Showing papers on "Breaking wave published in 2001"

A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom

Abstract: An accurate three-dimensional numerical model, applicable to strongly non-linear waves, is proposed. The model solves fully non-linear potential flow equations with a free surface using a higher-order three-dimensional boundary element method (BEM) and a mixed Eulerian–Lagrangian time updating, based on second-order explicit Taylor series expansions with adaptive time steps. The model is applicable to non-linear wave transformations from deep to shallow water over complex bottom topography up to overturning and breaking. Arbitrary waves can be generated in the model, and reflective or absorbing boundary conditions specified on lateral boundaries. In the BEM, boundary geometry and field variables are represented by 16-node cubic ‘sliding’ quadrilateral elements, providing local inter-element continuity of the first and second derivatives. Accurate and efficient numerical integrations are developed for these elements. Discretized boundary conditions at intersections (corner/edges) between the free surface or the bottom and lateral boundaries are well-posed in all cases of mixed boundary conditions. Higher-order tangential derivatives, required for the time updating, are calculated in a local curvilinear co-ordinate system, using 25-node ‘sliding’ fourth-order quadrilateral elements. Very high accuracy is achieved in the model for mass and energy conservation. No smoothing of the solution is required, but regridding to a higher resolution can be specified at any time over selected areas of the free surface. Applications are presented for the propagation of numerically exact solitary waves. Model properties of accuracy and convergence with a refined spatio-temporal discretization are assessed by propagating such a wave over constant depth. The shoaling of solitary waves up to overturning is then calculated over a 1:15 plane slope, and results show good agreement with a two-dimensional solution proposed earlier. Finally, three-dimensional overturning waves are generated over a 1:15 sloping bottom having a ridge in the middle, thus focusing wave energy. The node regridding method is used to refine the discretization around the overturning wave. Convergence of the solution with grid size is also verified for this case. Copyright © 2001 John Wiley & Sons, Ltd.

Modeling the alongshore current on barred beaches

Abstract: Mean alongshore currents observed on two barred beaches are compared with predictions based on the one-dimensional, time- and depth-averaged alongshore momentum balance between forcing (by breaking waves, wind, and 10–100 km scale alongshore surface slopes), bottom stress, and lateral mixing. The observations span 500 hours at Egmond, Netherlands, and 1000 hours at Duck, North Carolina, and include a wide range of conditions with maximum mean currents of 1.4 m/s. Including rollers in the wave forcing results in improved predictions of the observed alongshore-current structure by shifting the predicted velocity maxima shoreward and increasing the velocity in the bar trough compared with model predictions without rollers. For these data, wave forcing balances the bottom stress within the surfzone, with the other terms of secondary importance. The good agreement between observations and predictions implies that the one-dimensional assumption holds for the range of conditions examined, despite the presence of small alongshore bathymetric nonuniformities. With stronger bathymetric variations the model skill deteriorates, particularly in the bar trough, consistent with earlier modeling and laboratory studies.

Direct covariance air‐sea CO2 fluxes

Abstract: Direct covariance air-sea CO2 flux measurements over the open ocean are reported. These measurements were performed during June 1998 in the North Atlantic within a significant CO2 sink. These direct estimates are in general agreement with the traditional geochemical isotope constraints. The covariance, or eddy correlation, technique directly measures the air-sea CO2 flux over hour timescales by correlating the fluctuations of CO2 with the turbulent vertical velocity fluctuations in the atmospheric surface layer. These measurements quantify the transfer of CO2 between the atmosphere and ocean over a range of wind speeds and improve the understanding of the environmental factors controlling the flux. The relatively large flux of CO2 in the study region, together with improved analytical techniques, facilitated the measurements. The half-hour mean wind speeds varied from 0.9 to 16.3 m s−1 over the month-long experiment. The mean pCO2 during the study period was −85.8±16.0 μatm, and the mean covariance CO2 flux was estimated at 4.6 mol m−2 yr−1. The average observed wind speed was 7.7 m s−1. This is in close agreement with 3.9 mol m−2 yr−1, the approximate CO2 flux based on 14C parameterizations at this wind speed. At high winds, where the relationship between gas physical properties, surface processes, and air-sea gas exchange is still elusive, direct CO2 flux measurements are crucial. The measurements for winds in excess of 11 m s−1 show a general enhancement of gas transfer velocity over previous indirect measurements, and it is believed that this enhancement can be explained by the fact that the indirect methods cannot discriminate surface process variability such as atmospheric stability, upper ocean mixing, wave age, wave breaking, or surface films.

