Showing papers on "Breaking wave published in 1994"

Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer

Abstract: Until recently, measurements below the ocean surface have tended to confirm “law of the wall” behavior, in which the velocity profile is logarithmic, and energy dissipation decays inversely with depth. Recent measurements, however, show a sublayer, within meters of the surface, in which turbulence is enhanced by the action of surface waves. In this layer, dissipation appears to decay with inverse depth raised to a power estimated between 3 and 4.6. The present study shows that a conventional model, employing a “level 2½” turbulence closure scheme predicts near-surface dissipation decaying as inverse depth to the power 3.4. The model shows agreement in detail with measured profiles of dissipation. This is despite the fact that empirical constants in the model are determined for situations very different from this near-surface application. The action of breaking waves is modeled by a turbulent kinetic energy input at the surface. In the wave-enhanced layer, the downward flux of turbulent kinetic en...

Wavelet Spectrum Analysis and Ocean Wind Waves

Abstract: Wavelet spectrum analysis is applied to a set of measured ocean wind waves data collected during the 1990 SWADE (Surface Wave Dynamics Experiment) program. The results reveal significantly new and previously unexplored insights on wave grouping parameterizations, phase relations during wind wave growth, and detecting wave breaking characteristics. These insights are due to the nature of the wavelet transform that would not be immediately evident using a traditional Fourier transform approach.

'Downward control' of the mean meridional circulation and temperature distribution of the polar winter stratosphere

Abstract: According to the 'downward control' principle, the extratropical mean vertical velocity on a given pressure level is approximately proportional to the meridional gradient of the vertically integrated zonal force per unit mass exerted by waves above that level. In this paper, a simple numerical model that includes parameterizations of both planetary and gravity wave breaking is used to explore the influence of gravity wave breaking in the mesosphere on the mean meridional circulation and temperature distribution at lower levels in the polar winter stratosphere. The results of these calculations suggest that gravity wave drag in the mesosphere can affect the state of the polar winter stratosphere down to altitudes below 30 km. The effect is most important when planetary wave driving is relatively weak: that is, during southern winter and in early northern winter. In southern winter, downwelling weakens by a factor of 2 near the stratospause and by 20% at 30 km when gravity wave drag is not included in the calculations. As a consequence, temperatures decrease considerably throughout the polar winter stratosphere (over 20 K above 40 km and as much as 8 K at 30 km, where the effect is enhanced by the long radiative relaxation timescale). The polar winter states obtained when gravity wave drag is omitted in this simple model resemble the results of simulations with some general circulation models and suggest that some of the shortcomings of the latter may be due to a deficit in mesospheric momentum deposition by small-scale gravity waves.

Transport out of the lower stratospheric Arctic vortex by Rossby wave breaking

Abstract: The fine-scale structure in lower stratospheric tracer transport during the period of the two Arctic Airborne Stratospheric Expeditions (January and February 1989; December 1991 to March 1992) is investigated using contour advection with surgery calculations These calculations show that Rossby wave breaking is an ongoing occurrence during these periods and that air is ejected from the polar vortex in the form of long filamentary structures There is good qualitative agreement between these filaments and measurements of chemical tracers taken aboard the NASA ER-2 aircraft The ejected air generally remains filamentary and is stretched and mixed with midlatitude air as it is wrapped around the vortex This process transfers vortex air into midlatitudes and also produces a narrow region of fine-scale filaments surrounding the polar vortex Among other things, this makes it difficult to define a vortex edge The calculations also show that strong stirring can occur inside as well as outside the vortex

Breaking Rossby Waves in a Model Stratosphere Diagnosed by a Vortex-Following Coordinate System and a Technique for Advecting Material Contours

Abstract: This paper presents results from a single-layer, shallow-water, 100-day model integration that reproduces many features of the wintertime stratosphere, particularly in the tropics, more realistically than earlier single-layer integrations. The advective transport of passive tracers by breaking Rossby waves is examined using a new polar-vortex-following coordinate system and a technique for advecting material contours, in which they are followed very accurately using the contour-dynamics algorithm of Dritschel. Unlike any Eulerian tracer advection scheme, the technique for advecting material contours has no numerical diffusion and can handle the ultrafinescale, exponentially shrinking tracer features characteristic of chaotic advective transport or “stirring,” which is conspicuous here in the stratospheric “surfzone.” The technique may become important as a benchmark for quantitative comparison with Eulerian tracer advection schemes, such as those used in general circulation models. Averages with ...

