Showing papers on "Breaking wave published in 1974"

The instability of short waves on a vortex ring

Abstract: A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

On the incipient breaking of small scale waves

Abstract: It is shown that the surface wind drift in the ocean substantially reduces the maximum wave height ξx and wave orbital velocity that can be attained before breaking. If q is the magnitude of the surface drift at the point where the wave profile crosses the mean water level and c is the wave speed, then \[ \zeta_{\max} = \frac{c^2}{2g}\bigg(1-\frac{q}{c}\bigg)^2. \] Incipient breaking in a steady wave train is characterized by the occurrence of stagnation points at wave crests, but not necessarily 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. Some simple flow visualization studies indicate the general extent of the wake behind the breaking region.

Computation of set-up, longshore currents, run-up and overtopping due to wind-generated waves

Abstract: The main problem dealt with in this thesis is the calculation of certain effects caused by random waves breaking on a slope. The solution to this problem is greatly complicated by the fact that wave breaking is a highly nonlinear process. The flow field is further complicated by far stronger in homogeneities than those occurring outside the breaker zone, by air entrainment and by generation of turbulence. No realistic deductive treatment of it has been developed so far. Even for the simpler case of periodic waves, empirical knowledge of certain macroscopic properties of the breakers is still an integral part of calculations relating to the surf zone. An attempt has been made in this thesis to apply this knowledge in a formulation incorporating the stochastic nature of wind-generated waves. The computations are of two distinct categories, those relating to comparatively gentle slopes and those relating to comparatively steep slopes. A summary of the results will be given in the following. The energy variation is calculated in chapter 5 by clipping a fictitious wave height distribution, which theoretically would be present if breaking did not occur, at an upper limit which is determined from an adapted breaking criterion for periodic waves. The computed results are in fair agreement with measurements carried out on a plane slope. Knowledge of the energy variation permits the radiation stresses to be evaluated, which in turn are necessary for the calculation of the set-up and the longshore current velocity profiles. A comparison of the calculated set-up profiles with empirical data has not given conclusive results. Good agreement has been found with field data, but not with laboratory data, which locally showed a systematically smaller rise towards the shore than would be expected on the basis of the measured or calculated wave height variations. However, there is some uncertainty with respect to the system used for measuring the set-up in the laboratory, so that is not known to which extent the differences are real or apparent.

Wave breaking in the presence of wind drift and swell

Abstract: Wind, blowing over a water surface, induces a thin layer of high vorticity in which the wind stress is supported by molecular viscosity; the magnitude of the surface drift, the velocity difference across the layer, being of the order of 3% of the wind speed. When long waves move across the surface, there is a nonlinear augmentation of the surface drift near the long-wave crests so that short waves, super-imposed on the longer ones, experience an augmented drift in these regions. This is shown to reduce the maximum amplitude that the short waves can attain when they are at the point of incipient breaking. Theoretical estimates of the reduction are compared with measurements in wind-wave tanks by the authors and by Mitsuvasu (1966) in which long mechanically generated waves are superimposed on short wind-generated waves. The reductions measured in the energy density of the short waves by increasing the slope of the longer ones at constant wind speed are generally consistent with the predictions of the theory in a variety of cases. (Author)

Excitation of edge waves by waves incident on a beach

Abstract: It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth's rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann's (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.

On a variety of wave phenomena in chemical reactions

Abstract: A variety of wave phenomena are analyzed and discussed for systems in which chemical reactions and transport take place. Certain families of wave solutions of reaction‐transport equations arise owing to the weak stability of a reference state to a class of perturbations. We consider both wave induction by heterogeneities and autonomous waves and seek perturbation solutions which provide the dispersion relation and the wave vector dependence of the amplitude for one‐parameter families of waves characterized by the wave vector. For the case of an arbitrary reaction mechanism possessing a homogeneous steady state we derive, by use of bifurcation theory and frequency renormalization, small amplitude autonomous plane waves and standing and rotating waves. We find solutions corresponding to long wavelength waves, static structures, and phenomena existing only at intermediate frequencies and wavelengths. The theory is found to have a nonuniformity in convergence in the core region of pacemaker and spiral‐like so...