Theoretical model for scattering of radar signals in K u - and C-bands from a rough sea surface with breaking waves

Abstract: A small-slope approximation (SSA) is used for numerical calculations of a radar backscattering cross section of the ocean surface for both Ku- and C-bands for various wind speeds and incident angles. Both the lowest order of the SSA and the one that includes the next-order correction to it are considered. The calculations were made by assuming the surface-height spectrum of Elfouhaily et al for fully developed seas. Empirical scattering models CMOD2-I3 and SASS-II are used for comparison. Theoretical calculations are in good overall agreement with the experimental data represented by the empirical models, with the exception of HH-polarization in the upwind direction. It was assumed that steep breaking waves are responsible for this effect, and the probability density function of large slopes was calculated based on this assumption. The logarithm of this function in the upwind direction can be approximated by a linear combination of wind speed and the appropriate slope. The resulting backscattering cross section for upwind, downwind and cross-wind directions, for winds ranging between 5 and 15 m s −1 , and for both polarizations in both wave bands corresponds to experimental results within 1–2 dB accuracy.

On the deep water wave motion

Abstract: The problem of the propagation of surface waves over deep water is considered. We present a rigorous approach towards the only known (non-trivial) explicit solution to the governing equations for water waves - Gerstner's wave. Some properties of this solution, and how these relate to some basic conclusions about water waves that may be observed experimentally, are discussed.

Nearshore sandbar migration

Abstract: Field observations suggest that onshore sandbar migration, observed when breaking-wave-driven mean flows are weak, may be related to the skewed fluid accelerations associated with the orbital velocities of nonlinear surface waves. Large accelerations (both increases and decreases in velocity magnitudes), previously suggested to increase sediment suspension, occur under the steep wave faces that immediately precede the maximum onshore-directed orbital velocities. Weaker accelerations occur under the gently sloping rear wave faces that precede the maximum offshore-directed velocities. The timing of strong accelerations relative to onshore flow is hypothesized to produce net onshore sediment transport. The observed acceleration skewness, a measure of the difference in the magnitudes of accelerations under the front and rear wave faces, is maximum near the sandbar crest. The corresponding cross-shore gradients of an acceleration-related onshore sediment transport would cause erosion offshore and accretion onshore of the bar crest, consistent with the observed onshore migration of the bar crest. Furthermore, the observations and numerical simulations of nonlinear shallow water waves show that the region of strongly skewed accelerations moves shoreward with the bar, suggesting that feedback between waves and evolving morphology can result in continuing onshore bar migration.

The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions

Abstract: Strong turbulence at a water–air free surface can lead to splashing and a disconnected surface as in a breaking wave. Averaging to obtain boundary conditions for such flows first requires equations of motion for the two-phase region. These are derived using an integral method, then averaged conservation equations for mass and momentum are obtained along with an equation for the turbulent kinetic energy in which extra work terms appear. These extra terms include both the mean pressure and the mean rate of strain and have similarities to those for a compressible fluid. Boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer.A number of ‘new’ terms arise for which closure expressions must be found for practical use. Our knowledge of the properties of strong turbulence at a free surface is insufficient to make such closures. However, preliminary discussions are given for two simplified cases in order to stimulate further experimental and theoretical studies.Much of the turbulence in a spilling breaker originates from its foot where turbulent water meets undisturbed water. A discussion of averaging at the foot of a breaker gives parameters that may serve to measure the ‘strength’ of a breaker.

