Showing papers on "Breaking wave published in 2012"

A wave generation toolbox for the open‐source CFD library: OpenFoam®

Abstract: SUMMARY The open-source CFD library OpenFoam® contains a method for solving free surface Newtonian flows using the Reynolds averaged Navier–Stokes equations coupled with a volume of fluid method. In this paper, it is demonstrated how this has been extended with a generic wave generation and absorption method termed ‘wave relaxation zones’, on which a detailed account is given. The ability to use OpenFoam for the modelling of waves is demonstrated using two benchmark test cases, which show the ability to model wave propagation and wave breaking. Furthermore, the reflection coefficient from outlet relaxation zones is considered for a range of parameters. The toolbox is implemented in C++, and the flexibility in deriving new relaxation methods and implementing new wave theories along with other shapes of the relaxation zone is outlined. Subsequent to the publication of this paper, the toolbox has been made freely available through the OpenFoam-Extend Community. Copyright © 2011 John Wiley & Sons, Ltd.

Gravity Wave Characteristics in the Southern Hemisphere Revealed by a High-Resolution Middle-Atmosphere General Circulation Model

Abstract: Gravity wave characteristics in the middle- to high-latitude Southern Hemisphere are analyzed using simulation data over 3 yr from a high-resolution middle-atmosphere general circulation model without using any gravity wave parameterizations. Gravity waves have large amplitudes in winter and are mainly distributed in the region surrounding the polar vortex in the middle and upper stratosphere, while the gravity wave energy is generally weak in summer. The wave energy distribution in winter is not zonally uniform, but it is large leeward of the southern Andes and Antarctic Peninsula. Linear theory in the three-dimensional framework indicates that orographic gravity waves are advected leeward significantly by the mean wind component perpendicular to the wavenumber vector. Results of ray-tracing and cross-correlation analyses are consistent with this theoretical expectation. The leeward energy propagation extends to several thousand kilometers, which explains part of the gravity wave distribution aro...

Bidimensional Diagnostics, Variability, and Trends of Northern Hemisphere Blocking

Abstract: In this paper, Northern Hemisphere winter blocking is analyzed through the introduction of a set of new bidimensional diagnostics based on geopotential height that provide information about the occurrence, the duration, the intensity, and the wave breaking associated with the blocking. This analysis is performed with different reanalysis datasets in order to evaluate the sensitivity of the index and the diagnostics adopted. In this way, the authors are able to define a new category of blocking placed at low latitudes that is similar to midlatitude blocking in terms of the introduced diagnostics but is unable to divert or block the flow. Furthermore, over the Euro-Atlantic sector it is shown that it is possible to phenomenologically distinguish between high-latitude blocking occurring over Greenland, north of the jet stream and dominated by cyclonic wave breaking, and the traditional midlatitude blocking localized over Europe and driven by anticyclonic wave breaking. These latter events are uniform...

Observation-Consistent Input and Whitecapping Dissipation in a Model for Wind-Generated Surface Waves: Description and Simple Calculations

Abstract: A new wind-input and wind-breaking dissipation for phase-averaged spectral models of wind-generated surface waves is presented. Both are based on recent field observations in Lake George, New South Wales, Australia, at moderate-to-strong wind-wave conditions. The respective parameterizations are built on quantitative measurements and incorporate new observed physical features, which until very recently were missing in source terms employed in operational models. Two novel features of the wind-input source functionarethosethataccountfortheeffectsoffullairflowseparation(andthereforerelativereductionofthe input at strongwindforcing) andfor nonlinear behaviorofthis term. Thebreakingtermalsoincorporatestwo new features evident from observational studies; the dissipation consists of two parts—a strictly local dissipation term and a cumulative term—and there is a threshold for wave breaking, below which no breaking occurs. Four variants of the dissipation term are selected for evaluation, with minimal calibration to each. These fourmodels areevaluatedusing simplecalculationsherein.Resultsaregenerallyfavorable.Evaluation for more complex situations will be addressed in a forthcoming paper.

Wave Breaking Dissipation Observed with “SWIFT” Drifters

Abstract: Energy dissipation rates during ocean wave breaking are estimated from high-resolution profiles of turbulent velocities collected within 1 m of the surface. The velocity profiles are obtained from a pulse-coherent acoustic Doppler sonar on a wave-following platform, termed a Surface Wave Instrument Float with Tracking (SWIFT), and the dissipation rates are estimated from the structure function of the velocity profiles. The purpose of the SWIFT is to maintain a constant range to the time-varying surface and thereby observe the turbulence in breaking crests (i.e., above the mean still water level). The Lagrangian quality is also useful to prefilter wave orbital motions and mean currents from the velocity measurements, which are limited in magnitude by phase wrapping in the coherent Doppler processing. Field testing and examples from both offshore whitecaps and nearshore surf breaking are presented. Dissipation rates are elevated (up to 10−3 m2 s−3) during strong breaking conditions, which are confir...

