Showing papers on "Breaking wave published in 1997"

Transverse-Wake Wave Breaking

Abstract: A finite-width laser pulse of high intensity propagating in an underdense plasma excites a transversely inhomogeneous, finite amplitude wakefield. This wake wave undergoes a transverse wave breaking due to the increase of the wake front curvature, followed by the self-intersection of electron trajectories. Transverse break occurs at much lower wave amplitudes than the conventional one-dimensional wave break. The resulting structures have generic forms that can be described by modified curves parallel to a parabola. Simulations with the particle-in-cell electromagnetic relativistic code VLPL2D show such structures appearing. {copyright} {ital 1997} {ital The American Physical Society}

Breaking criterion and characteristics for solitary waves on slopes

Abstract: ABST.RACT: Sho~ling and breaki,ng of solitary waves is computed on slopes from 1:100 to 1:8 using an expenmentally validated fully nonhnear wave model based on potential flow equations. Characteristics of waves are computed at and beyond the breaking point, and geometric self-similarities of breakers are discussed as a fun?tion of w~ve height and bottom slope. No wave breaks for slopes steeper than 12°. A breaking criterion is denved for rmlde.r slopes, based on val~es of a nondimensional slope parameter So' This criterion predicts both whethe~ waves wIll bre~ or ~ot and which type of breaking will occur (spilling, plunging, or surging). Empirical expressIOns for the bre~ng mdex and for t~e depth and celerity at breaking are derived based on computations. All resul~s agree ~ell With laboratory expenments. The nonlinear shallow water equations fail to predict these results w~th sUfficle~t accuracy at the breaking point. Prebreaking shoaling rates follow a more complex path ~han prevlOus!y reah~ed. Postbreaking beha~iors exhibit a rapid (nondissipative) decay, also observed in exper­ Iments, associated With a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

Infrared remote sensing of breaking waves

Abstract: ENERGY dissipation due to deep-water wave breaking plays a critical role in the development and evolution of the ocean surface wave field. Furthermore, the energy lost by the wave field via the breaking process is a source for turbulent mixing and air entrainment, which enhance air–sea heat and gas transfer1–3. But the current lack of reliable methods for measuring energy dissipation associated with wave breaking inhibits the quantitative study of processes occurring at ocean surfaces, and represents a major impediment to the improvement of global wave-prediction models4. Here we present a method for remotely quantifying wave-breaking dynamics which uses an infrared imager to measure the temperature changes associated with the disruption and recovery of the surface thermal boundary layer (skin layer). Although our present results focus on quantifying energy dissipation—in particular, we show that the recovery rate of the skin layer in the wakes of breaking waves is correlated with the energy dissipation rate—future applications of this technique should help to elucidate the nature of important small-scale surface processes contributing to air–sea heat5 and gas6 flux, and lead to a fuller understanding of general ocean–atmosphere interactions.

Sound generation and air entrainment by breaking waves in the surf zone

Abstract: This paper presents the results of acoustic and optical measurements of individual breaking waves in the surf zone. Two hydrophones, horizontally separated and deployed in 2 m of water off La Jolla Shores beach, California, were used to measure the source spectrum of breaking surf, and characterize propagation through the surf zone over length scales of order 10 m. The acoustic data show an acoustically active region within a wave which propagates shoreward. The production of sound within the active region is associated with the formation of bubble plumes. Above 500 Hz, the sound is consistent with the radiation from individual bubble oscillations. Pictures were taken of the bubble plumes formed beneath the breaking surf, providing estimates of the plume size, and bubble size distribution and void fraction within a plume. The density of bubbles scales as a−2.5 for a 1 mm, where a is bubble radius, and total void fractions of 0.3–0.4 were measured. Theoretical calculations show that ra...

Nonlinear Ocean Waves

Abstract: Chapter 1 Wind-forced strong wave interactions and quasi-local equilibrium between wind and windsea with the friction velocity proportiionality Chapter 2 On the mathematics and approximation of the nonlinear wave-wave interactions. Chapter 3 Relating nonlinear energy cascades to wind input and wave breaking dissipation. Chapter 4 Turbulence of capillary waves - theory and numerical simulation. Chapter 5 The repsonse of waves to a sudden change in wind speed. Chapter 6 Wind wave nonlinear interactions owing to drift current: formation of the angular spectrum, wave groups and Lanmuir circulations. Chapter 7 Direct modeling of one-dimensional nonlinear potential waves.