Wind-tunnel study of atmospheric stable boundary layers over a rough surface

Abstract: Wind-tunnel simulations of theatmospheric stable boundary layer (SBL) developedover a rough surface were conducted by using athermally stratified wind tunnel at the Research Institutefor Applied Mechanics (RIAM), Kyushu University. Thepresent experiment is a continuation of the workcarried out in a wind tunnel at Colorado StateUniversity (CSU), where the SBL flows were developed over asmooth surface. Stably stratified flows were createdby heating the wind-tunnel airflow to a temperature ofabout 40–50°and by cooling the test-section floor toa temperature of about 10°. To simulate therough surface, a chain roughness was placed over thetest-section floor. We have investigated the buoyancyeffect on the turbulent boundary layer developed overthis rough surface for a wide range of stability,particularly focusing on the turbulence structure andtransport process in the very stable boundary layer.The present experimental results broadly confirm theresults obtained in the CSU experiment with the smoothsurface, and emphasizes the following features: thevertical profiles of turbulence statistics exhibitdifferent behaviour in two distinct stability regimes with weak and strong stability,corresponding to the difference in the verticalprofiles of the local Richardson number. The tworegimes are separated by the critical Richardsonnumber. The magnitudes in turbulence intensities andturbulent fluxes for the weak stability regime aremuch greater than those of the CSU experiments becauseof the greater surface roughness. For the very stableboundary layer, the turbulent fluxes of momentum andheat tend to vanish and wave-like motions due to theKelvin–Helmholtz instability and the rolling up andbreaking of those waves can be observed. Furthermore,the appearance of internal gravity waves is suggestedfrom cross-spectrum analyses.

A laboratory study of the focusing of transient and directionally spread surface water waves

Abstract: This paper describes a new laboratory study in which a large number of waves, of varying frequency and propagating in different directions, were focused at one point in space and time to produce a large transient wave group. A focusing event of this type is believed to be representative of the evolution of an extreme ocean wave in deep water. Measurements of the water–surface elevation and the underlying water–particle kinematics are compared with both a linear solution and a second–order solution based on the sum of the interactions first identified by Longuet–Higgins & Stewart. Comparisons between these data confirm that the directionality of the wavefield has a profound effect upon the nonlinearity of a large wave event. If the sum of the wave amplitudes generated at the wave paddles is held constant, an increase in the directional spread of the wavefield leads to lower maximum crest elevations. Conversely, if the generated wave amplitudes are increased until the onset of wave breaking, at or near the focal position, an increase in the directional spread allows larger limiting waves to evolve. An explanation of these results lies in the redistribution of the wave energy within the frequency domain. In the most nonlinear wave cases, neither the water–surface elevation nor the water–particle kinematics can be explained in terms of the free waves generated at the wave paddles and their associated bound waves. Indeed, the laboratory data suggest that there is a rapid widening of the free–wave regime in the vicinity of a large wave event. For a constant input–amplitude sum, these important spectral changes are shown to be strongly dependent upon the directionality of the wavefield. These findings explain the very large water–surface elevations recorded in previous unidirectional wave studies and the apparent contrast between unidirectional results and recent field data in which large directionally spread waves were shown to be much less nonlinear. The present study clearly demonstrates the need to incorporate the directionality of a wavefield if extreme ocean waves are to be accurately modelled and their physical characteristics explained.

SPH Modelling of Water Waves

Abstract: Advances in computational power have permitted the use of Lagrangian particle methods to model fluids, particularly separated flows and free surface flows with splashing. Here we present a smoothed particle hydrodynamics (SPH) approach to a numerical wave tank, capable of studying several types of waves impinging on structures and walls. INTRODUCTION Computer modeling of the details of wave breaking and the turbulence in the surf zone can only be done by intricate computational models, including such techniques as Direct Numerical Simulation (DNS) of the Navier-Stokes equations, Large Eddy Simulation (LES), and Volume of Fluid (VOF). All of these methods are Eulerian and have complicated algorithms to determine the instantaneous location of the free surface. The situation becomes more difficult when splashing and air entrainment becomes important. Recently, increases in computational power have led to the use of Lagrangian methods and, in particular, particle methods, which do not require any special techniques at the free surface or for rotational flows. For these methods, wave nonlinearities and wave breaking are naturally captured. There are a variety of particle methods that have been developed --al l involving applying Newton's Second Law to particles that represent large parcels of water molecules. One such method is Smoothed Particle Hydrodynamics (SPH), developed primarily by Lucy (1977) and Monaghan and colleagues over the last 30 years for astrophysics. More recently Monaghan (1994) has begun applying the technique to 2 D free surface flows, including the dam break problem, a bore, and waves shoaling on a beach. Monaghan and Kos (1999) have examined the run-up of a solitary wave (in 1 Davis Professor of Civil and F.nvironmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, USA. rad a~udel.edu 2 Associate Professor, Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA. knio@flame.jhu.edu

Turbulence Measurements in the Surf Zone

Abstract: Velocity measurements within 1 m of the bottom in approximately 4.5-m water depth on a sand beach provide estimates of turbulent Reynolds shear stress, using a dual-sensor technique that removes contamination by surface waves, and inertial-range estimates of dissipation. When combined with wave measurements along a cross-shore transect and nearby wind measurements, the dataset provides direct estimates of the terms in simplified equations for alongshore momentum and turbulence energetics and permits examination of semiempirical relationships between bottom stress and near-bottom velocity. The records are dominated by three events when the measurement site was in the outer part of the surf zone. Near-bottom turbulent shear stress is well correlated with (squared correlation coefficient r2 = 0.63), but smaller than (regression coefficient b = 0.51 ± 0.03 at 95% confidence), wind stress minus cross-shore gradient of wave-induced radiation stress, indicating that estimates of one or more of these ter...