Parameterization of the Cool Skin of the Ocean and of the Air-Ocean Gas Transfer on the Basis of Modeling Surface Renewal

Abstract: Heat and gas transport in molecular sublayers at the air-sea interface is governed by similar laws. A model of renewal type based on the physics of molecular sublayers allows the derivation of a parameterization of the temperature difference across the cool skin of the ocean and of the coefficient of the direct air-sea gas transfer. The surface Richardson number controls the transition from convective instability to wind-induced instability (“rollers” on breaking wavelets) and the Keulegan number controls the transition from the regime of rollers to long-wave breaking. A critical value of the surface Richardson number and of a nondimensional constant can be evaluated by comparing the parameterizations of the cool skin with field data. The critical value of the Keulegan number is determined from the wind speed at which long-wave breaking appears. The parameterizations have been compared with cool skin data obtained from campaigns in the tropical and subtropical Atlantic Ocean, while the gas transf...

A Spectral Wave Model for the Coastal Zone

Abstract: Spectral wave models that represent the evolution of the waves on a grid superior in several respects to conventional wave ray models. Spectral models on a grid have been developed for applications in the deep ocean and for shelf seas. However, they are not economically feasible in coastal waters due to numerical limitations. We present the first step in implementation of a version that does not have these limitations. we remove time as an independent variable (reducing the computations to stationery or quasi-stationery computations, which is proper considering the residence time of the waves in the area) and we use an unconditionally stable propagation scheme. The propagation scheme is successfully tested in academic cases, including a case with complete reversal of wave direction. As a preliminary test of propagation in an observed field case, computations are carried out for waves travelling across and around an extended (5 km) shoal. With a limited representation of the bottom induced processes (bottom friction and surf dissipation), realistic results are obtained for the significant wave height. This test also shows the relevance of the planned implementation of the wave-wave interactions (in particular grid interactions) and wind generation. The model is planned to be optionally second-or-third-generation (with or without predefined spectral constraints).

Shoaling of Solitary Waves on Plane Beaches

Abstract: Shoaling of solitary waves on both gentle (1:35) and steeper slopes ( 1:6.50) is analyzed up to breaking using both a fully nonlinear wave model and high-accuracy laboratory experiments. For the mildest slope, close agreement is obtained between both approaches up to breaking, where waves become very asymmetric and breaking indices reach almost twice the value for the largest stable symmetric wave. Bottom friction does not seem to affect the results at all. Wave celerity decreases during shoaling and slightly increases before breaking. At breaking, the crest particle velocity is almost horizontal and reaches 90% of the crest celerity, which is two to three times larger than the bottom velocity. The nonlinear shallow water equations and the Boussinesq approximation both fail to predict these results. Finally, shoaling rates for various wave heights and bottom slopes differ from the predictions of Green's or Boussinesq shoaling laws. On the mildest slope, shoaling rates roughly follow a "two-zone" model proposed earlier but on steeper slopes reflection becomes significant and wave heights change little during shoaling.

Energy Dissipation by Breaking Waves

Abstract: Recent field measurements by Agrawal et al. have provided evidence of a shallow surface mixed layer in which the rate of dissipation due to turbulence is one to two orders of magnitude greater than that in a comparable turbulent boundary layer over a rigid wall. It is shown that predictions by Phillips of the energy lost by breaking surface waves in an equilibrium regime and laboratory measurements by Rapp and Melville of the mixing and turbulence due to breaking together lead to estimates of the enhanced dissipation rate and the thickness of the surface layer consistent with the field measurements. Wave-age-dependent scaling of the dissipation layer is proposed. Laboratory measurements of dissipation rates in both unsteady and quasi-steady breaking waves are examined. It is shown that an appropriately defined dimensionless rate of dissipation in unsteady breaking waves is not constant, but increases with a measure of the wave slope. Differences between dissipation rates in quasi-steady and unste...

Gravity wave breaking in two and three dimensions: 2. Three‐dimensional evolution and instability structure

Abstract: A companion paper by Andreassen et al. (this issue) introduced and used a nonlinear, compressible, spectral collocation code to address the relative evolutions of two-dimensional motions obtained in two- and three-dimensional simulations of gravity wave breaking. That study illustrated the effects of instability on the wave field and mean flow evolution and suggested that two-dimensional models are unable to fully describe the physics of the wave breaking process. The present paper examines in detail the structure, evolution, and energetics of the three-dimensional motions accounting for wave instability as well as their associated transports of momentum and heat. It is found that this instability comprises counterrotating vortices which evolve very rapidly within the convectively unstable region of a breaking wave. Instability scales are selected based on wave geometry and vortices are elongated in the streamwise direction (horizontal wavenumber in the spanwise direction) and result in the rapid collapse of superadiabatic regions within the wave field. The resulting spectra show clearly the transition from gravity wave forcing of harmonics of the incident wave to instability onset and evolution. Fluxes of momentum and heat by the instability reveal the manner in which the gravity wave amplitude is constrained and the influences of instability on the wave transports of these quantities. The breakdown of the instability structure and its evolution toward isotropic small-scale structure is the subject of the companion paper by Isler et al. (this issue).

