Showing papers on "Breaking wave published in 1992"

Enhanced dissipation of kinetic energy beneath surface waves

Abstract: TRANSFER of momentum from wind to the surface layer of lakes and oceans plays a central part in driving horizontal and vertical circulation of water masses. Much work has been devoted to understanding the role of waves in momentum transfer across the air–sea interface, but less is known about the energetics of the near-surface turbulence responsible for the mixing of momentum and mass into the underlying water column. In particular, it has remained unclear whether the structure of the turbulence in the surface layer can be described by analogy to wall-bounded shear flows or whether waves, either through breaking or wave–current interaction, introduce new length- and timescales which must be modelled explicitly. Here we report observations of turbulence in Lake Ontario, taken under conditions of strong wave breaking, which reveal a greatly enhanced dissipation rate of kinetic energy close to the air–water interface, relative to the predictions of wall-layer theory. Because wave breaking is intermittent, short-term measurements of the kinetic energy dissipation in the near-surface layer may therefore result in considerable underestimates, and any general treatment of upper mixed layer dynamics will have to take wave breaking explicitly into account.

Internal solitary wave breaking and run-up on a uniform slope

Abstract: Laboratory experiments have been conducted to study the shoaling of internal solitary waves of depression in a two-layer system on a uniform slope. The shoaling of a single solitary wave results in wave breaking and the production of multiple turbulent surges, or boluses, which propagate up the slope. Significant vertical mixing occurs everywhere inshore of the breaking location. The kinematics of the breaking and bolus runup are described and a breaking criterion is found. The energetics of the breaking are investigated. Over the range of parameters examined, 15 (±5) % of the energy lost from first-mode wave motion inshore of the break point goes into vertical mixing.

Wave breaking in nonlinear-optical fibers

Abstract: An analytical investigation is made of the interplay between dispersion and nonlinearity in the creation of wave breaking in optical fibers. Wave breaking is found to involve two independent processes: (a) overtaking of different parts of the pulse and (b) nonlinear generation of new frequencies during overtaking. Analytical predictions for the distance of wave breaking are obtained and found to be in good agreement with numerical results.

Wave Runup on Smooth and Rock Slopes of Coastal Structures

Abstract: Knowledge on waverunup levels is important for a proper design of the crest height of coastal structures. An overall view of the literature supports the assertion that smooth slopes cause the highe...

A new numerical model of the middle atmosphere: 1. Dynamics and transport of tropospheric source gases

Abstract: Attention is given to a new model of the middle atmosphere which includes, in addition to the equations governing the zonal mean state, a potential vorticity equation for a single planetary-scale Rossby wave, and an IR radiative transfer code for the stratosphere and lower mesosphere, which replaces the Newtonian cooling parameterization used previously. It is shown that explicit computation of the planetary-scale wave field yields a more realistic representation of the zonal mean dynamics and the distribution of trace chemical species. Wave breaking produces a well-mixed 'surf zone' equatorward of the polar night vortex and drives a meridional circulation with downwelling on the poleward side of the vortex. This combination of mixing and downwelling produces shallow meridional gradients of trace gases in the subtropics and middle latitudes, and very steep gradients at the edge of the polar vortex. Computed distributions of methane and nitrous oxide are shown to agree well with observations.

Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles

Abstract: A review of papers investigating tsunami wave run-up on a beach is given and the control parameters of the problem are revealed. There are two such parameters in the case of ideal fluid: the bottom sloping angle and the breaking parameter. A stage-by-stage approach for finding run-up characteristics is formulated: the linear calculation of shoreline oscillations and the subsequent non-linear transformation of the solution according to the Riemann method. Solution of the nononedimensional problems of wave run-up on a beach in the linear formulation is obtained.

A model for the generation of two-dimensional surf beat

Abstract: A finite difference model predicting group-forced long waves in the nearshore is constructed with two interacting parts: an incident wave model providing time-varying radiation stress gradients across the nearshore, and a long-wave model which solves the equations of motion for the forcing imposed by the incident waves. Both shallow water group-bound long waves and long waves generated by a time-varying breakpoint are simulated. Model-generated time series are used to calculate the cross correlation between wave groups and long waves through the surf zone. The cross-correlation signal first observed by Tucker [1950] is well predicted. For the first time, this signal is decomposed into the contributions from the two mechanisms of leaky mode forcing. Results show that the cross-correlation signal can be explained by bound long waves which are amplified, though strongly modified, through the surf zone before reflection from the shoreline. The breakpoint-forced long waves are added to the bound long waves at a phase of π/2 and are a secondary contribution owing to their relatively small size.

