Showing papers on "Breaking wave published in 1996"

Estimates of Kinetic Energy Dissipation under Breaking Waves

Abstract: The dissipation of kinetic energy at the surface of natural water bodies has important consequences for many Physical and biochemical processes including wave dynamics, gas transfer, mixing of nutrients and pollutants, and photosynthetic efficiency of plankton. Measurements of dissipation close to the surface obtained in a large lake under conditions of strong wind forcing are presented that show a layer of enhanced dissipation exceeding wall layer values by one or two orders of magnitude. The authors propose a scaling for the rate of dissipation based on wind and wave parameters, and conclude that the dissipation rate under breaking waves depends on depth, to varying degrees, in three stages. Very near the surface, within one significant height, the dissipation rate is high (an order of magnitude greater than that predicted by wall layer theory) and roughly constant. Below this is an intermediate region where the dissipation decays as z−2. The thickness of this layer (relative to the significant...

The Role of Surface-Wave Breaking in Air-Sea Interaction

Abstract: Breaking serves to limit the height of surface waves, mix the surface waters, generate ocean currents, and enhance air-sea fluxes of heat, mass, and momentum through the generation of turbulence and the entrainment of air. Breaking may result from intrinsic instabilities of deep-water waves or through wavewave, wave-current, and wind-wave interactions. Observations in the field are made difficult by the fact that breaking is a strongly nonlinear intermittent process occurring over a wide range of scales. Controlled laboratory studies of breaking have proven useful in measuring the scaling relationships between the surface wave field and the kinematics and dynamics of breaking. Our inability to predict the occurrence and dynamics of breaking is a major impediment to the development of better wind-wave and mixed-layer models. Modern acoustic and electromagnetic oceanographic instrumentation should lead to significantly improved measurements of breaking in the near future.

Fully nonlinear internal waves in a two-fluid system

Abstract: We derive general evolution equations for two-dimensional weakly nonlinear waves at the free surface in a system of two fluids of different densities. The thickness of the upper fluid layer is assumed to be small compared with the characteristic wavelength, but no restrictions are imposed on the thickness of the lower layer. We consider the case of a free upper boundary for its relevance in applications to ocean dynamics problems and the case of a non-uniform rigid upper boundary for applications to atmospheric problems. For the special case of shallow water, the new set of equations reduces to the Boussinesq equations for two-dimensional internal waves, whilst, for great and infinite lower-layer depth, we can recover the well-known Intermediate Long Wave and Benjamin-Ono models, respectively, for one-dimensional uni-directional wave propagation. Some numerical solutions of the model for one-dimensional waves in deep water are presented and compared with the known solutions of the uni-directional model. Finally, the effects of finite-amplitude slowly varying bottom topography are included in a model appropriate to the situation when the dependence on one of the horizontal coordinates is weak.

A Laboratory Study of Nonlinear Surface Waves on Water

Abstract: This paper describes an experimental investigation in which a large number of water waves were focused at one point in space and time to produce a large transient wave group. Measurements of the water surface elevation and the underlying kinematics are compared with both a linear wave theory and a second-order solution based on the sum of the wave-wave interactions identified by Longuet-Higgins & Stewart (1960). The data shows that the focusing of wave components produces a highly nonlinear wave group in which the nonlinearity increases with the wave amplitude and reduces with increasing bandwidth. When compared with the first- and second-order solutions, the wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacent wave troughs are broader and less deep. The water particle kinematics are also strongly nonlinear. The accumulated experimental data suggest that the formation of a focused wave group involves a significant transfer of energy into both the higher and lower harmonics. This is consistent with an increase in the local energy density, and the development of large velocity gradients near the water surface. Furthermore, the nonlinear wave-wave interactions are shown to be fully reversible. However, when compared to a linear solution there is a permanent change in the relative phase of the free waves. This explains the downstream shifting of the focus point (Longuet-Higgins 1974), and appears to be similar to the phase changes which result from the nonlinear interaction of solitons travelling at different velocities (Yuen & Lake 1982).