An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves

Abstract: This paper describes an experimental study of two-dimensional surface water waves propagating on a depth-varying current with a non-uniform vorticity distribution. The investigation is divided into two parts. The first concerns the ‘equilibrium’ conditions in which the oscillatory wave motion and the current co-exist. Measurements of the water-surface elevation, the water-particle kinematics, and the near-bed pressure fluctuations are compared to a number of wave and wave–current solutions including a nonlinear model capable of incorporating the vertical structure of the current profile. These comparisons confirm that the near-surface vorticity leads to an important modification of the dispersion equation, and thus affects the nature of the wave-induced orbital motion over the entire water depth. However, the inclusion of vorticity-dependent terms within the dispersion equation is not sufficient to define the combined wave–current flow. The present results suggest that vorticity may lead to a significant change in the water-surface profile. If a current is positively sheared, dU/dz > 0, with negative vorticity at the water surface, as would be the case in a wind-driven current, a wave propagating in the same direction as the current will experience increased crest–trough asymmetry due to the vorticity distribution. With higher and sharper wave crests there is a corresponding increase in both the maximum water-particle accelerations and the maximum horizontal water-particle velocities. These results are consistent with previous theoretical calculations involving uniform vorticity distributions (Simmen & Saffman 1985 and Teles da Silva & Peregrine 1988).The second part of the study addresses the ‘gradually varying’ problem in which there are changes in the current, the wavelength and the wave height due to the initial interaction between the wave and the current. These data show that there is a large and non-uniform change in the current profile that is dependent upon both the steepness of the waves and the vorticity distribution. Furthermore, comparisons between the measured wave height change and a number of solutions based on the conservation of wave action, confirm that the vorticity distribution plays a dominant role. In the absence of a conservation equation for wave action appropriate for nonlinear waves on a depth-varying current, an alternative approach based on the conservation of total energy flux, first proposed by Longuet-Higgins & Stewart (1960), is shown to be in good agreement with the measured data.

Dependence of whitecap coverage on wind and wind-wave properties

Abstract: Using Phillips equilibrium range theory and observational data, we show first that the total rates of wave energy dissipation estimated by the Hasselmann and Phillips dissipation models are substantially consistent with each other, though their original forms are different. Both are proportional to the cube of air friction velocity, u*3, with a weak dependence on wave age. As a direct manifestation of the wave energy dissipation processes, we reanalyze previous observational data of whitecap coverage and find that it has greater correlation with the wind speed or friction velocity than the wave period or wave age. However, the data scatter decreases remarkably when the breaking-wave parameter RB= u*2/νωp is used, where ν is the kinematic viscosity of air, and ωp, the wind-wave spectral peak frequency. Physical interpretation of RB with some related issues, and a discussion of the probability models of whitecap coverage in terms of a threshold mechanism, are also presented. We conclude that RB is a good parameter to effectively express the overall wave breaking behavior for the case of wind-waves in local equilibrium with the wind. Since RB can be expressed as the product of u*3 and the wave age, this result demonstrates a stronger dependence of whitecap coverage on wave age than expected by the previous description by power-laws of u* and by the two theoretical models. Our conclusion suggests that current dissipation models should also be modified to represent full properties of wind-wave breaking.