A finite amplitude wave on a linear shear current

Abstract: A numerical perturbation procedure is presented that generates water waves propagating over a vertically varying linear shear current. The water surface profile of these waves may be symmetric about the crest, with given height and period, or they may have an irregular water surface profile that has been measured in water of known depth. For waves of the same height the effect of the current is to cause a change in wavelength and hence the kinematics under the wave. Further, the shape of the wave profile is changed significantly.

Stability of a sand bed under breaking waves

Abstract: The possible effect on the stability of a porous sand bed of the flow induced within the bed during the passage of near-breaking or breaking waves is considered. It is found that the horizontal flow rather than the vertical flow within the bed may affect its stability. An approximate analysis, used in geotechnical computations of slope stability, indicates that a momentary bed failure is likely to occur during the passage of the steep front slope of a near-breaking wave. Experimental results for the pressure gradient along the bottom under near-breaking waves are presented. These results indicate that the pressure gradient is indeed of sufficient magnitude to cause the momentary failure suggested by the theoretical analysis. The loss of stability of the bed material due to the flow induced within the bed itself may affect the amount of material set in motion during the passage of a near-breaking or breaking wave, in particular, in model tests employing light weight bed material. The failure mechanism considered here is also used as the basis for a hypothesis for the depth of disturbance of the bed in the surf zone. The flow induced in a porous bed is concluded to be an important mechanism which should be considered when dealing with the wave-sediment interaction in the surf zone.

Waves in the Jovian upper atmosphere

Abstract: We examine a propagating wave interpretation of the temperature profile features observed in the Jovian upper atmosphere by Veverka et al. (1974). Inertia-gravity waves with frequencies on the order of .003 per sec are consistent with the data. If the interpretation is correct, and if the waves carry energy upward, it implies (1) that there is excitation of such waves at lower levels, (2) that eddy diffusivities on the order of 1,000,000 sq cm/sec are probably generated by the waves, and (3) that the energy carried by waves is important to the upper atmospheric heat balance.

On the interaction of internal waves and surface gravity waves

Abstract: The perturbation of pre-existing surface gravity waves caused by the presence of an internal wave was studied both experimentally and analytically. An extensive series of experiments was performed, and quantitative results were obtained for the one-dimensional monochromatic interaction of internal waves and surface gravity waves. Internal wave-induced surface slope, amplitude and wavenumber modulations were measured for a wide range of interaction conditions. A complementary theoretical analysis, based on the conservation approach of Whitham (1962) and Longuet-Higgins & Stewart (1960,1961), was performed and a closed form solution obtained for the one-dimensional wave interaction. Both the theory and the experiment demonstrate that the effect increases with interaction distance. The maximum interaction effect is found to occur when the phase speed of the internal wave and the group velocity of the surface wave are matched. The phase of the internal wave at which maximum surface-wave modulation occurs is found to be a sensitive and continuous function of the relative wave speeds. The experimental data are in good agreement with the present theoretical analysis.

Propagation of waves along an impedance boundary

Abstract: A theoretical analysis of the scalar wave field due to a point source above a plane impedance boundary is presented. A surface wave is found to be an essential component of the total wave field. It is shown that, as a result of ducting of energy by the surface wave, the amplitude of the total wave near the boundary can be greater than it would be if the boundary were perfectly reflecting. Asymptotic results, valid near the boundary, are obtained both for the case of finite impedance (the soft-boundary case) and for the limiting case in which the impedance becomes infinite (the hard-boundary case). In the latter, the wave amplitude in the farfield decreases essentially inversely as the horizontal propagation distance; in the former (if the surface-wave term is neglected), it decreases inversely as the square of the horizontal propagation distance.

