Showing papers on "Breaking wave published in 1968"

Breaker type classification on three laboratory beaches

Abstract: Breaker type, for waves on smooth concrete slopes, depends on beach slope m, wave period T, and either deep-water or breaker height, H0 or Hb. For forty-three varied laboratory conditions, breaker type can be sorted fairly well by either of two dimensionless combinations of these variables, an offshore parameter, H0/(L0m2) or an inshore parameter, Hb/(gmT2). As either of these parameters increases, breaker type changes from surging or collapsing to plunging to spilling. For the offshore and inshore parameters, respectively, the surge-plunge transition values are about 0.09 and 0.003 and the plunge-spill transition values are about 4.8 and 0.068. The deep-water heights in the offshore parameter were computed from linear, wave-generator theory. Breaker type data were obtained from films of breaking waves for conditions that produced a dominant breaker type, free from interference by secondary waves.

Planetary Rossby Waves Propagating Vertically Through Weak Westerly Wind Wave Guides

Abstract: The role of horizontal wind shears in the vertical propagation of planetary Rossby waves is investigated using an adiabatic linear model. We discuss wave guides formed by regions of weak westerly wind. If the wave guide is formed by trapping of waves between strong westerlies and/or the geometric poles, the ducting occurs as a wave propagation in discrete normal modes of the internal wave guide. On the other hand, for wave guides formed by one or more lines of zero wind, waves are absorbed rather than reflected at the zero wind line so that there are no normal modes of the wave guide. Disturbances excited in the lower stratosphere in the equatorial zero wind wave guide will terminate somewhere in the equatorial stratosphere, but eddy motions may be maintained in the tropics at higher levels by leakage from the Aleutian high planetary wave propagating vertically in a polar wave guide. The Aleutian high should he significantly attenuated by such leakage. The theory of zero wind line absorption sugg...

On standing internal gravity waves of finite amplitude

Abstract: Two-dimensional internal gravity waves in a rectangular container are examined theoretically and experimentally in (a) fluids which contain a single density discontinuity and (b) fluids in which the density gradient is everywhere continuous. The fractional density difference between the top and bottom of the fluid is small.Good agreement is found between the observed and calculated wave profiles in case (a). Unlike surface standing waves, which tend to sharpen at their crests as the wave amplitude increases, and which eventually break at the crests when fluid accelerations become equal to that of gravity, internal wave crests are found to be flat and exhibit no instability. In the case (a) breaking is found to occur at the nodes of the interfacial wave, where the current shear, generated by the wave itself, is greatest. For sufficiently large wave amplitudes, a disturbance with the form of a vortex but with direction of rotation reversing twice every cycle, grows at the wave node and causes mixing. This instability is found to be followed by the generation of cross-waves, of which two different forms are observed.Several modes of oscillation can be generated and are observed in a fluid with constant density gradient. The wave frequencies and shape are well predicted by theory. The experiments failed to establish any limitation of the possible wave amplitudes.

On the generation, dissipation, and prediction of ocean wind waves

Abstract: A method based on the equation of radiative transfer has been developed for predicting the two-dimensional wind wave spectrum in the North Atlantic Ocean. The model takes account of wave generation by both resonance and instability mechanisms. A simple representation for wave breaking is also included, as are the effects of nonlinear wave interactions. This combination of energy transfer mechanisms is used to compute wave spectra that are in reasonable accord with observations. The results question the concept of a ‘fully developed’ spectrum. The work also points up a lack of understanding of the particulars of various energy transfer mechanisms, as well as the shortcomings of the basic predictive input data.

Longshore transport of sand

Abstract: Simultaneous field measurements of the energy flux of breaking waves and the resulting longshore transport of sand in the surf zone have been made along three beaches and for a variety of wave conditions. The measurements indicate that the longshore transport rate of sand is directly proportional to the longshore component of wave power.

Refraction of Water Waves

Abstract: An investigation is presented of the propagation of three-dimensional, harmonic waves of small amplitude through water of constant depth or gradually varying depth. Within the framework of linear theory for potential flow, the results are exact for propagation over horizontal bottoms, e.g., diffraction, and approximate for propagation over sloping bottoms, e.g., refraction combined with diffraction. An expression is given for the velocity potential of three-dimensional waves, harmonic in time. The velocity potential must fulfill the classical hydrodynamical conditions. An analysis of the resulting relationships shows that the magnitudes of phase speed and energy flux are affected by amplitude variations. The time-averaged energy flux is directed along wave rays, regardless of amplitude gradients along the wave crests. The expressions for phase speed and energy flux do not involve wave rays; they provide the basis of a computational scheme in which the wave characteristics are computed in grid points which have a predetermined location. Such method may be an alternative for existing methods which utilize wave rays.