Spectral modeling of wave breaking: Application to Boussinesq equations

Abstract: The nonlinear transformation of wave spectra in shallow water is considered, in particular, the role of wave breaking and the energy transfer among spectral components due to triad interactions Energy dissipation due to wave breaking is formulated in a spectral form, both for energy-density models and complex-amplitude models The spectral breaking function distributes the total rate of random-wave energy dissipation in proportion to the local spectral level, based on experimental results obtained for single-peaked spectra that breaking does not appear to alter the spectral shape significantly The spectral breaking term is incorporated in a set of coupled evolution equations for complex Fourier amplitudes, based on ideal-fluid Boussinesq equations for wave motion The model is used to predict the surface elevations from given complex Fourier amplitudes obtained from measured time records in laboratory experiments at the upwave boundary The model is also used, together with the assumption of random, independent initial phases, to calculate the evolution of the energy spectrum of random waves The results show encouraging agreement with observed surface elevations as well as spectra

Satellite observations of atmospheric variances: A possible indication of gravity waves

Abstract: The Microwave Limb Sounder (MLS) on the Upper Atmosphere Research Satellite has now produced the first global maps of small-scale variances in the middle atmosphere. Initial analyses are presented here that suggest these variances are due to gravity waves, and the technique used to extract gravity wave information from saturated radiance measurements is described. Observations at 30–80km altitudes show that the variances of horizontal scales less than ∼100km are strongly correlated with upper tropospheric convection, surface topography and stratospheric jetstreams. MLS monthly averages during solstice periods suggest that the normalized variance amplitude grows exponentially with height in the stratosphere, and saturates in the mesosphere as expected from wave breaking and dissipation at these altitudes.

Field study of wave attenuation on an offshore coral reef

Abstract: A major field experiment was conducted which obtained measurements of the attenuation and transformation of short gravity waves as they cross the windward edge of an offshore coral reef. Water level data were collected for over 3000 individual time series during a wide range of environmental conditions. At the innermost measurement site, which is located on the horizontal reef flat after the completion of wave breaking, the upper bound of significant and maximum wave heights is limited to less than 40% and 60% of the reef flat water depth, respectively. As with significant wave height, both the shape and energy level of the reef flat spectra are strongly affected by changes in reef flat water depth. For higher tide levels the spectra on the reef flat closely mimic the corresponding incident spectra. However, the attenuation is greater for both lower frequencies and higher-energy portions of the spectra. This causes the reef flat spectra to be broader than those measured windward of the reef. At lower water levels, considerable energy losses due to wave breaking and bottom friction occur. Most of the energy loss comes from the vicinity of the spectral peak, and energy shifts to harmonics of the peak of the spectrum can be seen.

Observations and predictions of run‐up

Abstract: For a significant range of offshore wave conditions and foreshore slopes, run-up observations are compared to semiempirical formulations and predictions of an existing numerical model based on the depth-averaged one-dimensional nonlinear shallow water equations with bore-like breaking wave dissipation and quadratic bottom friction. The numerical model is initialized with time series of sea surface elevation and cross-shore velocity observed in 80 cm mean water depth (approximately 50 m offshore of the mean shoreline) on a gently sloping beach and in 175 cm water depth (100 m offshore of the shoreline) on a steep concave beach. Run-up was measured with a stack of resistance wires at elevations 5, 10, 15, 20, and 25 cm above and parallel to the beach face. At sea swell frequencies (nominally 0.05 < f ≤ 0.18 Hz), run-up energy is limited by surf zone dissipation of shoreward propagating waves so that increasing the offshore wave height above a threshold value does not substantially increase the predicted or observed sea swell run-up excursions (e.g., run-up is “saturated”). Existing semiempirical saturation formulations are most consistent with the observations and numerical model predictions of run-up excursions nearest the bed. In contrast, at infragravity frequencies (0.004 < f ≤ 0.05 Hz) where surf zone dissipation is relatively weak and reflection from the beach face is strong (e.g., saturation formulas are not applicable), the run-up excursions increase approximately linearly with increasing offshore wave height. The numerical model also accurately predicts that the tongue-like shape of the run-up results in sensitivity of run-up measurements to wire elevation. For instance, run-up excursions and mean vertical superelevation (above the offshore still water level) increase with decreasing wire elevation, and continuous thinning of the run-up tongue during the wave uprush can result in large phase differences between run-up excursions measured at different wire elevations. Numerical model simulations suggest that run-up measured more than a few centimeters above the bed cannot be used to infer even the sign of the fluid velocities in the run-up tongue.