Observations of turbulence in the surf zone

Abstract: : The turbulence generated by waves breaking on a natural beach is examined using hotfilm anemometer data. Turbulence intensity is estimated from the dissipation rate and an appropriate length scale (a fraction of the water depth). The dissipation rates are determined from wavenumber spectra found by applying Taylor's hypothesis to frequency spectra of short (1/8s) hotfilm time series. The resulting Froude-scaled turbulence intensities are relatively uniform throughout the water column and are similar in vertical structure but lower in magnitude than in existing laboratory studies. The magnitudes of the turbulence intensity observed in both the field and laboratory are consistent with an existing macroscopic model of bore dissipation in the surf zone. Scaling by this bore model relates turbulence intensity levels of monochromatic waves in small-scale laboratory experiments to random waves in the natural surf zone.... Surfzone, Turbulence, Wave breaking, Wave dissipation.

Modeling Spectral Dissipation in the Evolution of Wind Waves. Part I: Assessment of Existing Model Performance

Abstract: This study examines the performance of a state-of-the-art spectral wind wave model that uses a full solution to the nonlinear interaction source term. The situation investigated here is fetch-limited wind wave evolution, for which a significant observational database exists. The authors consider both the evolutionary characteristics such as the predicted development of wave energy and peak wave frequency with fetch, as well as the predicted local features of the directional wavenumber spectrum: the spectral shape of the dominant wave direction slice, together with the directional spreading function. In view of the customary practice of constraining the shape of the spectral tail region, this investigation required relaxing the constrained tail assumption. This has led to new insight into the dynamic role of the spectral tail region. The calculations have focused on the influence of two of the source terms in the spectral evolution (radiative transfer) equation for the energy density spectrum—thos...

Gravity wave breaking in two and three dimensions: 1. Model description and comparison of two‐dimensional evolutions

Abstract: A nonlinear, compressible, spectral collocation code is employed to examine gravity wave breaking in two and three spatial dimensions. Two-dimensional results exhibit a structure consistent with previous efforts and suggest wave instability occurs via convective rolls aligned normal to the gravity wave motion (uniform in the spanwise direction). Three-dimensional results demonstrate, in contrast, that the preferred mode of instability is a series of counterrotating vortices oriented along the gravity wave motion, elongated in the streamwise direction, and confined to the region of convective instability within the wave field. Comparison of the two-dimensional results (averaged spanwise) for both two- and three-dimensional simulations reveals that vortex generation contributes to much more rapid wave field evolution and decay, with rapid restoration of near-adiabatic lapse rates and stronger constraints on wave energy and momentum fluxes. These results also demonstrate that two-dimensional models are unable to describe properly the physics or the consequences of the wave breaking process, at least for the flow parameters examined in this study. The evolution and structure of the three-dimensional instability, its influences on the gravity wave field, and the subsequent transition to quasi-isotropic small-scale motions are the subjects of companion papers by Fritts et al. (this issue) and Isler et al. (this issue).

Three-dimensional wave instability near a critical level

Abstract: The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.

Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system

Abstract: The excitability properties of a two-variable cubic autocatalysis model for chemical oscillations are examined. The reaction-diffusion behaviour of this model is studied in a one-dimensional configuration with differing relative diffusivities of the species. Wave reflection at no-flux boundaries is examined and described in terms of reactant depletion in the wave front and reactant influx in the wave back. Waves are also reflected upon collision with other waves. Wave splitting, the spontaneous initiation of a wave from the trailing edge of another wave, is found to occur for some relative diffusivities. Successive wave splittings give rise to stationary Turing patterns at long times.

OH emission and gravity waves (including a breaking wave) in all-sky imagery from Bear Lake, UT

Abstract: A new type of all-sky imager, using a high resolution, bare CCD, was operated at Utah State University Observatory at Bear Lake Utah during fall-winter, 1991–2 on clear nights. The purpose was to image OH airglow in the 7500–9000 A spectral region for correlative measurements with UARS satellite instrumentation. Examination of some 20 nights of data, some OH wave activity (interpreted as gravity wave phenomena) has been observed on all images and the spatial extent of the waves typically covered the entire viewing field (including overhead). Images are presented including examples of multiple wave sources and a (one time observed) complex breaking wave. The unique chaotic structure, which evolved over an hour, developed a distorted phase front followed by a very short wavelength ‘rippled’ structure.

