Showing papers on "Breaking wave published in 1973"

Heuristic Models of Sand Transport in the Surf Zone

Abstract: Physical mechanisms are described for both the onshore/offshore and longshore modes of sand transport within the surf zone. The onshore/offshore mode of motion is based on consideration of whether the initial sand suspended during the wave breaking undergoes a net shoreward or seaward displacement as it falls to the bottom. The two important parameters are the wave steepness and ratio of fall velocity to wave period. Using data from three earlier investigators, and choosing one empirical constant, it is found that these two parameters can predict the correct onshore or offshore direction of sand motion in 161 of 184 individual experimental runs. The longshore mode of motion (littoral drift) is considered to be the advection, by the longshore current, of the sand suspended by the breaking waves. The quantity of sand suspended is taken to be an amount which, during its fall to the bottom, consumes a fixed portion of the wave energy flux into the surf zone. The average longshore current is based on the simplest representation by Longuet - Higgins. The resulting expression for littoral drift is quite similar to earlier empirically determined equations; however, the relationship here obtained includes beach slope, sand grain diameter, beach roughness, etc. These models should be useful in beach restoration projects and other coastal engineering projects concerned with sand transport within the surf zone.

On the existence of critical levels with applications to hydromagnetic waves

Abstract: It is proved that a critical level, at which a wave packet is neither reflected nor transmitted, can exist only if the wave normal curve, which is formed by taking the cross-section through the wave normal surface in the plane of propagation, possesses an asymptote which is parallel to the direction of variation of the properties of the medium through which the wave packet moves. This condition, when applied to various types of hydromagnetic waves (such as hydromagnetic waves of the inertial or gravity type, or slow magnetoacoustic waves), shows that critical levels for such waves can exist only if the direction of spatial variations of the medium is perpendicular to the ambient magnetic field. Provided that the angle between the gravitational acceleration, or the rotation axis, and the magnetic field is not zero, hydromagnetic critical levels, characteristic of the gravity or inertial type, act like ‘valves’ in the sense that the wave packet can pierce the critical level from one side and is captured from the other side. It is also pointed out that critical-level behaviour is to some extent a consequence of the WKBJ approximation since the other limit, namely when the waves feel an almost discontinuous behaviour in the properties of the medium, gives markedly different results, particularly in the presence of streaming, which can give rise to the phenomenon of wave amplification.

Water wave models and wave forces with shear currents

Abstract: Water wave modeIs, incorporating shear currents, are developed for linear and nonlinear waves. The first model assumes a constant vorticity over the depth of the fluid; the case for a wave propagating on a linear shear current. For greater generality, a second model is presented which assumes that the fluid is composed of two layers, each with a different, but constant, vorticity. The nonlinear solutions require the use of a numerical perturbation procedure. The last wave model, using a finite difference approach, generates waves propagating on arbitrary vorticity distributions. Examples of the effect of the vorticity on the waves are presented. Further, the use of two of these models in the analysis of actual measured wave data is shown. Wave force measurement programs conducted for the purposes of obtaining drag and inertia coefficients on structures are affected by the presence of currents, and the biases introduced into these coefficients by neglecting the currents are investigated via small amplitude wave theory. Further, an approximate procedure for de termining currents for measured wave force data is presented, as weIl as some results from Wave Project 11 data, which were obtained during Hurricane Carla in the Gulf of Mexico.

Critically Refracted Waves in a Spherically Symmetric Radially Heterogeneous Earth Model

Abstract: Summary A theoretical analysis of acoustic waves refracted by a spherical boundary across which velocity and density increase abruptly and below which velocity and density may either increase or decrease continuously with depth is formulated in terms of waves generated at a harmonic point source and scattered by a radially heterogeneous spherical body. Through the application of an Earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as an integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient with depth. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle: (1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), waves interacting with the boundary at the critical angle of incidence have the same form as the classical head wave for flat, homogeneous layers. (2) For gradients more negative than critical, the amplitude of waves incident at the critical angle decay more rapidly with distance than the classical head wave. (3) For gradients that are positive, null, and less negative than critical, the amplitude of waves near the critical angle decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave field can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

Numerical simulation of the generation and breaking of internal gravity waves

Abstract: A numerical model is presented that permits the simulation of stratified fluid phenomena in which gravitationally unstable regions are present. The influence of subgrid scale turbulence generation due to convective instability is parameterized by relating eddy viscosity coefficients to the local Rayleigh number in unstable regions. The model is used to study three different laboratory scale flow problems involving gravity wave generation, wave breaking, and penetrative convection. The numerical solutions show good agreement with available experimental and analytic results as well as with a numerical solution obtained by other investigators.