Numerical Modeling of Wave Breaking Induced by Fixed or Moving Boundaries

Abstract: 374 Abstract In this paper, several numerical aspects of an existing model for fully nonlinear waves are improved and validated to study ware breaking due to shoaling over a gentle plane slope and wave breaking induced by a moving lateral boundary. The model is based on fully nonlinear potential flow theory and combines a higher-order Boundary Element Method (BEM) for solving Laplace's equation at a given time and Lagrangian Taylor expansions for the time updating of the free surface position and potential. An improved numerical treatment of the boundary conditions at the intersection between moving lateral boundaries and the free surface (corner) is implemented and tested in the model, and the free surface interpolation method is also improved to better model highly curved regions of the free surface that occur in breaking waves. Finally, a node regridding technique is introduced to improve the resolution of the solution dose to moving boundaries and in breaker jets. Examples are presented for solitary wave propagation, shoaling, and breaking over a 1:35 slope and for wave breaking induced by a moving vertical boundary. Using the new methods, both resolution and extent of computations are significantly improved compared to the earlier model, for similar computational efforts. In all cases computations can be carried out up to impact of the breaker jets on the free surface.

Influence of Barotropic Shear on the Poleward Advection of Upper-Tropospheric Air

Abstract: The characteristics of the poleward advection of upper-tropospheric air are investigated using meteorological analyses and idealized numerical models. Isentropic deformations of the tropopause during Northern Hemisphere winter are examined using maps of Ertel's potential vorticity together with contour advection calculations. Large poleward excursions of upper-tropospheric air are observed during Rossby wave breaking events. These “poleward” breaking events occur in regions of diffluence (over the eastern Atlantic Ocean-Europe region, and over the eastern Pacific Ocean-North America region), and the evolution of the tropospheric air depends on the local, meridional shear: in anticyclonic (or weak cyclonic) shear the tropospheric air tilts downstream, broadens, and wraps up anticyclonically, whereas in cyclonic shear the tropospheric air tilts upstream, thins, and is advected cyclonically. The role of ambient barotropic flow is further examined by considering the flow in two numerical models: a pl...

Nonlinear Flow Past an Elliptic Mountain Ridge

Abstract: The hydrostatic flow over an elliptical mountain of aspect ratio 5 is explored by numerical experiments. The upstream profiles of wind and stability are constant, the Coriolis effect is ignored, and there is free slip at the lower boundary. In these conditions, the, flow characteristics depend mainly on the nondimensional mountain height, Nh/U. The authors have conducted experiments with Nh/U varying from 0.500 to 6.818. For low values of Nh/U, the results confirm the linear theory of Smith, which predicts stagnation aloft, leading to wave breaking and, on the upstream slope, leading to flow splitting. For higher values of Nh/U, the authors find that wave breaking ceases on the axis of symmetry but continues on each side of this axis. Even for the highest value of Nh/U used (6.818), significant areas of wave breaking and wave activity aloft are found. For all values of Nh/U, a substantial part of the flow is diverted vertically above the mountain. The detailed study of the kinematic pattern withi...

An experimental study of deep water plunging breakers

Abstract: Plunging breaking waves are generated mechanically on the surface of essentially deep water in a two‐dimensional wave tank by superposition of progressive waves with slowly decreasing frequency. The time evolution of the transient wave and the flow properties are measured using several experimental techniques, including nonintrusive surface elevation measurement, particle image velocimetry, and particle tracking velocimetry. The wave generation technique is such that the wave steepness is approximately constant across the amplitude spectrum. Major results include the appearance of a discontinuity in slope at the intersection of the lower surface of the plunging jet and the forward face of the wave that generates parasitic capillary waves; transverse irregularities occur along the upper surface of the falling, plunging jet while the leeward side of the wave remains very smooth and two dimensional; the velocity field is shown to decay rapidly with depth, even in this strongly nonlinear regime, and is simila...