Non‐Linear Three‐Dimensional Effects On Gravity‐Wave Drag: Splitting Flow and Breaking Waves

Abstract: A study has been made of some aspects of frictionless stratified flow past three-dimensional isolated mountains. the study uses a three-dimensional non-hydrostatic numerical model to investigate the behaviour of the flow as a function of the Froude number, and produces a picture of the dependence of the gravity-wave drag on the Froude number for a wide range of that parameter. At the same time, the results of the numerical experiments clarify the behaviour of the flow in the transition from high to low Froude number, showing the relative importance of wave breaking and flow splitting in the transitional regime.

Electron acceleration by Alfvén waves in the magnetosphere

Abstract: The self-consistent electron kinetics of Alfven waves on the electron inertial scale is studied using a 2D hybrid-kinetic description. The ions follow a fluid description for Alfven waves at frequencies below the ion cyclotron frequency. The parallel electron dynamics is treated kinetically using particle-in-cell techniques. In this model, the electron plasma mode is eliminated, and only the physics of the Alfven waves is retained. At sufficiently large amplitudes, it is found that oblique Alfven waves break due to finite electron inertia in a cold plasma. The consequence of wave breaking is the formation of an electron beam which can be unstable to the beam-plasma instability. The electrons supporting the parallel current thermalize into a non-Maxwellian distribution with an energetic tail up to several keV, assuming a reasonable magnetospheric Alfven speed. In hot plasma simulations, electron trapping is the principal mechanism of electron acceleration. It is proposed that wave breaking or electron trapping of oblique Alfven waves at 1 R(E) can result in electron acceleration and may explain some observed auroral phenomena.

Rossby-wave breaking, microbreaking, filamentation, and secondary vortex formation-The dynamics of a perturbed vortex

Abstract: The behavior of an isolated vortex perturbed by topographically forced Rossby waves is studied using the method of Contour Dynamics. For a single-contour vortex a distinct forcing threshold exists above which the wave breaks in a dynamically significant way, leading to a disruption of the vortex. This breaking is distinguished from the process of weak filamentary breaking described by Dritschel and classified here as microbreaking; the latter occurs in nondivergent flow even at very small forcing amplitudes but does not affect the vortex in a substantial manner. In cases with finite Rossby deformation radius (comparable with the vortex radius) neither breaking nor microbreaking occurs below the forcing threshold. In common with previous studies using high-resolution spectral models, the vortex is not diluted by intrusion of outside air, except during remerger with a secondary vortex shed previously from the main vortex during a breaking event. The kinematics of the breaking process and of the vor...

Bubble clouds and the dynamics of the upper ocean

Abstract: This is a review of turbulence in the upper ocean close to the sea surface, particularly of the information that has been obtained from sonar observations of bubble clouds produced by breaking wind waves. These clouds provide tracers of the turbulent motions and are important, especially at high wind speeds, in the process of air-sea gas transfer. the observations of bubble clouds are here related to other measurements of turbulence, particularly to direct measurements of currents and temperatures in lakes or at sea, and to laboratory studies. Some novel observations of bubble clouds and breaking waves, their frequency and relation to Langmuir circulation, are presented. There is now emerging a pattern of clues that point to the dominance of breaking surface gravity waves as a source of turbulence to a depth below the surface of 0.04 to 0.2 times the wavelength of the dominant breaking waves, although the effect of swell has yet to be clarified. the relative depth appears to increase with increasing values of W,1/c, where W10 is the wind speed and c the phase speed of the dominant waves. Below this region the generation of turbulence may be dominated by shear-stress or convection. Here, turbulence is generally similar to that in the atmospheric boundary layer. There are, however, coherent motions on the scale of the mixing layer that persist for periods of a few minutes to an hour or so, to which the transport of a large part of the momentum and heat fluxes can be attributed, and which strongly affect the dispersion of buoyant particles or bubbles. These motions deserve special study to establish their contribution to heat and momentum transport, and hence to determine if, or when, they should be specifically represented in models of the upper ocean devised, for example, to describe the dispersion of passive and non-passive tracers or the air-sea transfer of gases.