Breaking probabilities for dominant surface waves on water of finite constant depth

Abstract: This paper extends our previous study of the breaking probability of dominant deep water gravity surface waves into the finite water depth environment. It reports a unified behavior of the mean breaking statistics once the effects of finite water depth are taken into account. The shallow water wave data that form the basis of this study were acquired at a field experiment site at Lake George, New South Wales, Australia. The breaking events were detected through visual observation of videotaped records of the wave field in combination with acoustic signatures of the breaking waves from a collocated hydrophone. Following Banner et al. [2000], we argue that when constant finite depth bottom influence is operative, nonlinear hydrodynamical effects associated with energy and momentum fluxes within deforming wave groups remain the primary determinant of breaking onset. This underpins our proposed finite depth water parameterization for the environmental dependence of dominant wave breaking probability, given by the average number of breakers passing a fixed point per dominant wave period. The additional influence of bottom interaction with the wind drift current shear and wind forcing are also included in our finite constant depth formulation. This is a natural extension of our recently proposed deep water dependence and reduces to it as the significant wave height becomes much smaller than the water depth. In common with the deep water case we propose that there exists a threshold of the significant peak steepness below which negligible dominant wave breaking occurs. The available data show encouraging agreement with our proposed dependence, with a correlation coefficient approaching 0.9.

Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 1. Dynamics of steep three-dimensional waves

Abstract: We develop an efficient high-order boundary-element method with the mixed-Eulerian-Lagrangian approach for the simulation of fully nonlinear three-dimensional wave-wave and wave-body interactions. For illustration, we apply this method to the study of two three-dimensional steep wave problems. (The application to wave-body interactions is addressed in an accompanying paper: Liu, Xue & Yue 2001.) In the first problem, we investigate the dynamics of three-dimensional overturning breaking waves. We obtain detailed kinematics and full quantification of three-dimensional effects upon wave plunging. Systematic simulations show that, compared to two-dimensional waves, three-dimensional waves generally break at higher surface elevations and greater maximum longitudinal accelerations, but with smaller tip velocities and less arched front faces. For the second problem, we study the generation mechanism of steep crescent waves. We show that the development of such waves is a result of three-dimensional (class II) Stokes wave instability. Starting with two-dimensional Stokes waves with small three-dimensional perturbations, we obtain direct simulations of the evolution of both L 2 and L 3 crescent waves. Our results compare quantitatively well with experimental measurements for all the distinct features and geometric properties of such waves.

Field observations of wave-driven setdown and setup

Abstract: Wave-driven setdown and setup observed for 3 months on a cross-shore transect between the shoreline and 5 m water depth on a barred beach are compared with a theoretical balance between cross-shore gradients of the mean water level and the wave radiation stress. The observed setdown, the depression of the mean water level seaward of the surf zone, is predicted well when radiation stress gradients are estimated from the observations using linear theory at each location along the transect. The observed setdown also agrees with analytical predictions based on offshore wave observations and the assumption of linear, dissipationless, normally incident waves shoaling on alongshore homogeneous bathymetry. The observed setup, the superelevation of the mean water level owing to wave breaking, is predicted accurately in the outer and middle surf zone, but is increasingly underpredicted as the shoreline is approached. Similar to previous field studies, setup at a fixed cross-shore location increases with increasing offshore wave height and is sensitive to tidal fluctuations in the local water depth and to bathymetric changes. Numerical simulations and the observations suggest that setup near the shoreline depends on the bathymetry of the entire surf zone and increases with decreasing surf zone beach slope, defined as the ratio of the surf zone-averaged water depth to the surf zone width. A new empirical formula for shoreline setup on nonplanar beaches incorporates this dependence.

Bubble entrainment by breaking waves and their influence on optical scattering in the upper ocean

Abstract: Breaking waves at the ocean's surface inject bubbles and turbulence into the water column. During periods of rough weather the scales of wave breaking will increase with increasing sea states and result in mixing of the surface waters and the turbulent transport of bubbles to depth. Depending on their concentrations and size distribution, the entrained bubbles can significantly change the optical properties of water, introducing potentially significant errors in retrieval of remotely sensed hyperspectral data products. In this paper, the effects of bubbles on optical scattering in the upper ocean are investigated through optical scattering calculations based on field measurements of bubble populations. The field measurements were obtained offshore Point Conception, California, in June 1997, using an acoustical technique which measured the bubble size distribution at 2 Hz from a surface buoy designed to follow the longer waves. The effects of the bubbles on the bulk optical scattering and backscattering coefficients, b and bb, respectively, are determined by using the acoustically measured size distributions, and size-dependent scattering efficiencies based on Mie scattering calculations. Time series of the bubble distributions measured in rough conditions (wind speed, U10 = 15 m/s, significant wave height, H1/3 = 3.2 m) suggest that the bubble contribution to light scattering is highly variable near the ocean surface, with values spanning roughly 5 decades over time periods of O(10) minutes. Bubble size distributions measured at a 0.7-m depth indicate that the optical effects of the bubbles on bb, and hence the remote sensing reflectance, will be significant at bubble void fractions above 10−6 and that the bubble contribution to total bb will exceed values of 10−2 m−1 inside bubble clouds.