Dynamics of the non-linear interaction of magnetohydrodynamic waves

Abstract: The dynamics of four non-linearly interacting coherent magnetohydrodynamic (MHD) waves (plasmons) is investigated. Exact analytical solutions are obtained which describe the time behaviour of the amplitudes and phases of the waves. The analysis of the solutions shows that they vary periodically. The periods of variation are also found for various types of coherent interacting MHD waves.

A Method of Analyzing Transient Waves by Space-Time Cross Spectra

Abstract: Spectral formulas for analyzing transient waves are presented. Cross-spectral analysis of space-Fourier coefficients isolates travelling waves and standing wave oscillations, and provides statistical information concerning their structure and energetics.

On small scale breaking waves

Abstract: : It is shown that the surface wind drift in the ocean substantially reduces the maximum wave height and wave orbital velocity that can be attained before breaking. Incipient breaking is characterized by the occurrence of stagnation points at wave crests, but not by discontinuities in slope. After breaking, there is in the mean flow a stagnation point relative to the wave profile near the crest of the broken wave, on one side of which the water tumbles forward and behind which it recedes more smoothly to the rear. Flow visualization studies indicate the general extent of the wake behind the breaking region; it is shown to be turbulent but momentumless. (Author)

Elastic waves generated from sudden vanishing of rigidity in a spherical region

Abstract: As a special case of a relaxation source, a theoretical study is made of the seismic wave radiation from the sudden formation of a spherical fluid region in an infinite elastic medium subjected to pre-existing shear stress. The results are discussed in comparison with those for a spherical void cavity model in the same initial stress field. Almost or exactly identical results be-tween the present liquefaction model and the cavity model are found for (1) the spectral density of zero frequency limit at a large distance, Which coincides also with the displacement amplitude expected for an equivalent double-couple point source, (2) the ratio of P wave to S wave corner fre-quency, which is approximately equal to the velocity ratio of P waves to S waves, and (3) the total wave energy. Differences between the two models appear in (1) the predominant period of the displacement spectrum, (2) waveform of P waves in particular, and (3) the energy ratio of S waves to P waves (6.8 for the liquefaction model and 4.7 for the cavity model).

Mass-transport in water waves of very small amplitude

Abstract: It is shown analytically that even for waves whose amplitude is small compared with boundary-layer thickness there are at least three possible solutions for the mass-transport velocity in the interior of the fluid. Masstransport velocity profiles were observed in a wave tank and were found to be similar to those given by one of these solutions but significantly different from LONGUIT-HIGGINS' "conduction" solution even for waves of very small amplitude. It was also observed that when the wave amplitude dropped below a certain value the mass-transport velocity in the boundary layer at the bed ceased to be in the direction of wave propagation.

Gross and Wave Load on a Large Vertical Cylinder - Theory and Experiment

Abstract: This paper discusses a study wherein the dynamic effects on a large vertical circular cylinder due to waves were measured experimentally in a wave tank in the form of pressures and forces. Because of the large diameter of the cylinder compared to the wave lengths, appreciable diffraction of the waves from the surface of the cylinder was expected. Expressions of pressures, forces and moments were developed following the classical analysis of Havelock on a fixed obstacle in waves and which includes wave diffraction effects. The viscous effects were neglected in the analysis on the assumption that for a cylinder of this size the inertia force is most predominant. Linear wave theory was applied in the study of the interaction of waves with a bottom-mounted object. The prediction results from this theory compared favorably with the experimentally measured data.