The influence of bubble plumes on air-seawater gas transfer velocities

Abstract: Laboratory results have demonstrated that bubble plumes are a very efficient air-water gas transfer mechanism. Because breaking waves generate bubble plumes, it could be possible to correlate the air-sea gas transport velocity kL with whitecap coverage. This correlation would then allow kL to be predicted from measurements of apparent microwave brightness temperature through the increase in sea surface microwave emissivity associated with breaking waves. In order to develop this remote-sensing-based method for predicting air-sea gas fluxes, a whitecap simulation tank was used to measure evasive and invasive kL values for air-seawater transfer of carbon dioxide, oxygen, helium, sulfur hexafluoride, and dimethyl sulfide at cleaned and surfactant-influenced water surfaces. An empirical model has been developed that can predict kL from bubble plume coverage, diffusivity, and solubility. The observed dependence of kL on molecular diffusivity and aqueous-phase solubility agrees with the predictions of modeling studies of bubble-driven air-water gas transfer. It has also been shown that soluble surfactants can decrease kL even in the presence of breaking waves.

Wave Breaking and Transition to Turbulence in Stratified Shear Flows.

Abstract: In a previous study the authors used a nonlinear, compressible, spectral collocation numerical model to examine the evolution of a breaking gravity wave in two and three dimensions. The present paper extends that effort to examine the implications of higher resolution and smaller dissipation for wave and instability evolutions, transports, and energetics in shear flows aligned with and having a component transverse to the direction of wave propagation. A component of mean shear transverse to the direction of wave propagation (denoted as a skew shear) results in the alignment of instability structures with the background shear flow rather than in the direction of wave propagation. This alignment leads to asymmetric instability structures and less rapid instability growth relative to the parallel shear flow. Slower instability evolution due to a skew shear has several implications for wave breakdown, including a delayed state of maximum instability, a larger wave amplitude prior to and throughout w...

Turbulent structure beneath surface gravity waves sheared by the wind

Abstract: New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave-turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave-turbulence interactions.

Doppler radar measurements of wave groups and breaking waves

Abstract: A 3-GHz Doppler radar has been used to study wave dynamics and backscatter from the sea surface at low grazing angles. Vertical polarization results are dominated by Bragg scatter even at low (∼8°) grazing angles. Horizontal polarization results, however, show a strong upwind-downwind asymmetry with additional, high-velocity intermittent scatter in the upwind direction associated with steep or breaking waves. These characteristics have been exploited to distinguish spilling breaking events from the background Bragg scatter. While these “spikes” at a single range may appear random in time, the combined range and time information reveals a well-determined propagation pattern. It is shown that for a developing sea in deep water, group behavior modulates the occurrence of wave breaking. The frequency-wavenumber spectrum shows a clear separation between the linear dispersion curve and nonlinear effects related to breaking. The most important nonlinear feature is a line near the dominant wave group velocity which is identified with the spectrum of breaking intermittency. The slope of this line suggests that the wave components which are most likely to break lie at frequencies significantly above the dominant wave frequency.

Velocity profiles and surface roughness under breaking waves

Abstract: Recent measurements under wave-breaking conditions in the ocean, lakes, and tanks reveal a layer immediately below the surface in which dissipation decays as depth to the power −2 to −4 and downwind velocities are approximately linear with depth. This behavior is consistent with predictions of a conventional, one-dimensional, level 2.5 turbulence closure model, in which the influence of breaking waves is parameterized as a surface source of turbulent kinetic energy. The model provides an analytic solution which describes the near-surface power law behavior and the deeper transition to the “law of the wall.” The mixing length imposed in the model increases linearly away from a minimum value, the roughness length, at the surface. The surface roughness emerges as an important scaling factor in the wave-enhanced layer but is the major unknown in the formulation. Measurements in the wave-affected layer are still rare, but one exceptional set, both in terms of its accuracy and proximity to the surface, is that collected by Cheung and Street [1988] in the Stanford wind tunnel. Their velocity profiles first confirm the accuracy of the model, and, second, allow estimation, via a best fit procedure, of roughness lengths at five different wind speeds. Conclusions are tentative but indicate that the roughness length increases with wind speed and appears to take a value of approximately one sixth the dominant surface wavelength. A more traditional wall-layer model, which ignores the flux of turbulent kinetic energy, will also accurately reproduce the measured velocity profiles. In this case, enhanced surface turbulence is forced on the model by the assumption of a large surface roughness, three times that required by the full model. However, the wall-layer model cannot predict the enhanced dissipation near the surface.

Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries

Abstract: Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with forcing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optical wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauchy integral code. Experiments show that contact-line effects increase the viscous natural frequency and alter the neutral stability curves. Hence, as expected, the addition of the wetting agent Photo Flo significantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplitude for some forcing frequencies higher than 3.30 Hz. Reducing contact-line effects by Photo-Flo addition suppresses these modulations. Perturbation analysis predicts that some of this modulation is caused by noise in the forcing signal through ‘sideband resonance’, i.e. the introduction of small sideband forcing can generate large modulations of the Faraday waves. The analysis is verified by our numerical simulations and physical experiments. Finally, we observe experimentally a new form of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper crest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classical standing wave and a surface tension far smaller than that for a Wilton ripple. In both physical and numerical experiments, a stronger second harmonic (in time) and temporal asymmetry in the wave forms suggest a 1:2 resonance due to a non-conventional quartet interaction. Increasing wave steepness leads to a new form of breaking standing waves in physical experiments.

The Impact of Parameterized Subgrid-Scale Orographic Forcing on Systematic Errors in a Global NWP Model

Abstract: The global momentum budget for December 1993, diagnosed from a series of two-time-step integrations of the U.K. Meteorological Office global Unified Model, suggests that the parameterized mechanical dissipation in the model is underestimated. The initial momentum imbalance is consistent with the zonal mean systematic errors in zonal wind. Further diagnosis suggests that (i) the momentum budget residual is largest in the boundary layer and over the orography and (ii) too much gravity wave drag is applied in the model stratosphere. Two new parameterizations are proposed to alleviate this problem. The first is a new gravity wave drag scheme incorporating (i) anisotropy in the orography into the expression for surface gravity wave stress and (ii) low-level wave breaking mechanisms such as trapped Ice waves and high drag states. The second parameterization deals with the form drag due to subgrid-scale orography, a process currently ignored in the model. This is parameterized using an effective roughne...

Instability and breakdown of internal gravity waves. I. Linear stability analysis

Abstract: We have performed three‐dimensional linear stability analysis, based on Floquet theory, to study the stability of finite amplitude internal gravity waves. This analysis has been used to compute instability growth rates over a range of wave amplitudes and propagation angles, especially waves above and below overturning amplitude, and identifies several new characteristics of wave instability. Computation of instability eigenfunctions has allowed us to analyze the energetics of the instability and to clarify the paths of energy transfer from the base wave to the instability. We find that the presence of wave overturning has no qualitative effect on the wave instability, except for the limiting case when the wavenumber vector is vertical. Instabilities which are nearly two‐dimensional are closely related to second‐order wave–wave interactions. But the three‐dimensional instabilities, more prominent at higher wave amplitudes, may be caused by higher order resonance interactions. The energetics of the instabilities range from being shear driven to being driven by ‘‘density gradient’’ production (the potential energy analog of ‘‘shear’’ production); this characteristic is strongly dependent on wave propagation angle and the three‐dimensionality of the instability.

Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing

Abstract: An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength, which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other...

The two‐day wave in a middle atmosphere GCM

Abstract: A strong signal of the two-day wave is diagnosed in a middle atmosphere GCM, with characteristics very similar to those of the observed two-day wave. It results from an instability, but its global structure shows similarities to a Rossby-gravity planetary normal mode. It has a remarkable potential vorticity structure in wave 3 and sometimes wave 4 and higher wavenumbers. It is shown that gravity wave drag is important in maintaining the unstable zonal mean state.

Convergence of a Boundary Integral Method for Water Waves

Abstract: We prove nonlinear stability and convergence of certain boundary integral methods for time-dependent water waves in a two-dimensional, inviscid, irrotational, incompressible fluid, with or without surface tension. The methods are convergent as long as the underlying solution remains fairly regular (and a sign condition holds in the case without surface tension). Thus, numerical instabilities are ruled out even in a fully nonlinear regime. The analysis is based on delicate energy estimates, following a framework previously developed in the continuous case [Beale, Hou, and Lowengrub, Comm. Pure Appl. Math., 46 (1993), pp. 1269--1301]. No analyticity assumption is made for the physical solution. Our study indicates that the numerical methods must satisfy certain compatibility conditions in order to be stable. Violation of these conditions will lead to numerical instabilities. A breaking wave is calculated as an illustration.