A Synthesis on Wave Run-Up

Abstract: A critical survey of existing theories and experiments on wave run-up is carried out. The theories of run-up of nonbreaking waves are analyzed first. Breaking criteria and the main theories of run-up of breaking waves are presented, including the theories for the run-up of a bore, the nonsaturated breaker theory, and the numerical method for calculating run-up. This set of various theories is compared with experimental investigations. A simple case illustrates how the wave run-up can be enhanced by resonance effects.

Experimental investigation op shock pressures against breakwaters

Abstract: This paper describes an experimental investigation of shock pressures against breakwaters caused by "breaking waves. The study only considers shocks of a compressive type, which occur if the wave front is formed in such a way that an air cushion is entrapped between the wave and the wall. In this case the compression and expansion of the air cushion plays an important role m the pressure variation. Only waves preceded by non-breaking waves were used. For different combinations of bottom geometry and water depth the occurrence of shock pressures of different magnitudes was studied varying the wave height and the wave period. For some interesting combinations of bottom geometry and wave dimensions a series of tests were made to investigate the distribution over the wall of shock pressure and of shock impulse. The results, presented m diagrams and tables, have been commented on and analysed with special respect to the chosen test procedure.

The effect of wave energy spectra on wave run-up

Abstract: Previous investigations carried out "by the Delft Hydraulics laboratory have shown the necessity of applying irregular waves m studies on wave run-up. The installation of a wave generator driven "by hydraulic actuators has created the possibility of producing irregular waves with arbitrary wave spectra. Investigations performed with this type of wave generator show the influence of the shape of the energy spectrum on the wave run-up on smooth straight slopes of 1:4 and 1:6. The results are compared with run-up figures derived from experiments with wind generated waves and with monochromatic waves.

Wave forges on boundaries and submerged bodies

Abstract: A qualitative description is given of the physics of wave forces. Besides the well-known case of non-breaking waves with rigid boundaries, the paper describes the mechanism of breaking and the very intense but short pressure pulses caused by breaking waves. The effects of flexible boundaries are also briefly discussed. In a given locality the problem of resisting wave forces depends for each organism on its shape and compliance. Favourable shapes and strength properties are suggested.

A Numerical Study of Transient Rossby Waves in a Wind-Driven Homogeneous Ocean

Abstract: The primitive hydrostatic equations for a rectangular homogeneous ocean with a free surface on a β-plane are integrated numerically for 60 days from an initial state of rest and undisturbed depth of 400 m. A zonal wind stress (maximum 2 dyn cm−2) and a lateral eddy viscosity (108 cm2 sec−1) are assumed. A series of transient Rossby waves of approximately 1000-2000 km in length form in the central and eastern basin, and undergo a well-marked life cycle of amplification and decay as they propagate westward at ∼1 m sec−1 relative to the zonal current. The northward boundary current in the west (∼1 m sec−1) and the counter-currents in the northwest (∼10 cm sec−1) may be identified as the first stationary members of a continuing series of waves, with subsequent transients showing characteristics of reflected Rossby waves and reaching progressively smaller maximum amplitudes. The standing wave pattern (wavelength ∼600 km) in the north-west is a characteristic nonlinear effect, and is associated with th...

Nature of Electron‐Fluid‐Dynamical Waves

Abstract: A one‐dimensional, inviscid, multifluid model is employed to describe a constant velocity, steady‐profile, ionizing electron‐fluid‐dynamical wave propagating into a pure atomic gas subjected to an applied electric field E0. It is demonstrated that the electron‐fluid equations can be decoupled from the remaining equations allowing description of the wave in terms of electron variables only. Wave speed and resultant degree of ionization are derived as functions of applied field and initial gas pressure. Certain limiting conditions governing the existence of such steady‐profile waves and comparison with the experimental work on breakdown waves are also presented.