Relationship Between Vertical Distribution of Water Particle Velocity and Type of Breakers on Beaches

Abstract: In order to clarify the water particle velocity field of breaking waves on beaches, experiments were carried out for three kinds of beach slopes (1/10, 1/20 and 1/30). Neutrally buoyant particles were used as tracers to measure the velocities with a 16 mm high speed cinecamera. Since photographs of the wave profile near breaking were also taken in the same films, the change of the wave profile near breaking was also examined. It was found that vertical distributions of horizontal water particle velocities at the crest and trough phases of breaking waves on beaches cannot be explained by the finite amplitude wave theories for uniform depth. Then, they were discussed in comparison with the breaker types. As a result, it was shown that the dimensionless vertical distribution of horizontal water particle velocity at the crest phase of breaking waves is determined by the combination of the beach slope and the deep-water wave steepness.

Linear ion acoustic waves in a density gradient

Abstract: Both the experimental and theoretical behavior of linear ion acoustic waves in density gradients formed in a collisionless discharge plasma have been studied. The experiment and the theory both show a strong spatial growth of the density perturbation produced by the wave when the wave propagates in the direction of increasing density and a damping when the wave propagates in the direction of decreasing density. Theoretically, the growth and damping rates are found to be proportional to n01/2, where n0 is the local unperturbed density. By using the measured density profile, good agreement is found between experiment and the linearized fluid theory. Although the wave amplitude n1, itself, decreases as the wave propagates into a region of lower density, the relative amplitude n1/n0 increases. This can be expected to lead to wave steepening and shock‐like behavior, as noted previously by others. The work reported here is mainly concerned with the range where the wavelength is smaller than the characteristic l...

Computation of longshore currents

Abstract: The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.

Surface Shear Waves

Abstract: Two examples of steep very large amplitude waves are described. One occurs on flows below weirs or sluices and is known as the wave hydraulic jump. A simple analysis is presented to describe its main features. The other example occurs in backwash from surf and has not previously been described. A hypothesis of flow separation in these latter waves links them with the first example. The general name, surface shear waves is proposed for both wave types since their steep rounded crests may be explained by a thin fast surface layer of water.

Turbulent dispersion of ion cyclotron waves: Theory and experiment

Abstract: Particles in or near resonance with a plasma wave undergo perturbations of their equilibrium orbits due to stochastic fields. This contributes added diffusion damping to any wave in the plasma. In a steady‐state experiment this mechanism can cause the saturation of a wave. A theory of the current‐driven ion cyclotron instability modified by turbulent damping based on addition of a damping term to the linear dispersion relation is presented. The turbulent damping is interpreted as an upper bound on the linewidth of the wave. As current varies, the frequency and line width of the mode alter. Once the frequency of the ion cyclotron wave is lowered to nearly the ion cyclotron frequency, mode coupling to an ion‐acoustic wave seems to occur, damping the oscillations. Until this point, detailed predictions of theory agree well with experiment.

Large Amplitude Waves in Bounded Media. III. The Deformation of an Impulsively Loaded Slab: The Second Reflexion

Abstract: Representations are derived that describe the interactions of the waves that are reflected from both perfectly rigid and perfectly free interfaces during the arrival of a centred wave with any wave travelling in the opposite direction. These are used to analyse the early stages of the deformation produced when the traction at the loaded boundary continues to vary after changing discontinuously.

Breaking wave forces on a large diameter cell

Abstract: Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length.

The development from two‐dimensional to three‐dimensional turbulence generated by breaking waves

Abstract: An investigation is made of transition of the turbulence spectrum within the mixed layer of Lake Ontario following the passage of several well-defined meteorological disturbances. Observations were taken during the summer of 1972 with a ducted propeller current meter. Spectral analysis of the records revealed a transformation from a spectral law corresponding to two-dimensional turbulence into a wave number dependence corresponding to Kolmogorov's −5/3 law indicating three-dimensional structure. The appearance of the recordings, the energy peaks and energy levels, the mean velocities, and the rms fluctuations show concomitant changes indicating that wave-generated turbulence may be transmitted downward in the epilimnion of lakes.