A Simulated Spectrum of Convectively Generated Gravity Waves: Propagation from the Tropopause to the Mesopause and Effects on the Middle Atmosphere

Abstract: This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. [1995] that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.

On Frequency-Focusing Unidirectional Waves

Abstract: Phase convergence to within lOin mechanically generated waves was achieved at a specified point in a wave flume by frequency focusing. Owing to the presence of nonlinear waves, the crest elevation reaches a maximum somewhat further from the waveboard, where also breaking occurs if the waves are of sufficient size. The critical amplitude for breaking was not in close agreement with previous measurements when normalized with respect to the central wave number of mechanically generated waves. It is suggested however that the limiting conditions are related to the phase speed near the focus point, where the wave group propagates with a considerable degree of coherence not present in a linear model. Predictions of a time-dependent nonlinear numerical model of Baldock and Swan (1994) are found to be in good agreement with the behavior of the crest in this region.

Suspended-sediment transport in the surf zone: response to breaking waves

Abstract: A field experiment designed to investigate the influence of wave breaking on suspended-sediment transport was conducted at Duck, NC, from 6 to 9 September 1985. Arrays of optical backscatter sensors, electromagnetic current meters and pressure sensors were deployed at five positions on a shore-normal transect that spanned the surf zone. At each position measurements were made of cross-shore and longshore velocity, sea-surface fluctuations, and suspended sediment at five levels above the bed. Experimental data runs were conducted when incident swell waves ( Hs = 0.5m, T= 10–12s) broke (primarily plunging) within the experimental transect. This paper describes the spatial characteristics of the plunge-to-bore tranformation region and describes (1) the cross-shore variability of sediment resuspension, including the mean concentrations and mean suspended load; (2) the net longshore and cross-shore flux across the surf zone; (3) mean suspended-sediment profiles as a function of wave type, e.g. plunging, spilling and bore, and unbroken at four positions across the surf zone; and (4) discusses the relative contribution of each wave type to the net longshore and cross-shore sediment flux.

Radar backscatter and surface roughness measurements for stationary breaking waves

Abstract: In this study the surface features and the radar backscatter associated with breaking waves generated by a uniform flow past a stationary submerged hydrofoil were examined. The level of energy dissipation due to breaking was varied by changing the foil angle of attack. Time series of surface elevation profiles were obtained for the breaking crest region and the following waves. Radar backscatter (X-band) was also measured for an incidence angle of 45° with the radar looking both upwave and downwave for HH and VV polarizations. These measurements were compared to model predictions of radar backscatter using the surface elevation data as inputs to the model. The breaking crest region exhibited the largest surface disturbances, as measured by the temporal variance of the surface elevation. The maximum in the variance was associated with large low-frequency disturbances in the ‘toe’ region. Downstream-moving waves appear just ahead of the crest and, due primarily to interaction with the spatially varying current set up by the stationary wave, decrease in amplitude by an order of magnitude as they propagate downstream. These surface disturbances remain at a low level thereafter. A maximum radar cross-section per unit area of about 0.5 was observed near the breaking crest, for both HH and VV polarization in the upwave look direction. The maximum value for the upwave look direction was about twice as large as for the downwave look direction. Downstream of the breaking crest, the radar cross-section decreased rapidly and then leveled off, and an increasing difference between the VV and HH backscatter was observed as the overall backscatter level decreased. Near the second crest, there was a small increase in the height variance and in the radar cross-section. The surface-elevation measurements were used as inputs for a Bragg-scattering model and the expected radar backscatter was calculated. The variations in the observed radar cross-section downstream of the breaking crest are satisfactorily explained by the Bragg model when surface-tilt effects are taken into account. However, the backscatter from the breaking crest itself is not accurately predicted since, in this region, the small-scale surface roughness exceed the limits of validity for the Bragg model.