Hyperbolic waves and their shoaling

Abstract: Is is very difficult for engineers to deal with the cnoidal wave theory for practical application, since this theory contains the Jacobian elliptic functions, their modulus k, and the complete elliptic integrals of the first and second kinds, K and E respectively. This paper firstly proposes formulae for various wave characteristics of new waves named "hyperbolic waves", which are derived from the cnoidal wave theory under the condition that k = 1 and E = 1 but K is not infinite and are a function of T/g/h and H/h, so that cnoidal waves can be approximately expressed as hyperbolic waves by primary functions only, in which T is the wave period, h the water depth and H the wave height. Secondly, as an application of the hyperbolic wave theory, the present paper deals with wave shoaling, that is, changes in the wave height, the wave crest height above still water level, and the wave velocity, when the waves proceed into shallow water from deep water.

Beaches Produced by Waves of Low Phase Difference

Abstract: A theoretical and experimental study of the action of swell waves on model beaches shows that the beach slope and the distance from the shore to the breakers correlate with the breaker height, wave period and grain diameter. The experiments were carried out using quartz sands and wave periods in the range of 0.8 sec to 1.34 sec. Wave heights were used up to a maximum breaker height of 6 cm. The waves employed were of low phase difference, i.e., the ratio of time of uprush to wave period being less than 0.7. When this ratio is exceeded, the wave period ceases to be important. Using a continuity approach it is shown that the energy lost in breaking, friction and turbulence and in moving material, amounts to about 25% of the incident wave energy when the beach angle is highest, to about 50% when the beach is at its lowest level within the range considered.

Nonlinear Interaction of Electromagnetic Waves in a Cold Magnetized Plasma

Abstract: The nonlinear interaction of electromagnetic waves propagating in a cold plasma across a magnetic field is investigated The amplitude of the generated wave is evaluated, and numerical computations are given for two cases of interest: (a) the interaction of an extraordinary wave with an ordinary wave leading to the generation of an ordinary wave; (b) the interaction of two ordinary waves leading to the generation of an extraordinary wave The results show that under appropriate conditions the detection of generated wave is feasible and the scheme should provide a diagnostic method for measuring the local density and its fluctuations in magnetized plasmas

Breaking wave criteria; a study employing a numerical wave theory

Abstract: Although it is well recognized that wave systems in nature are irregular, comprising a spectrum of fundamental periods, there is still a need for improving our understanding of near-breaking nonlinear wave systems which contain a single fundamental period. For example, most of the shallow water design situations and other cases including forces on small diameter structures in which drag forces predominate are more directly treated in terms of a "design wave" rather than a wave spectrum. This situation is contrasted to many important engineering design problems in which the dynamics of the system are paramount; for example, in the case of a moored drilling vessel. Finally, one may reasonably expect that accurate solutions to the problem of nonlinear wave systems with a single fundamental period will lend insight regarding productive approaches to the more realistic problem of a spectrum of nonlinear waves. This paper investigates the applicability of the stream function wave theory1 for the representation of breaking and near-breaking waves. This particular problem has received little attention, although considerable progress has occurred on two related problems: 1. The development of wave theories covering a wide range of relative water depths and wave heights, and 2. The development of wave theories which apply at breaking conditions. In general, although these theories may be applicable for the limiting wave conditions, their basis of derivation is such that they cannot be extended to non-breaking waves. The purpose of the present investigation, then, is to establish whether or not the stream function wave theory can be applied to span the range extending up to breaking conditions.

The effects of bottom configuration on the deformation, breaking and run-up of solitary waves

Abstract: Experiments were conducted to determine the various effects on the shoaling, breaking and run-up of solitary waves resulting from the bottom configuration. An initial set of experiments investigated the effect of the initial bottom slope on the breaking and run-up of a wave on a second, higher slope. A second set of experiments considered the effect of a continental shelf configuration on the transmissibility of waves in the shoreward direction, and the decomposition of the waves due to the shallower water depth on the continental shelf. It was found that, in order to make predictions at or near the shoreline for waves generated in deep water, it is necessary to consider the total configuration of the bottom leading to the shoreline.

Waves in shallow water due to arbitrary surface disturbances

Abstract: The velocity potential and the surface elevation are calculated for the three-dimensional motion of surface waves excited by any local disturbance of the surface of a sea with constant depth. Approximate values of the resulting wave integrals are given for large values of time and distance. The results are illustrated using physically plausible distributions of the initial disturbance. Some features of the waves are discussed.