On Wave Deformation after Breaking

Abstract: Waves will dissipate their energy rapidly after breaking. In this paper, the three factors , (i) formation of a horizontal roller,(11) bottom friction, and (in) turbulence with air entrainment, which will contribute to the energy dissipation, are dealt with experimentally and theoretically The horizontal roller formed by a plunging breaker is approximated as a Rankme-type vortex by experiments, and it is calculated that 15$-30%of wave energy is dissipated due to the formation of horizontal roller alone from a breaking point to a point of the roller disappearance. A bottom shear stress due to a breaker is measured by the shear meter deviced by the authors and it is clarified that the energy dissipation due to bottom friction is a little Mam part of the energy dissipation is taken to be caused by the turbulence with air entrainment. It is indicated that an incident monocromatic wave is transformed into a higher frequency wave due to the turbulence. Furthermore, a new basic equation for breaking waves with a turbulence term expressed by a Reynolds stress is presented The theoretical curves computed numerically have a consistent agreement with the experimental results.

Effects of a breakwater on nearshore currents due to breaking waves

Abstract: : This study provides a semiempirical theory of nearshore currents due to breaking waves in the presence of a shore-connected breakwater or an offshore breakwater. The effects of diffraction are studied in addition to refraction by shoaling waters. The concept of radiation stresses applied to uniform longshore current and rip currents forms the starting point of the theory. Many empirical relations included in this study with regard to the surf zone are similar to, and extrapolations of, the ones used in related works. Ignoring convective inertia and lateral turbulent diffusion, the governing equations are solved numerically by the method of finite differences. Sample results for stream functions and mean sea levels are plotted for various beach profiles or incidence angles. For the offshore breakwater, the predicted current pattern is consistent with available laboratory observations and the known tendency of tombolo formation; for the shore-connected breakwater. the computed flow pattern exhibits cells in both downwave and upwave regions. Directly relevant observations have not been found but part of the predicted features has some indirect experimental support. More experimental and theoretical work is suggested.

Nonlinear Wave Interactions in Turbulent Plasmas

Abstract: The second order nonlinear current density is calculated for a magnetized turbulent plasma. Processes of decay and fusion of three waves can then be considered.

On resonant interactions of atmospheric waves.

Abstract: A nonlinear interaction between acoustic-and internal gravity waves in an inhomogeneous atmosphere is considered. Due to wave motion from a dense to a less dense medium, we conclude that the importance of the non-linear effect is increasing with height. The coupling coefficients are calculated, and the problem concerning resonance conditions is considered. It is shown that a transfer of energy between the waves can take place more rapidly than in the case of a wave interaction in a homogeneous medium.

Phase and amplitude discrepancies in the surface wave due to a wedge-ended hull form

Abstract: A deep surface-piercing wedge-ended hull model was towed through still water. Measurements of the surface wave pattern confirmed earlier findings for ship models, that the measured bow-wave cusp line often lies well forward of the position predicted by thin-ship theory, and that this shift increases with bow water-line angle and with decreasing model speed. Two possible explanations are considered here in terms of changes of wave phase speed with wave convection and steepness. Calculations based on a transformation method due to Guilloton predict more realistic wave profiles than linear theory, but account for less than half the observed shift. Some tentative conclusions are drawn.The singularity in the Green's function double integral is removed by an improved method, which simplifies the numerical integration. The new integrand decays within one oscillation.

Experimental Study of Breaking Wave Force on a Vertical Circular Cylinder

Abstract: A model study was performed to investigate the wave forces acting on a vertical circular cylinder located on a sloping beach. The wave forces and their moments about the bottom were measured at var...