Unidirectional energy transfer in nonlinear wave--wave interactions

Abstract: In this paper, the wave‐energy transfer in a system of three nonlinearly interacting waves is studied. Sufficient conditions for the unidirectional transfer of energy into any wave from the remaining waves and bounds for the wave amplitudes are established. Also, a relation governing the rates of energy transfer between the waves is derived. The results are applied to a magnetized plasma with three nonlinearly interacting waves.

Propagation of electrohydrodynamic surface waves in a conducting fluid

Abstract: A comprehensive study is made of the electrohydrodynamic surface wave phenomena in an inviscid, incompressible conducting fluid in the presence of an external steady electric field due to an arbitrary periodic surface pressure distribution. The initial value wave problem has been solved by the Laplace and the generalized Fourier transforms in conjunction with asymptotic techniques — as advanced in a previous work ofDebnath andRosenblat [12]. An explicit steady state solution related to short and long wave approximations is found. The asymptotic behaviour of the transient solution for large time is demonstrated. It is shown that there are two surface wave-trains propagating in the conducting medium, one of which corresponds to the classical surface wave train and the other is originated entirely due to the interactions of the electric field with gravity. The simultaneous effects of the electric field and surface tension on the propagation of small amplitude surface waves are analyzed. The implications of the wave solutions related to very deep and shallow fluids are explored. A discussion of the electrohydrodynamic wave motions with their characteristic features is presented.

Breaking and turbulent transition in ion acoustic waves

Abstract: New wave-particle processes determining the evolution of large-amplitude, low-frequency ion waves have been observed in numerical and laboratory experiments.

Interfacial Wave Breaking in Stratified Liquids

Abstract: Experimental results are presented which support the hypothesis that interfacial instability is controlled largely by the difference in density, Δ P , and the thickness of the transition region, δ, between the two layers. The horizontal velocities of the upper and lower layers associated with an internal seiche episode in a stratified lake are examined analytically in relation to critical shear gradients necessary for the growth of unstable short period interfacial waves with frequency close to the Brunt-Vaisala frequency. Experimental results obtained from steady nonuniform surface flows over a stagnant denser fluid are presented which help to clarify the conditions for the occurrence of the short period waves.

Investigation of the velocity field over waves using a wave follower

Abstract: : The turbulent velocity field over simple propagating waves is investigated by hot-film sensors in a wind and wave facility. Use is made of a wave follower to obtain measurements below the wave crest level. Turbulence measurements are obtained in a wave following frame over the range 1.75 - 25 cm above the instantaneous water level. The measurements are transformed to an Eulerian frame and compared to measurements obtained from fixed probes over a height range 10-50 cm above the mean water level. In the overlap region the transformed wave following results are in reasonable agreement with the fixed probes results. The measurements below the crest level indicate rapid variations in Reynolds stresses and wave induced velocities. The results suggest nonlinear wave induced perturbations close to the water surface and reveal weaknesses in assumptions adopted in recent theoretical models of turbulent shear flows over waves. (Author)

A Shallow Water Design Wave Procedure Applicable to Small Cays and Submerged Reefs

Abstract: A procedure is described for determining design waves for engineering structures located near the shore-line in tropical waters, where the off-shore topography consists of a near-vertical reef edge, followed by relatively shallow water over a horizontal bottom leading up to the shore-line. The work was originally developed to provide design waves for the installation of Automatic Weather Stations on sand cays which have accumulated on small coral reefs forming part of the Australian Great Barrier Reef. The procedure depends only on a knowledge of the deep-water design waves (assumed generated by tropical cyclones), and an idealised near-shore geometry, and traces the wave transformations through three steps: energy transmission at the reef edge, and the reforming of a solitary wave in shallow water; propagation of this wave through the shallow water; final shoaling and breaking of the wave at the shoreline. A number of assumptions must be made to facilitate the procedure, together with estimates of the changes in mean water to facilitate the procedure, together with estimates of the changes in mean water level caused by wave breaking processes. However, the final figure are believed conservative.