Wave breaking signatures in OH airglow and sodium densities and temperatures: 1. Airglow imaging, Na lidar, and MF radar observations

Abstract: The Collaborative Observations Regarding the Nightglow (CORN) campaign took place at the Urbana Atmospheric Observatory during September 1992. The instrumentation included, among others, the Aerospace Corporation narrowband nightglow CCD camera, which observes the OH Meinel (6–2) band (hereafter designated OH) and the O2 atmospheric (0–1) band (hereafter designated O2) nightglow emissions; the University of Illinois Na density/temperature lidar; and the University of Illinois MF radar. Here we report on observations of small-scale (below 10-km horizontal wavelength) structures in the OH airglow images obtained with the CCD camera. These small-scale structures were aligned perpendicular to the motion of 30- to 50-km horizontal wavelength waves, which had observed periods of about 10–20 min. The small-scale structures were present for about 20 min and appear to be associated with an overturned or breaking atmospheric gravity wave as observed by the lidar. The breaking wave had a horizontal wavelength of between 500 and 1500 km, a vertical wavelength of about 6 km, and an observed period of between 4 and 6 hours. The motion of this larger-scale wave was in the same direction as the ≈30- to 50-km waves. While such small-scale structures have been observed before, and have been previously described as ripple-type wave structures [Taylor and Hapgood, 1990], these observations are the first which can associate their occurrence with independent evidence of wave breaking. The characteristics of the observed small-scale structures are similar to the vortices generated during wave breakdown in three dimensions in simulations described in Part 2 of this study [Fritts et al., this issue]. The results of this study support the idea that ripple type wave structures we observe are these vortices generated by convective instabilities rather than structures generated by dynamical instabilities.

Spectral evolution of shoaling and breaking waves on a barred beach

Abstract: Field observations and numerical model predictions are used to investigate the effects of nonlinear interactions, reflection, and dissipation on the evolution of surface gravity waves propagating across a barred beach. Nonlinear interactions resulted in a doubling of the number of wave crests when moderately energetic (about 0.8-m significant wave height), narrowband swell propagated without breaking across an 80-m-wide, nearly flat (2-m depth) section of beach between a small offshore sand bar and a steep (slope = 0.1) beach face, where the waves finally broke. These nonlinear energy transfers are accurately predicted by a model based on the nondissipative, unidirectional (i.e., reflection is neglected) Boussinesq equations. For a lower-energy (wave height about 0.4 m) bimodal wave field, high-frequency seas dissipated in the surf zone, but lower-frequency swell partially reflected from the steep beach face, resulting in significant cross-shore modulation of swell energy. The combined effects of reflection from the beach face and dissipation across the sand bar and near the shoreline are described well by a bore propagation model based on the nondispersive nonlinear shallow water equations. Boussinesq model predictions on the flat section (where dissipation is weak) are improved by decomposing the wave field into seaward and shoreward propagating components. In more energetic (wave heights greater than 1 m) conditions, reflection is negligible, and the region of significant dissipation can extend well seaward of the sand bar. Differences between observed decreases in spectral levels and Boussinesq model predictions of nonlinear energy transfers are used to infer the spectrum of breaking wave induced dissipation between adjacent measurement locations. The inferred dissipation rates typically increase with increasing frequency and are comparable in magnitude to the nonlinear energy transfer rates.

Defining and quantifying microscale wave breaking with infrared imagery

Abstract: Breaking without air entrainment of very short wind-forced waves, or microscale wave breaking, is undoubtedly widespread over the oceans and may prove to be a significant mechanism for enhancing the transfer of heat and gas across the air-sea interface. However, quantifying the effects of microscale wave breaking has been difficult because the phenomenon lacks the visible manifestation of whitecapping. In this brief report we present limited but promising laboratory measurements which show that microscale wave breaking associated with evolving wind waves disturbs the thermal boundary layer at the air-water interface, producing signatures that can be detected with infrared imagery. Simultaneous video and infrared observations show that the infrared signature itself may serve as a practical means of defining and characterizing the microscale breaking process. The infrared imagery is used to quantify microscale breaking waves in terms of the frequency of occurrence and the areal coverage, which is substantial under the moderate wind speed conditions investigated. The results imply that ”bursting“ phenomena observed beneath laboratory wind waves are likely produced by microscale breaking waves but that not all microscale breaking waves produce bursts. Oceanic measurements show the ability to quantify microscale wave breaking in the field. Our results demonstrate that infrared techniques can provide the information necessary to quantify the breaking process for inclusion in models of air-sea heat and gas fluxes, as well as unprecedented details on the origin and evolution of microscale wave breaking.