Nonlinear water waves at a submerged obstacle or bottom topography

Abstract: Nonlinear diffraction of low-amplitude gravity waves in deep water due to a slightly submerged obstacle is studied experimentally in a wave channel and theoretically. The obstacle is either a circular cylinder or a rectangular shelf. The incoming waves (with wavelength λ) undergo strong nonlinear deformations at the obstacle when the wave amplitude is finite. An infinite number of superharmonic waves are then introduced to the flow. Their wavelengths far away from the obstacle are λ/4, λ/9, λ/16,…, due to the dispersion relation being quadratic in the wave frequency. The superharmonic wave amplitudes grow with increasing incoming wave amplitude up to saturation values. They are found to be prominent at the obstacle's lee side and vanishingly small at the weather side. The second- and third-harmonic wave amplitudes are, surprisingly, in several examples found to be comparable to the incoming wave amplitude. Up to 25% of the incoming energy flux may be transferred to the shorter waves. The theoretical model accounts for nonlinearity by the Boussinesq equations in the shallow region above the obstacle, with patching to linearized potential theory in the deep water. The theory explains both qualitatively and quantitatively the trends observed in the experiments up to breaking.

Measurements of bubble plumes and turbulence from a submarine

Abstract: An experiment using turbulence probes and an array of side‐scan and vertically pointing pencil beam sonars mounted on the U.S. submarine Dolphin was carried out to measure turbulence in near‐surface regions of acoustic scattering, in particular, those caused by subsurface bubbles produced by breaking wind waves. The dataset collected during winds of 5–9 m s−1 reveals the banded patterns of bubbles associated with Langmuir circulation, even though no surface manifestations were visible. A forward‐pointing side‐scan sonar determined the “age” of bubble clouds after their generation by breaking waves. There is enhanced turbulent dissipation in the bubble clouds, and the dissipation rate close to the surface exceeds that predicted using conventional calculations based on the law of the wall and buoyancy flux. The correspondence between bubbles and turbulence implies a horizontally patchy turbulent structure near the surface. Below the base of the bubble clouds the distance between turbulent patches i...

Field observations of the fluid‐granular boundary layer under near‐breaking waves

Abstract: Numerous synchronized time series from video cameras, pressure sensors, current meters, and hot film anemometers on natural beaches show that boundary layer development under the crest of near-breaking waves can be idealized as a process composed of three distinct regimes here referred to as streaking, roiling, and pluming. The roiling and pluming regimes fail to develop under the trough. As a consequence, there is a pronounced asymmetry in instantaneous sand transport and boundary layer phenomena between the wave crest and trough. However, laboratory waves with field scale periods and wave heights over thin sand beds do not exhibit this crest-trough boundary layer asymmetry, indicating that a critical element of similitude is absent in laboratory experiments. We suggest that wave induced boundary ventilation is responsible.

The Effect of Rain in Calming the Sea

Abstract: The effect of rain in damping surface waves appears to be significant in the estimation of wind speed from the backscatter of radar signal from the sea surface. The radar backscatter depends on the small-scale roughness of the sea surface. This is modified by the generation of capillary and gravity-capillary ripples by raindrops and by the increased damping of the wavelengths of 10-cm scale. The phenomenon is also important in wave generation and wave breaking, since in both cases the short wavelengths play a key role. A laboratory experiment has been performed to investigate the damping of water waves by rain in the absence of wind. Rain of intensity of 300 mm h−1 falls on mechanically generated progressive waves. The wave amplitude is measured before the wave enters and after it exits the rain section of a tank 2.35 m long. On the assumption of exponential damping, it is found that the effect of rain can be described by an eddy viscosity νE ≈ 0.3 cm2 s−1. The major part of the damping is attrib...

