism when the interaction is sufficiently weak in the sense that characteristic interaction times are much greater than wave periods. Often this is not the case, e.g. planetary waves, internal gravity waves and plasma waves which commonly are of large amplitude, interacting in times comparable to wave periods. At still larger amplitude, interaction will occur in times shorter than wave periods and the motion becomes a wave-modified kind of turbulence. By re-examining the RI assumptions, this paper describes a systematic extension to include stronger wave interactions, obtaining in the limit of large amplitude a spectral theory of turbulence. The present method has been used to calculate anisotropic evolution of barotropic planetary (Rossby) waves and of linear waves propagating in a, strongly randomly inhomogeneous medium, in both cases in agreement with resuIts of numericai-hydrodynamic simulations...

Radar imaging of the ocean surface

Abstract: Radar sensors are being used to provide two-dimensional imagery of the ocean surface The radar image has a brightness variation which is proportional to the local backscatter cross-section of the surface at the wavelength of observation The backscatter cross-section is, in turn, a function of the local surface topography and, in the case of a coherent radar system, of the surface dynamics The synthetic-aperture radar imaging technique produces very high resolution images essentially independent of the distance to the surface being imaged This technique is discussed in some detail The emphasis is on recent observations of a large variety of ocean surface patterns Deep ocean waves have been observed under a variety of weather conditions, including hurricanes Breaking waves are observed because of the increase in roughness and the presence of foam Discrete wave-like patterns, which resemble internal wave trains, have been observed in numerous locations; and eddy-shaped, linear, curvilinear and periodic slicks have also been seen The different models for wave image formations are briefly reviewed Specifically, the roughness modulation, tilt modulation, and orbital velocity models are discussed Finally, it is shown that surface randomness does not destroy the coherence of the signal needed to generate the synthetic-aperture image because of the short-term coherence of the small Bragg waves

Shallow-Water Waves and Fluid-Mud Dynamics, Coast of Surinam, South America.

Abstract: : Time series measurements of shallow-water waves and fluid-mud density variations, taken simultaneously with tide elevation and suspended sediment data, indicate that wave/fluid-mud interactions in the nearshore may be largely responsible for the present-day accumulation of fine-grained sediment on the open, unprotected coast of northeastern South America. Results of field experiments conducted along the central Surinam coast show that accumulations of fluid mud, which can be found up to 1.5 m thick on western flanks of migrating shore-attached mudbanks, affect incoming swell by changing their form from sinusoidal to solitary-like and by preventing wave breaking except for occasional spilling. As long-period swell (T = 12-16 sec) propagates over shallow banks of fluid mud, the wave height to water depth ratio remains nearly constant at 0.23; the steady decrease in wave height with shoaling water depth indicates that substantial amounts of wave energy are lost to a fluid-mud bottom even though breaking does not occur. Using the concept of wave-associated currents, it has been shown, in taking angle of wave approach, average observed concentration of sediment in suspension, and net drift as given by solitary wave theory, that volume transports can be explained by waves alone. If a hypothesis of mud transport by solitary waves is accepted, then the continuous shoreward transport of suspended fluid mud, combined with the high rate of wave energy dissipation, explains in part the ability of muddy coasts to protect their shorelines.

Hydromagnetic-gravity wave critical levels in the solar atmosphere

Abstract: It is shown that the discontinuous jump in the vertical wave energy flux of slow hydromagnetic-gravity waves, occurring at a critical level, which is accompanied by wave absorption, and the existence of a reflection point imply that slow waves are trapped in the solar atmosphere. Thus such a system behaves as a leaky wave guide.

Uniform Potential Vorticity Flow: Part II. A Model of Wave Interacions.

Abstract: Interactions between waves that satisfy uniform potential vorticity are considered. The formal analysis is restricted to a triad of eigenfunctions and the reduced system is constrained to satisfy conservation of total energy and conservation of available potential energy on plane rigid horizontal boundaries. A linear stability analysis is used to establish the properties of unstable waves in two cases: basic flows with anti-symmetry, and basic flows with symmetry in the vertical direction. A necessary condition for instability is that the vertical wavenumber of the basic flow must fall between the vertical wavenumbers associated with the perturbation waves. The properties of unstable waves in both cases are compared and analogies with the stability properties of the two-layer model are pointed out.