Reflection of a high-amplitude solitary wave at a vertical wall

Abstract: (Received 29 February 1996 and in revised form 25 October 1996) The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976). In this paper we consider the reflection at a vertical wall of a solitary wave, using a boundary-integral numerical code, a perturbation method, and re-analysis of cine film taken during the study by Maxworthy (1976). Most attention is given to that part of the motion during which the point of greatest free-surface elevation (the crest) lies close to the wall. The problem of solitary wave reflection has received attention in studies of the interaction between solitary waves, of which the head-on collision of two equal waves is a special case equivalent to that studied here. When weakly nonlinear solitary waves overtake or collide with one another there may be a spatial phase shift but no loss of energy from either wave once sucient time has passed for the two waves to separate; this is the feature by which a soliton is defined (Zabusky & Kruskal 1965). Recent studies have shown that large-amplitude solitary water waves do not behave like solitons. A long time after the collision between two equal waves there is a loss to secondary waves, and a reduction in wave speed. The reduced wave speed necessarily produces a spatial phase shift that increases without bound as t U¢ . It is useful to briefly review certain aspects of the phenomena we wish to study, some of which bear on the interpretation of results to be presented later. In what follows, f(x, t) is the free-surface elevation about the quiescent fluid level and e fl a}h is the dimensionless solitary wave amplitude, a being the amplitude of the incident wave travelling on a fluid of constant still-water depth h. Byatt-Smith (1971) investigated the interaction between two weakly nonlinear solitary waves travelling in opposite

Toward a Unified Theory of Gravity Wave Stability.

Abstract: This paper reveals relationships among linear instabilities of internal gravity waves often supposed to be independent. Using a Floquet analysis of a monochromatic wave propagating in a uniformly stratified background without shear, which accounts for finite wave amplitude, spatial and temporal periodicity, tilted phase planes, and 3D disturbances, it is demonstrated that the dominant instabilities of overturning waves are the large-wave-amplitude manifestations of resonant and slantwise instabilities of small amplitude waves, and that they possess no threshold amplitudes. An energy budget analysis examines the relation of parametric instabilities at large wave amplitude to vertical dynamic and static instabilities; however, the instability characteristics for propagating waves are very different from those inferred by analogy to Kelvin–Helmholtz instability and Benard convection in simpler backgrounds. At small amplitudes, resonant instabilities rely on horizontal or slantwise gradients of wave ...

A model for Brewster angle damping and multipath effects on the microwave radar sea echo at low grazing angles

Abstract: Brewster angle damping and local multipath effects are considered as sources of polarization differences in low grazing angle sea scatter characteristics. The authors show that at least five observed polarization differences can be explained by local multipath interference effects that occur due to the illumination of discrete nonlinear ocean surface features, such as bores and small scale breaking waves. The illumination gain factor (IGF) is defined at a point in space, as the total power at that point relative to the power in the incident plane wave. The IGF resulting from local multipath from the sea surface forward of a discrete scatterer produces strong interference patterns that can vary both with grazing angle and scatterer height. As a result, IGF values up to a factor of 16 (12 dB) can occur for horizontal polarization (HH) when the interference is constructive; a corresponding strong cancellation occurs for destructive interference. These extreme variations can cause strong HH NRCS amplitude modulations due either to a change of local wave slope or a change of scatterer shape with time. However, Brewster angle damping of the forward scatter path for grazing angles below 20/spl deg/ occurs for vertical (VV) polarization, and reduces the VV IGF in magnitude and dynamic range, eliminating such strong modulations. This effect scales with radar wavelength, and higher wave features are required to produce equivalent effects for radar frequencies far below 10 GHz. As an illustration, six radar bands are compared: L (1.4 GHz), S (3.5 GHz), C (5 GHz), X (10 GHz), K/sub u/ (15 GHz), and K/sub a/ (35 GHz), for a sea water dielectric. X-band results indicate that 12-dB IGFs can occur for water surface features just a centimeter above the mean surface. As an application of these results, the influence of these HH and VV IGF patterns is modeled for discrete scatterers distributed uniformly along an ocean gravity wave. The dynamic range of the HH IGF for a distribution of bore scatterers up to 5 cm high is found to he significantly larger than for VV at all locations on the long wave. Moreover, the IGF HHVV polarization ratio forward of the crest, where the largest number of small scale breaking wave scatterers occurs, is larger than at all other regions of the long wave, of the order of 20 dB. These results suggest that HH polarization may be sensitive to small scale breaking features on the ocean surface at low grazing angles, and thus may be a sensitive measure of air-sea fluxes.