Transient development of capillary-gravity waves in a running stream

Abstract: An initial value investigation is made of the propagation of capillary-gravity waves generated by an oscillating pressure distribution acting at the free surface of a running stream of finite, infinite, and shallow depth. The solution for the free surface elevation is obtained explicitly by using the generalized Fourier transform and its asymptotic expansion. It is found that the solution consists of both the steady state and the transient components. The latter decays asymptotically as t → ∞ and the ultimate steady state is attained. It is shown that the steady state consists of two or four progressive capillary-gravity waves travelling both upstream and downstream according as the basic stream velocity is less or greater than the critical speed. Special attention is given to the existence of the critical values associated with the running stream of finite, infinite, and shallow depth. A comparison is made between the unsteady wave motions in an inviscid fluid with or without surface tension.

On the surface-to-bulk mode conversion of Rayleigh waves.

Abstract: Surface-to-bulk wave conversion phenomena occurring at a discontinuity characterized by a surface contour deformation are shown to be usable as a means for tapping Rayleigh waves in a nonpiezoelectric solid. A boundary perturbation technique is used in the treatment of the mode conversion problem. A systematic procedure is presented for calculating not only the first-order scattered waves, which include the reflected surface wave and the converted bulk wave, but also the higher order terms.

The Kinematics of Water Particle Velocities of Breaking Waves within the Surf Zone.

Abstract: Simultaneous measurements of waves, and vertical and horizontal water particle velocities were made at the breaker-line within the surf zone using a capacitance type penetrating wave staff, a pressure wave gauge, and an electromagnetic current meter. Wave measurements were also made at seaward and shoreward locations. The wave energy-density spectral components were converted to velocity spectral components using linear wave theory. These computed values compared well qualitatively with the measured velocity spectra. Quantitatively, the results showed that linear theory underpredicted wave-induced horizontal velocity spectral components by about 50 percent at the frequency of peak energy. Probability density functions were computed and compared to Gaussian and Gram-Charlier distributions using the chi-square goodness-of-fit test. The Gram-Charlier distribution qualitatively gave the better fit to the data. (Modified author abstract)

Stability of Armour Units against Breaking Waves

Abstract: The stability of rubble mound breakwaters is investigated for armour units of graded rock, Tribars and Dolosse when subjected to breaking waves. Damage history with wave duration is studied and expressions relating the stability coefficient in Hudson's equation with percentage damage determined. Pattern placement of Tribars is shown to substantially increase their stability against wave attack but if design conditions are exceeded, failure tends to be catastrophic. The other units tested showed progressively increasing damage with increasing wave height up to a damage level of 20 per cent.

Atmospheric Gravity Waves and the Energy of the Jet Stream

Abstract: We propose that traveling internal gravity waves, like the lee waves referred to by Lilly, can have a significant effect in the vertical transfer of kinetic energy and momentum from the westerly flow. A program to study the effect is described here.

Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

Abstract: The stability of a periodic ion-acoustic wave of a finite amplitude propagating in a nonisothermal plasma is investigated. It is demonstrated that such a wave is unstable with respect to the splitting into a large number of satellite waves with effective wave numbers different from the wave number of the initial wave. The phase velocity of the satellite waves differs therefore from that of the initial pulse. Hence, the satellite waves with bigger phase velocity will “overtake” the initial pulse and turbulize the upstream plasma. The scattering of ions and electrons by the fluctuations of electric field of turbulent oscillations will cause the energy dissipation of the initial ion-acoustic wave translational motion and produce a collisionless shock wave.

On the generation of capillary-gravity waves due to two-dimensional sources

Abstract: With the aid of the generalized function method, a study is made of the linearized theory of transient development of capillary-gravity waves in an inviscid, incompressible and homogeneous liquid of finite and infinite depth due to an arbitrary oscillating source situated at a finite depth below the undisturbed free surface of the liquid. The initial value problem is solved by using Laplace-Fourier transforms combined with asymptotic methods. The asymptotic solution is found to consist of the steady state and the transient components which are independently modified by surface tension. The latter decays more rapidly as timet → ∞ due to the presence of surface tension than in the case where surface tension is neglected. It is predicted that the principal effect of surface tension is to increase both the phase and group velocity of the waves and make the energy more readily available among the rapidly travelling progressive surface waves. In addition to the effects of surface tension on the physical properties of the wave motions, our method of solution provides an interesting illustration of the applicability of generalized functions in water wave phenomena.