Instrumentation for the measurement of void-fraction in breaking waves: laboratory and field results

Abstract: The authors report on the development and use of an impedance probe to measure the volume fraction of air (void-fraction) in bubble plumes generated by breaking waves. The void-fraction gauge described was found to be most useful in the initial period after breaking when large void-fractions prevail. The authors describe the instrumentation at length and report on its use in the laboratory and in the field. The instrument is found to be capable of rendering the space-time evolution of the void-fraction field from controlled laboratory breaking waves. Field results show measurements of void-fractions (up to 24%) which are several orders of magnitude greater than time averaged values previously reported. Preliminary measurements show that the fraction of breaking waves per wave is dependent on significant wave height and wind speed. The dependence on wind speed is compared with data of previous investigators. Underwater video photography from the field shows the formation and evolution of distinct bubble plumes and the presence of large bubbles (at least 6-mm radius) generated by breaking. >

Momentum Transport by Gravity Waves

Abstract: The momentum flux by orographic gravity waves and the turbulent heat flux in wave-breaking regions are estimated from aircraft data from ALPEX. The fluxes on 6 March 1982 are controlled by low-level directional shear of the mean flow and associated critical level with wave stress decreasing toward the critical level. On 25 March 1982 a critical level does not occur and wave stress is approximately constant with height within the observational domain. The calculation of these fluxes appears to be the first direct comparison between simple models of gravity-wave momentum flux and observed atmospheric fluxes. To develop a simple formulation of gravity wave drag for large-scale models, the gravity-wave stress super-saturation theory by Lindzen is generalized for the application to vertically varying mean flows. The wave momentum flux estimated from the generalized model agrees well with the observations for the two ALPEX days. For the 6 March case, the vertical divergence of wave momentum flux below ...

Irregular wave setup and run-up on beaches

Abstract: The one-dimensional equations of mass, momentum, and energy are derived from the two-dimensional continuity and Reynolds equations in order to elucidate the approximations involved in these one-dimensional equations, which have been used previously to predict normally incident wave motions on coastal structures and beaches. The numerical model based on these equations is compared qualitatively with the wave setup and swash statistics on a moderately steep beach with a nearshore bar. The numerical model is shown to predict the irregular wave transformation and swash oscillation on the barred beach, at least qualitatively. The computed setup and swash heights are found to follow the lower bound of the scattered data points partly because of the neglect of the longshore variability on the natural beach and low-frequency components in the specified incident wave train. A more quantitative comparison is also made with the spectrum of the shoreline oscillation measured on a 1:20 plane beach, for which the corresponding wave spectrum was given. The numerical model is shown to predict the dominant low-frequency components of the measured spectrum fairly well.

Prediction of storm/normal beach profiles

Abstract: Using the results of large‐scale wave tank tests of monochromatic waves breaking on sandy beaches, Larson and Kraus have shown that storm (barred) and normal (nonbarred) equilibrium beach profiles can be segregated in terms of two‐dimensionless parameters, which involve wave and sediment characteristics. Here, by rearranging their results, a single dimensionless parameter is developed that predicts the occurrence of storm or normal profiles. The profile parameter (P=gH02/(w3T)) uses deep‐water wave characteristics to distinguish the two profile types. Using shallow‐water data the shallow‐water Dean number, Hb/(wT) can serve the same purpose. Further, a Froude number representation of the sediment fall velocity, w2/(gH0), is shown to be an important parameter for equilibrium profiles.

Three‐Dimensional Scattering of Solitary Waves by Vertical Cylinder

Abstract: This is a study of the scattering and diffraction of a solitary wave by a surface-piercing vertical cylinder held fixed in shallow water. Particular interest is focused on the roles played by the nonlinear effects and the dispersive effects in this fully three-dimensional problem of strong interaction between a solitary wave and a solid structure. The theoretical model adopted here for predicting the scattering and propagation of three-dimensional long waves in shallow water is the generalized Boussinesq (gB) two-equation model, developed by Wu. Using this model, the predicted flow field, the free-surface elevations, the wave-induced forces acting on the cyiindcr during the wave impact, and the subsequent evolution of the scattered wave field are numerically evaluated. The numerical results show that the front of the scattered wave field propagates very nearly in a circular belt, which is concentric to the cylinder as an overall topographical structure. This remarkable asymptotic geometrical feature of the resulting scattered wave cannot be obtained without the basic equations being able to correctly model the three-dimensional effects, and without bias toward the direction of wave propagation. The role of the nonlinear, dispersive, and linear wave effects during the wave-structure interaction are discussed in detail.

Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium.

Abstract: The spatial effects of cross-phase modulation on a weak probe beam as it copropagates with an intense pump beam through a self-defocusing medium are investigated. Experimental results are presented that demonstrate induced focusing, beam deflection, and the spatial analog of optical wave breaking. The experimental results are in good qualitative agreement with theoretical predictions.

A simple numerical technique for turbulent flows with free surfaces

Abstract: A simple technique is presented for the numerical solution of two-dimensional time-dependent flows, either laminar or turbulent, involving multiple free surfaces of arbitrary configuration The governing equations are the Reynolds equations for incompressible fluids with Boussinesq closure, the k- and ϵ-equations and an additional equation describing the fluid configuration This technique can potentially describe the propagation, deformation and overturning of pre-breaking waves and the mean flow, surface configuration and turbulence field after breaking The properties of the method are illustrated by several calculational examples The main parts of the algorithm are optimized for vector processing in a form suitable for installation in supercomputer facilities

Ray-tracing simulation of the global propagation of inertia gravity waves through the zonally averaged middle atmosphere

Abstract: The global propagation of large-horizontal-wavelength inertia gravity waves through a zonally averaged geostrophic wind and temperature climatology of the middle atmosphere is investigated using numerical ray-tracing techniques. Strong meridional shear in the zonal wind acts to refract waves horizontally (azimuthally), leading to changes in the local propagation azimuth, horizontal wavelength, and ground-based horizontal phase speed of the wave. Unlike other identified mechanisms which can produce such changes, this refraction effect is linear and does not require (nor forbid) that the wave amplitude be unstable for it to occur. Careful treatment of wave amplitudes indicates that such refracted waves are suppressed in amplitude far less by radiative damping and saturation than previous modeling has suggested, due to the use of a more accurate radiative damping parameterization. Refraction therefore is potentially important in modifying the waves' characteristics as they propagate through the middle atmosphere, and simulations reveal modifications which agree broadly with some observational data. Multiray simulations, using a horizontally isotropic source “spectrum” of waves with equal initial amplitudes, produce wave amplitudes at a height of 60 km which exhibit variations with latitude, season, and vertical wavenumber which have much in common with observations. A dearth of waves with large horizontal wavelengths also arises, in agreement with collated observations in the upper middle atmosphere. Significant differences in the latitude-season structure of the mean wave amplitudes of the northern and southern hemisphere are simulated. The simulations reproduce the well-known change in mean azimuthal wave propagation from eastward in summer to westward in winter, but the simulated westward phase invariably exceeds 6 months in duration, and in places the eastward summer phase is very weak and of limited duration. In addition, a smaller but nonetheless distinct poleward component to the mean propagation directions arises, due in part to horizontal refraction. Comparison of measured and simulated distributions of wave propagation azimuths reveals good agreement at some locations. Mid-latitude winter distributions around North America are well simulated when only c = 0 waves are retained. However, significant differences also occur, which may reflect the importance of features omitted from this model, such as zonal atmospheric variability and/or wave source effects. These and other limitations of the present model are highlighted; it is recommended that subsequent simulations incorporate zonal refraction due to planetary Rossby wave structure, and that higher-frequency waves be included so that the impact of refraction on the vertical flux of horizontal wave momentum can be assessed.

Wave Exchange between the Ground Surface and a Boundary-Layer Critical Level

Abstract: Gravity waves induced by two- and three-dimensional terrain features are examined theoretically in the planetary boundary layer (PBL) using a linear wave model that includes reabsorption at a critical level. The PBL structure is characterized by a constant Brunt-Vaisala frequency and a hyperbolic tangent wind speed profile, which can be adjusted to produce critical levels. It is found that for typical values of wind speed and thermal stratification in the stable PBL and for even mild terrain disturbances, the Reynolds stress and surface drag caused by surface-generated waves can be at least as large as those conventionally associated with surface friction. The wave drag will act on the PBL flow where wave dissipation occurs, for example, at a critical level or in regions of wave breaking. The drag over a given crosswind section of a two-dimensional ridge is about twice as great as that over a three-dimensional of approximately the same horizontal area. An entirely new result is the prediction tha...