Microscale wave breaking and air‐water gas transfer

Abstract: Laboratory results showing that the air-water gas transfer velocity k is correlated with mean square wave slope have been cited as evidence that a wave-related mechanism regulates k at low to moderate wind speeds [Jahne et al., 1987; Bock et al., 1999]. Csanady [1990] has modeled the effect of microscale wave breaking on air-water gas transfer with the result that k is proportional to the fractional surface area covered by surface renewal generated during the breaking process. In this report we investigate the role of microscale wave breaking in gas transfer by determining the correlation between k and AB, the fractional area coverage of microscale breaking waves. Simultaneous, colocated infrared (IR) and wave slope imagery is used to verify that AB detected using IR techniques corresponds to the fraction of surface area covered by surface renewal in the wakes of microscale breaking waves. Using measurements of k and AB made at the University of Washington wind-wave tank at wind speeds from 4.6 to 10.7 m s−1, we show that k is linearly correlated with AB, regardless of the presence of surfactants. This result is consistent with Csanady's [1990] model and implies that microscale wave breaking is likely a fundamental physical mechanism contributing to gas transfer.

On the parameterization of mixing in three‐dimensional Baltic Sea models

Abstract: As mixing plays a dominant role for the physics of an estuary like the Baltic Sea (seasonal heat storage, mixing in channels, deepwater mixing), different mixing parameterizations for use in three-dimensional (3-D) Baltic Sea models are discussed. Within the Swedish regional climate modeling program, SWECLIM, a 3-D coupled ice-ocean model for the Baltic Sea has been coupled with an improved version of the two-equation k-e turbulence model using a corrected dissipation term, flux boundary conditions to include the effect of a turbulence enhanced layer due to breaking surface gravity waves, and a parameterization for breaking internal waves. Results of multiyear simulations are compared with observations. The seasonal thermocline (the main focus of this paper) is simulated satisfactory. During the stagnation period between 1983 and 1993, simulated salinity in the lower layer of the Baltic Sea decreases as observed. Unsolved problems of the k-e model are discussed. To replace the controversial equation for dissipation, the performance of a hierarchy of k models has been tested and compared with the k-e model. In addition, it is shown that the results of the 1-D turbulence submodel depend very much on the dimensionality of the hydrodynamic model. Using the same turbulence parameterization, vertical velocity shear and density gradients are simulated differently in 1-D column models compared to 3-D ocean circulation models. Finally, the impact of two mixing parameterizations on Baltic Sea climate is discussed.

The Impact Of Air-Flow Separation On The Drag Of The Sea Surface

Abstract: An approach that allows assessment ofthe impact of air-flow separation (AFS) fromwave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumedthat the dynamics of the AFS from wave breaking crests is similar to thatfrom the backward facing step. The form drag supported by an individualbreaker is described by the action of the pressure drop distributed alongthe forward face of the breaking front. The total stress due to the AFS isobtained as a sum of contributions from breaking fronts of different scales.Outside the breaking fronts the drag of the sea surface is supported by theviscous surface stress and the wave-induced stress. To calculate the stressdue to the AFS and the wave-induced stress a physical model of the wind-wavespectrum is used. Together with the model of the air flow described in termsof surface stresses it forms a self-consistent dynamical system for the seasurface-atmosphere where the air flow and wind waves are strongly coupled.Model calculations of the drag coefficient agree with measurements. It is shownthat the dimensionless Charnock parameter (roughness length normalized onthe square of the friction velocity and the acceleration of gravity)increases with the increase of the wind speed in agreement with fieldmeasurements. The stress due to the AFS normalized on the square of thefriction velocity is proportional to the cube of wind speed. At low windsthe viscous surface stress dominates the drag. The role of the form drag,which is the sum of the stress due to the AFS and the wave-induced stress, isnegligible. At moderate and high winds the form drag dominates. At windspeeds higher than 10 m s-1 the stress supported by the AFS becomescomparable to the wave-induced stress and supports up to 50% of the totalstress.