Void-fraction measurements and sound-speed fields in bubble plumes generated by breaking waves

Abstract: Recent field and laboratory experiments have confirmed that low‐frequency sound (10 to 300 Hz) is generated under breaking waves. It has been proposed that collective oscillations of the bubble plume generated by breaking may be the mechanism responsible for the generation of this sound. Confirmation of this process requires independent measurement of the void fraction, and therefore sound speed, in the bubbly mixture. Detailed measurements are presented of the evolution of the void‐fraction field in bubble plumes generated by large‐scale three‐dimensional (3‐D) laboratory breaking waves. Various moments of the void‐fraction field are calculated and compared with results from two‐dimensional (2‐D) laboratory breaking waves [Lamarre and Melville, Nature 351, 469–472 (1991)]. The kinematics of the bubble plume reveals that the initial horizontal velocity of the plume is approximately 0.7C, where C is the wave phase speed. The centroid of the bubble plume is found to deepen at a speed of approximately 0.2H/T, where H and T are the wave height at breaking and the wave period, respectively. The radial dependence of the void‐fraction and sound‐speed field is characterized in terms of simple functions of time. Finally, the void‐fraction measurements described here, along with independent measurements of the pressure fluctuations under breaking waves [Loewen and Melville, J. Acoust. Soc. Am. 95, 1329–1343 (1994)], support the hypothesis that low‐frequency sound is generated by the collective oscillations of the bubble plume.

The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water

Abstract: The stability of an axisymmetric vortex with a single radial discontinuity in potential vorticity is investigated in rotating shallow water. It is shown analytically that the vortex is always unstable, using the WKBJ method for instabilities with large azimuthal mode number. The analysis reveals that the instability is of mixed type, involving the interaction of a Rossby wave on the boundary of the vortex and a gravity wave beyond the sonic radius. Numerically, it is demonstrated that the growth rate of the instability is generally small, except when the potential vorticity in the vortex is the opposite sign to the background value, in which case it is shown that inertial instability is likely to be stronger than the present instability.

Characteristics of Solitary Wave Breaking Induced by Breakwaters

Abstract: Laboratory experiments are presented for the breaking of solitary waves over breakwaters. A variety of behaviors is observed, depending on both breakwater and incident wave height: for emerged breakwaters, waves may collapse over the crown, or break backward during rundown; and for submerged breakwaters, waves may break forward or backward, downstream of the breakwater. The limit of overtopping and wave transmission and reflection coefficients are experimentally determined. It is seen that transmission is large over submerged breakwaters (55–90%), and may also reach 20–40% over emerged breakwaters. Computations using a fully nonlinear potential model agree well with experimental results for the submerged breakwaters, particularly for the smaller waves (\IH/d\N<0.4). For emerged breakwaters, computations correctly predict the limit of overtopping, and the backward collapsing during rundown.

The formation of spilling breaking water waves

Abstract: Photographs from high‐speed movies of the profiles of a mechanically generated, gentle spilling breaking water wave are presented. It is found that as the wave steepens a bulge forms on the forward face of the wave near the crest and capillary waves form on the water surface ahead of the ‘toe’ of the bulge (see Fig. 1). The toe of the bulge then moves rapidly down the forward face of the wave and a train of large‐amplitude waves with short wavelength grows rapidly on the surface of the bulge. These waves quickly break down into a random pattern indicating that the flow has become turbulent.

Observations of Breaking Surface Wave Statistics

Abstract: Breaking surface waves were observed during the Surface Wave Process Program with a novel acoustical instrument that makes use of underwater ambient sound to track individual breaking events. The spatial and temporal statistics of braking waves such as duration, velocity, spacing and breaking probability were determined under various wind and wave conditions. Statistical models are developed to assess and when appropriate, correct for any bias resulting from limitations of the measurement approach. Empirical relations of these statistics with wind speed are obtained. Comparison of the observed distributions with simultaneously measured directional wave spectra suggests that wave breaking occurs at multiple scales and that the mean scale of breaking is substantially smaller than the associated with the dominant wind wave component. Preliminary analysis indicates that the dependence of breaking probability on the fourth moment of the wave spectrum is consistent with a linear statistical model.