Arrangement for concentrating sea waves

Abstract: An arrangement for concentrating sea waves, includes a grid-like structure of stopping and/or delaying elements adapted to influence the amplitude and/or phase of the waves and located in such positions in the water that the elements in interaction with the incident sea waves form an interference pattern which gives a concentration of the wave energy in a limited area (concentration area). When the wave energy is to be utilized for power production, the grid-like element structure is designed to give a concentration of the wave energy in a concentration area located in the short-range field of the element structure. Preferably the elements in the structure are mainly situated in front of the concentration area with respect to the dominant wave incident directions. Moreover, the element structure may have an extension (aperture) which is substantially larger than the wave length of the dominant waves at the location.

On the scattering of sound by internal waves in the ocean

Abstract: The parabolic approximation to the wave equation is applied to the calculation of the spectral density of amplitude and phase fluctuations of a plane sound wave propagating through a random field of internal waves in the ocean. The dependence of the predicted spectra on wave number and frequency shows that the lowest‐mode internal waves dominate the phase variance, while the amplitude fluctuations are controlled by intermediate scales. The results are compared with previous theories and available data. There is a discrepancy between observed amplitude spectra and predictions based on the internal wave models. It is concluded that internal waves are not solely responsible for the scattering of sound in the ocean and that other effects must contribute.

Suspension and transportation of fluid mud by solitary-like waves

Abstract: The suspension and transportation of fluid muds in the nearshore zone by shallow-water, solitary-like waves has been investigated along the coast of Surinam, South America. Accumulations of fluid mud which front the coast at a spacing of 30-60 km affect incoming swell by changing the wave profile from sinusoidal to solitary-like and by preventing wave breaking except for occasional spilling. Simultaneous time-series measurements of wave height and period, fluid-mud density, and tide elevation, along with results of suspended-sediment measurements, indicate that in cases when the bulk density is less than 1.20 g/cm and where water depths are less than 5 m fluid mud is suspended from the bottom in two frequency modes: wave-by-wave suspension (-10 sec) and tide related suspension (-12.4 hr) . Surface-water suspensate concentrations exceed 3.4 x 10 mg/1 as up to 0.5 m of fluid mud is periodically removed from the bottom. High concentrations of suspended fluid mud, together with solitary-like waves from the northeast throughout the year, can lead to extraordinarily high sediment transport volumes. Calculations based on solitary wave theory and on data obtained from this ft ^ study indicate that 15-65 x 10 m of mud can move along shore each year without involving breaking waves, the concept of radiation stress and a nearshore circulation cell, or bed-load transport. These values are 10 to 100 times greater than typical transport rates along sandy coasts.

Transfers across an air‐water interface at high wind speeds: The effect of spray

Abstract: The generation of spray under high wind speed conditions has been investigated in a laboratory wind, water wave research facility. An electrostatic capacitance wire probe system was used to measure spray. Mean energy transfers were determined by a standard boundary layer integral technique. For a given wind velocity the spray concentration decreases logarithmically with increased distance from the mean water surface. The spray concentration and distribution results of this study are consistent with field and other laboratory studies (with one exception). While wave breaking, whitecapping, and bubble bursting during spray formation contribute to increased interface roughness, calculations based on the laboratory data show that the latent and sensible heat transfers from the spray drops make a negligible contribution to the energy transfer observed. The marked increase in measured energy transport under spray conditions is due almost entirely to increased transfer from the roughened interface (there is a linear correlation between the latent and total heat transfers and the root-mean-square water surface displacement).However, extrapolation of the laboratory results suggests strongly that spray drops make a significant contribution to the energy transfer in field situations with wind, temperature, and humidity conditions equivalent to those in the laboratory because of greatly increased droplet boundary layer thicknesses in the field.

Effects of wave-induced diffusion on thermospheric acoustic-gravity waves

Abstract: When wave-induced diffusion is included in the equations governing acoustic-gravity wave propagation in an atmosphere in diffusive equilibrium, it is found that phase and amplitude relationships between the density fluctuations of individual atmospheric constituents agree with AE-C satellite observations of wavelike structure only over a narrow range of wave periods. For a 400-km horizotal wavelength, the observations are consistent with internal gravity waves of periods 11.5-22 minutes propagating at phase speeds 300-600 m/sec.