High Range Resolution Radar Measurements of the Speed Distribution of Breaking Events in Wind-Generated Ocean Waves: Surface Impulse and Wave Energy Dissipation Rates

Abstract: A set of X-band radar measurements, backscattered from the sea surface at near grazing incidence with very high spatial and temporal resolution (30 cm in range and 2000-Hz pulse repetition frequency) in moderate wind conditions, are dominated by moving discrete events (sea spikes). They have radar cross sections of up to about 1 m2 and are found to possess the characteristics of breaking wave fronts. Contributions from Bragg backscattering appear to be at least two orders of magnitude smaller. The number of events detected per unit area per unit time was of the same order as found by Ding and Farmer at almost the same wind speed, but the distribution of event speeds was narrower—the fastest breaking wave events observed had line-of-sight speeds of about 0.6 of the dominant wave speed. The measured histograms of number of events versus event speed c suggested that the smaller events with c < 3 m s−1 were only incompletely counted so that the characteristics of only the faster events (3–6 m s−1) we...

Simultaneous particle image velocimetry and infrared imagery of microscale breaking waves

Abstract: We report the results from a laboratory investigation in which microscale breaking waves were detected using an infrared (IR) imager and two-dimensional (2-D) velocity fields were simultaneously measured using particle image velocimetry (PIV). In addition, the local heat transfer velocity was measured using the controlled flux technique. To the best of our knowledge these are the first measurements of the instantaneous 2-D velocity fields generated beneath microscale breaking waves. Careful measurements of the water surface profile enabled us to make accurate estimates of the near-surface velocities using PIV. Previous experiments have shown that behind the leading edge of a microscale breaker the cool skin layer is disrupted creating a thermal signature in the IR image [Jessup et al., J. Geophys. Res. 102, 23145 (1997)]. The simultaneously sampled IR images and PIV data enabled us to show that these disruptions or wakes are typically produced by a series of vortices that form behind the leading edge of the breaker. When the vortices are first formed they are very strong and coherent but as time passes, and they move from the crest region to the back face of the wave, they become weaker and less coherent. The near-surface vorticity was correlated with both the fractional area coverage of microscale breaking waves and the local heat transfer velocity. The strong correlations provide convincing evidence that the wakes produced by microscale breaking waves are regions of high near-surface vorticity that are in turn responsible for enhancing air–water heat transfer rates.

Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery

Abstract: Remote sensing methods have been developed to estimate bathymetry through the use of a theoretical relationship between wave speed and water depth known as the linear, finite depth, dispersion equation for surface gravity waves. The authors describe a validation effort encompassing several hundred observations of wavenumber magnitude for sea-swell frequencies obtained over a wide variety of conditions to investigate possible error sources resulting from the practical application of this relationship. These wavenumber estimates were computed from pressure gauge signals using signal processing algorithms that can be equivalently applied to measurements of wave phase as imaged through remote sensors. The major goal was to determine the accuracy of the dispersion relation while attempting to minimize errors associated with sensor positioning, tidal variations, and Doppler shifts due to mean currents. For water depths outside the surf zone, the linear dispersion relation is highly accurate, with average depth estimation errors on the order of 3-9% of the observed depth. In shallower regions, nominally less than 4 m for this field site, where wave breaking is evident and nonlinear shoaling effects are more pronounced, normalized depth errors of over 50% were commonly observed with most predictions being deeper than observations. Strong correlation between these bias errors and measured wave heights emphasizes the importance of accounting for wave amplitude in the calculation of shallow water phase speeds for depth estimation. A simple depth correction is provided to allow for bathymetry estimation within the surf zone.

Wavelet analysis and the governing dynamics of a large‐amplitude mesoscale gravity‐wave event along the East Coast of the United States