Seismic wave propagation on a heterogeneous polar ice sheet

Abstract: Seismic wave propagation in a heterogeneous wave guide was studied using data obtained from several antarctic expeditions The upper part of a polar ice sheet forms a wave guide in which a variety of body wave phases and surface waves can be propagated The relative energy in successive compressional wave multiples can be predicted approximately from classical ray theory and measured velocity data A compressional wave train observed on the Ross Ice Shelf appears to result from constructive interference of successive compressional wave multiples Such wave trains are not recorded on the polar plateau, since the conditions for constructive interference do not exist Analysis of surface wave dispersion from sites on the polar plateau and the Ross Ice Shelf suggests that the plateau wave guide is essentially isotropic but that the wave guide on the shelf is transversely isotropic and that compressional wave velocity anisotropy of up to 20% may be found This suggests that the base of the wave guide is probably deeper than indicated by refraction data

An experimental study of breaking-wave pressures

Abstract: : Tests were conducted to gain more information concerning the shock pressures created by water waves breaking against vertical barriers. These wave pressures were studied using small-scale oscillatory waves in a flume fitted with a beach slope and test wall. The variation of pressure with both time and position on the wall was determined for several wave heights, wave periods, water depths, and beach slopes. Great scatter in the magnitude of the shock pressure was observed for each of the wave conditions tested. This variation in the value of the shock pressure is believed to be caused by slight variations in the shape of the incident breaking wave. Therefore, many tests were made using the same wave conditions in order to more accurately determine the magnitude of the shock pressure.

Pressures by breaking waves on composite-type breakwaters

Abstract: The intensity and vertical distribution of pressures exerted by water waves on the vertical walls of composite-type breakwaters vary in a very wide range from those of high shock pressures exerted by severe breaking waves to those of low pressures similar to hydrostatic pressure due to standing waves, depending upon the shape of the composite-type breakwaters, the characteristics of incoming waves, and the depths of water where the breakwater are located. In this paper are presented the intensity and vertical distribution of pressures exerted by various kinds of breaking waves on the vertical walls of composite-type breakwaters with low and large base-rubble-mounds constructed m comparaticely deep water.

Bow Wave Analysis of A Simple Hull Form

Abstract: Hitherto the wave analysis has been applied mainly to the direct determination of the total wave-making resistance component and not to the improvement of either the current wave-making resistance theory or the hull form design procedure. To obtain full understanding of the actual wave-making phenomena, the analysis of the bow wave alone, not of the resultant wave, particularly the detection of the inherent wave amplitude is most indispensable.This paper presents the first example to analyze the wave amplitude function from the measured bow free wave (not from the resultant free wave). Asymptotic expansion of the exact expression for the free wave elevation was applied.A 2.5 m Wigley model was adopted to measure the bow wave, where a capacity-typed wave recorder was applied. The analyzed bow wave amplitude is compared with the calculation assuming that the equivalent singularity distribution is given by Michell's thin ship approximation. Noticeable is the reduction of the actual wave amplitude not only at the higher θ range but also at the lower θ range. The former may be attributed to the extremely steep wave slope there as is easily expected from the working limit of the linearized theory. However it is very important to clarify the real cause for the inconsistency at the lower θ range. Presently the authors suppose that this may come from the so-called “blocking effect” of ship hull.To determine this, further approach is urgently desired both from experiment and from theory.

Wave forces on piles in relation to wave energy spectra

Abstract: The determination of wave forces on piles is for an important part based upon data obtained with regular laboratory waves. Nonlmearities m the mechanism that underlies these forces may lead to deviations when applying the data to predict forces exerted by irregular waves. Experiments have been performed with irregular waves to investigate wave forces, more particularly to study the influence of the energy density spectrum of the waves. Within the range of conditions m the experiments, the wave motion is sufficiently characterized by its energy and the frequency (or wave period) at which the energy density is maximum to determine the probability distribution of wave forces.

Dynamics of three-wave processes in plasmas

Abstract: Travelling waves with a frequency of the order of 109 c/s were excited in a plasma column and their non-linear interaction with the ionic sound waves (f = 104 c/s) was observed.At various distances from the input the authors recorded combination spectra showing the dynamics of the processes involved: the travelling wave amplitude decreases and, at a distance of 29 cm from the input, falls to zero, its energy being redistributed to numerous satellites. The energy redistribution process is not periodic.The characteristic wave interaction time is found to be short (τ ~ 10−8 s), which indicates the efficiency of the process and enables conclusions to be drawn regarding the determinacy of the interacting wave phases (δωτ 1).