Electron trapping in self-modulated laser wakefields by raman backscatter

Abstract: : Simultaneous measurements of high energy electrons and plasma wave characteristics have been conducted in a self-modulated laser wakefield accelerator Approximately 10(exp 8) electrons were accelerated from the background plasma to energies greater than 1 MeV with a peak energy of approximately 30 MeV A strong correlation between the plasma wave amplitude and electron production was measured with no evidence of wave breaking Simulations indicate plasma electrons are trapped by the low phase velocity beat waves produced by backward Raman scattering

Fetch limited drag coefficients

Abstract: Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Riso Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.

Elliptical diagnostics of stratospheric polar vortices

Abstract: Diagnostics based on the spatial moments of isopleths of a long-lived tracer, or of potential vorticity, are presented that enable the structure and evolution of stratospheric polar vortices to be concisely summarized and quantified. The area, centre, aspect ratio and orientation of the ‘equivalent ellipse’ of the vortex, on an isentropic surface, are defined using the second- and lower-order spatial moments of contours within the vortex-edge region. By examining the variations of these ‘elliptical’ diagnostics with time and altitude, the temporal evolution and vertical structure of the polar vortices can be quantified. The usefulness of the diagnostics is assessed by examining nitrous oxide data from the Geophysical Fluid Dynamics Laboratory ‘SKYHI’ general-circulation model. The diagnostics show, and quantify, several differences between the Arctic and Antarctic vortices in the SKYHI model. The Arctic vortex moves further off the pole, is generally more elongated, and has a more complicated vertical structure than the Antarctic vortex (with larger variations of both the vortex centre and elongation with height). The elliptical diagnostics also identify the occurrence of large-scale Rossby-wave breaking events, both at the vortex edge and in the subtropics, in the model.

On the structure of bow waves on a ship model

Abstract: Particle image velocitmetry (PIV) measurements and free-surface visualizations around a ship model focus on the flow within the attached liquid sheet, upstream of the point at which the bow wave separates from the model, the origin and structure of the bow wave and the flow downstream of the wave crest. The measurements are performed at Reynolds numbers ranging between 2.8 x 10 6 and 7.4 x 10 6 and Froude numbers between 0.17 and 0.45 (both are based on ship length L). Representative velocity and vorticity distributions at Fr L = 0.28 and Fr L = 0.45 demonstrate the characteristic structure of mild and steep waves, respectively. Very close to the bow the attached sheet is thin and quite unsteady. With increasing distance from the nose the sheet becomes thicker and its development involves considerable vorticity production. In the mild case this vorticity is originated at the free surface, whereas in the steep wave case, boundary layer separation occurs on the model, which also transports vorticity into the sheet. This vorticity and its associated induced lateral flow remain near the model downstream of the bow wave. By calculating the acceleration component tangent to the free surface of the sheet it is shown that the peaks in the near-surface vorticity appear in regions with high viscous flux of vorticity from the surface. Formation of a bow wave also involves considerable production of vorticity. Similar to two-dimensional breakers, the primary origin of this vorticity is at the toe of the breaker. However, unlike the two-dimensional cases, the region containing vorticity in the ship wave does not appear as an extended shear layer. Instead, this vorticity is convected out of the plane of the laser sheet in a series of distinct vortex filaments. The ship wave also has powerful counter-rotating vorticity concentrated near the wave crest that has been observed in two-dimensional waves, but not of the same strength. Breaking becomes weaker, i.e. there is less vorticity production, with increasing distance from the model, but it persists even at the 'tail' of the bow wave. The sites of vorticity entrainment of both signs are consistent with the computed near-surface acceleration. Estimates of the three-dimensional velocity distribution and head losses within the wave are also provided.

Frequency downshift in three-dimensional wave trains in a deep basin

Abstract: The conservative evolution of weakly nonlinear narrow-banded gravity waves in deep water is investigated numerically with a modified nonlinear Schrodinger equation, for application to wide wave tanks. When the evolution is constrained to two dimensions, no permanent shift of the peak of the spectrum is observed. In three dimensions, allowing for oblique sideband perturbations, the peak of the spectrum is permanently downshifted. Dissipation or wave breaking may therefore not be necessary to produce a permanent downshift. The emergence of a standing wave across the tank is also predicted.