Abstract: Detailed diagnostic analyses are performed upon a mesoscale numerical simulation of a well-observed gravity-wave event that occurred on 4 January 1994 along the East Coast of the United States. The value of using wavelet analysis to investigate the evolving gravity-wave structure and of using potential vorticity (PV) inversion to study the nature of the flow imbalance in the wave generation region is demonstrated. The cross-stream Lagrangian Rossby number, the residual in the nonlinear balance equation, and the unbalanced geopotential-height field obtained from PV inversion are each evaluated for their usefulness in diagnosing the flow imbalance. All of these fields showed clear evidence of strong imbalance associated with a middle-to-upper tropospheric jet streak, and tropopause fold upstream of the large-amplitude gravity wave several hours before the wave became apparent at the surface. Analysis indicates that a train of gravity waves was continuously generated by geostrophic adjustment in the exit region of the unbalanced upper-level jet streak as it approached the inflection axis in the height field immediately downstream of the maximum imbalance associated with the tropopause fold. A split front in the middle troposphere, characterized by the advance of the dry conveyor belt above the warm front, was overtaken by one of these propagating waves. During this merger process, a resonant interaction resulted, which promoted the rapid amplification and scale contraction of both the incipient wave (nonlinear wave development) and the split front (frontogenesis). The gravity wave and front aloft became inseparable following this merger. The situation became even more complex within a few hours as the vertical motion enhanced by this front-wave interaction acted upon a saturated, potentially unstable layer to produce elevated moist convection. An analysis of the temporal changes in the vertical profile of wave energy flux suggests that moist convective downdraughts efficiently transported the wave energy from the midlevels downward beneath the warm-front surface, where the wave became ducted. However, pure ducting was not sufficient for maintaining and amplifying the waves; rather, wave-CISK (Conditional Instability of the Second Kind) was crucial. This complex sequence of nonlinear interactions produced a long-lived, large-amplitude gravity wave that created hazardous winter weather and disrupted society over a broad and highly populated area. Although gravity waves with similar appearance to this large-amplitude wave of depression occasionally have been seen in other strong cyclogenesis cases involving a jet streak ahead of the upper-level trough axis, it is unknown whether other such events share this same sequence of interactions.

Wave-driven currents and vortex dynamics on barred beaches

Abstract: We present a theoretical and numerical investigation of longshore currents driven by breaking waves on beaches, especially barred beaches. The novel feature considered here is that the wave envelope is allowed to vary in the alongshore direction, which leads to the generation of strong dipolar vortex structures where the waves are breaking. The nonlinear evolution of these vortex structures is studied in detail using a simple analytical theory to model the effect of a sloping beach. One of our findings is that the vortex evolution provides a robust mechanism through which the preferred location of the longshore current can move shorewards from the location of wave breaking. Such current dislocation is an often-observed (but ill-understood) phenomenon on real barred beaches.To underpin our results, we present a comprehensive theoretical description of the relevant wave–mean interaction theory in the context of a shallow-water model for the beach. Therein we link the radiation-stress theory of Longuet-Higgins & Stewart to recently established results concerning the mean vorticity generation due to breaking waves. This leads to detailed results for the entire life-cycle of the mean-flow vortex evolution, from its initial generation by wave breaking until its eventual dissipative decay due to bottom friction.In order to test and illustrate our theory we also present idealized nonlinear numerical simulations of both waves and vortices using the full shallow-water equations with bottom topography. In these simulations wave breaking occurs through shock formation of the shallow-water waves. We note that because the shallow-water equations also describe the two-dimensional flow of a homentropic perfect gas, our theoretical and numerical results can also be applied to nonlinear acoustics and sound–vortex interactions.

Sand suspension, storage, advection, and settling in surf and swash zones

Abstract: A time-dependent cross-shore sediment transport model in the surf and swash zones on beaches is developed to predict both beach accretion and erosion under the assumptions of alongshore uniformity and normally incident waves. The model is based on the depth-integrated sediment continuity equation, which includes sediment suspension by turbulence generated by wave breaking and bottom friction, sediment storage in the entire water column, sediment advection by waves and wave-induced return current, and sediment settling on the movable bottom. The hydrodynamic input required for this sediment transport model is predicted using the finite-amplitude shallow-water equations including bottom friction. The developed model is compared with three large-scale laboratory tests with accretional, neutral (little), and erosional beach profile changes under regular waves. The model predicts sediment suspension under the steep front of breaking waves and due to bottom friction in the swash zone. The computed depth-averaged sediment concentration does not respond to local sediment suspension instantaneously because of the sediment storage and advection. The mean sediment concentration becomes large in comparison to the oscillatory concentration with the decrease of the normalized sediment fall velocity. The net cross-shore sediment transport rate is shown to be the small difference between the onshore transport rate due to the positively correlated oscillatory components of the suspended sediment volume per unit area and the horizontal sediment velocity and the offshore transport rate due to the product of the mean suspended sediment volume and the mean horizontal sediment velocity. Relatedly, the net accretion or erosion rate of the movable bottom is determined by the small difference between the mean sediment settling rate and the mean suspension rate caused by wave breaking and bottom friction. The present computation is limited to the initial beach profile change, but the numerical model is capable of predicting the accretional, erosional, and neutral profile changes.