Experimental investigation of the vorticity generation within a spilling water wave

Abstract: Sources of vorticity are examined for a laboratory-generated spilling breaking wave. Two cases are studied. For the first case, based on the breaker height, the Reynolds and Froude numbers are 7370 and 2.04, respectively. The breaker is preceded by 1 mm wavelength capillary waves, with the largest amplitude-to-wavelength ratio equal to 0.18. For this case, it is found that the dominant source of vorticity flux is a viscous process, due to the deceleration of a thin layer of the surface fluid. For the second case, the Reynolds and Froude numbers based on the wave height are 1050 and 1.62, respectively. No breaking is observed for this case; rather a capillary–gravity wave is observed with 4 mm wavelength capillaries preceding the gravity wave. The largest amplitude-to-wavelength ratio of these capillaries is 0.28. This case shows that capillary waves do not contribute to the vorticity flux; rather the only dominant source of the vorticity flux into the flow is the free-surface fluid deceleration. Lastly, a thin free-surface jet that is relatively vorticity-free is found to precede the spilling breaker. Analyses suggest that our wave-breaking phenomena can be modelled by a hydraulic jump phenomenon where the Froude number is based on the thickness of the free-surface jet, and on the velocity of the free-surface jet just prior to breaking. We believe this to be a more physically descriptive value of the Froude number. For the high-speed case, the Froude number based on the thickness of the free-surface jet is 4.78, while for the lower-speed case it is 2.14.

The surface marker and micro cell method

Abstract: SUMMARY A new method is presented for the simulation of two-dimensional, incompressible, free surface fluid flow problems. The surface marker and micro cell (SMMC) method is capable of simulating transient free surface fluid flow problems that include multivalued free surfaces, impact of free surfaces with solid obstacles and converging fluid fronts (including wave breaking). New approaches are presented for the advection of the free surface, the calculation of the tentative velocity, final velocity and pressure fields and the use of multivalued velocities to treat converging fluid fronts. Simulation results are compared with experimental results for water sloshing in a tank to demonstrate the validity of the new method. Convergence of the new method is demonstrated by a grid refinement study. # 1997 John Wiley & Sons, Ltd.

Modeling spectra of breaking surface waves in shallow water

Abstract: Predictions from Boussinesq-equation-based models for the evolution of breaking surface gravity waves in shallow water are compared with field and laboratory observations. In the majority of the 10 cases investigated, the observed spectral evolution across the surf zone is modeled more accurately by a dissipation that increases at high frequency than by a frequency-independent dissipation. However, in each case the predicted spectra are qualitatively accurate for a wide range of frequency-dependent dissipations, apparently because preferential reduction of high-frequency energy (by dissipation that increases with increasing frequency) is largely compensated by increased nonlinear energy transfers to high frequencies. In contrast to the insensitivity of predicted spectral levels, model predictions of skewness and asymmetry (statistical measures of the wave shapes) are sensitive to the frequency dependence of the dissipation. The observed spatial evolution of skewness and asymmetry is predicted qualitatively well by the model with frequency-dependent dissipation, but is predicted poorly with frequency-independent dissipation. Although the extension of the Boussinesq equations to breaking waves is ad hoc, a dissipation depending on the frequency squared (as previously suggested) reproduces well the observed evolution of wave frequency spectra, skewness, and asymmetry.

Numerical prediction of breaking waves and currents with a boussinesq model

Abstract: This paper describes the extension of a comprehensive numerical model for simulating the propagation and transformation of ocean waves in coastal regions and harbours to include wave breaking, runup and breaking-induced currents. The numerical model is based on a time-domain solution of a fully nonlinear set of Boussinesq-type equations for wave propagation in intermediate and shallow water depths. The equations are able to describe most of the phenomena of interest in the nearshore zone including shoaling, refraction, diffraction, reflection, wave directionality and nonlinear wave-wave interactions. The Boussinesq model is extended to the surf and swash zones by coupling the mass and momentum equations with a one-equation model for the temporal and spatial evolution of the turbulent kinetic energy produced by wave breaking. The waves are assumed to start breaking when the horizontal component of the orbital velocity at the wave crest exceeds the phase velocity of the waves. Numerical and experimental results are presented for the shoaling and runup of regular and irregular waves on a constant slope beach and wave-induced currents behind a detached breakwater.

Solitary waves with a vortex core in a shallow layer of stratified fluid

Abstract: This paper is concerned with a theoretical model for large amplitude solitary waves with a vortex core in a shallow layer of stratified fluid with a nearly uniform stratification. Previous work has shown that solitary waves can be calculated up to a critical amplitude for which the horizontal velocity, in a frame for which the wave is at rest, approaches zero at the boundary point beneath the wave crest for a wave of elevation (or above the wave crest for a wave of depression). Here we calculate waves with amplitudes slightly greater than the critical amplitude by incorporating a vortex core located near the aforementioned boundary point. The effect of the vortex core is to introduce into the governing equation for the wave amplitude an extra nonlinear term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude. We find that as the wave amplitude increases above the critical amplitude, the wave broadens, which is in marked contrast to the case of small amplitude waves. Further, the wave speed is found to depend nonlinearly on the wave amplitude, again in marked contrast to the linear dependence for small amplitude waves. The specific case of linearly stratified fluid is examined in detail.