Wave‐breaking characteristics of midlatitude blocking

Abstract: In this article, Northern Hemisphere winter midlatitude blocking is analysed through its wave-breaking characteristics. Rossby wave breaking is identified as a key process in blocking occurrence, as it provides the mechanism for the meridional reversal pattern typical of blocking. Two indices are designed to detect the major properties of wave breaking, i.e. the orientation (cyclonic/anticyclonic–direction of breaking or DB index) and the relative contribution of air masses (warm/cold–relative intensity or RI index). The use of the DB index differentiates between the anticyclonic cases over Europe and Asia and the cyclonic events over the oceanic basins. One of the three regions displaying cyclonic type was found over the Atlantic Ocean, the other two being over the Pacific Ocean. The first of these is located over the western side of the Pacific and is dominated by warm air extrusions, whereas the second is placed northward of the exit region of the jet stream, where the meridional θ gradient is much weaker. Two European blocking types have been detected using the RI index, which separates out the cases dominated by warm and cold air masses. The latter cases in particular exhibited a well-structured dipole, with associated strong anomalies in both temperature and precipitation. Copyright © 2011 Royal Meteorological Society

Numerical Wave Modeling in Conditions with Strong Currents: Dissipation, Refraction, and Relative Wind

Abstract: Currents effects on waves have led to many developments in numerical wave modeling over the past two decades, from numerical choices to parameterizations. The performance of numerical models in conditions with strong currents is reviewed here, and observed strong effects of opposed currents and modulations of wave heights by tidal currents in several typical situations are interpreted. For current variations on small scales, the rapid steepening of the waves enhances wave breaking. Using different parameterizations with a dissipation rate proportional to some measure of the wave steepness to the fourth power, the results are very different, none being fully satisfactory, which points to the need for more measurements and further refinements of parameterizations. For larger-scale current variations, the observed modifications of the sea state are mostly explained by refraction of waves over currents and relative wind effects, that is, the wind speed relevant for wave generation is the speed in the ...

The Wavy Ekman Layer: Langmuir Circulations, Breaking Waves, and Reynolds Stress

Abstract: Large-eddy simulations are made for the canonical Ekman layer problem of a steady wind above a uniformly rotating, constant-density ocean. The focus is on the influence of surface gravity waves: namely, the wave-averaged Stokes-Coriolis and Stokes-vortex forces and parameterized wave breaking for momentum and energy injection. The wave effects are substantial: the boundary layer is deeper, the turbulence is stronger, and eddy momentum flux is dominated by breakers and Langmuir circulations with a vertical structure inconsistent with both the conventional logarithmic layer and eddy viscosity relations. The surface particle mean drift is dominated by Stokes velocity with Langmuir circulations playing a minor role. Implications are assessed for parameterization of the mean velocity profile in the Ekman layer with wave effects by exploring several parameterization ideas. The authors find that the K-profile parameterization (KPP) eddy viscosity is skillful for the interior of the Ekman layer with wave-...

Coastal vulnerability assessment based on video wave run-up observations at a mesotidal, steep-sloped beach

Abstract: Coastal imagery obtained from a coastal video monitoring station installed at Faro Beach, S. Portugal, was combined with topographic data from 40 surveys to generate a total of 456 timestack images. The timestack images were processed in an open-access, freely available graphical user interface (GUI) software, developed to extract and process time series of the cross-shore position of the swash extrema. The generated dataset of 2% wave run-up exceedence values R 2 was used to form empirical formulas, using as input typical hydrodynamic and coastal morphological parameters, generating a best-fit case RMS error of 0.39 m. The R 2 prediction capacity was improved when the shore-normal wind speed component and/or the tidal elevation η tide were included in the parameterizations, further reducing the RMS errors to 0.364 m. Introducing the tidal level appeared to allow a more accurate representation of the increased wave energy dissipation during low tides, while the negative trend between R 2 and the shore-normal wind speed component is probably related to the wind effect on wave breaking. The ratio of the infragravity-to-incident frequency energy contributions to the total swash spectra was in general lower than the ones reported in the literature E infra/E inci > 0.8, since low-frequency contributions at the steep, reflective Faro Beach become more significant mainly during storm conditions. An additional parameterization for the total run-up elevation was derived considering only 222 measurements for which η total,2 exceeded 2 m above MSL and the best-fit case resulted in RMS error of 0.41 m. The equation was applied to predict overwash along Faro Beach for four extreme storm scenarios and the predicted overwash beach sections, corresponded to a percentage of the total length ranging from 36% to 75%.

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Abstract: Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well-defined test cases, in two dimensions, of waves generated by a heaving semi-immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open-source code SPHysics (http://www.sphysics.org)§Update made here after initial online publication. is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11:529–551). For wave loading on a half-submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105:421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL-based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.

Nonlinear tides in close binary systems

Abstract: We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.

Dynamical Control of the Middle Atmosphere

Abstract: This review recapitulates the concept of the wave-driven residual circulation in the stratosphere and mesosphere. The residual circulation is defined as the conventional mean meridional circulation corrected by the quasi-linear Stokes drift due to atmospheric waves. Only when the zonal-mean primitive equations are transformed using the residual circulation, they reflect the causality arising from the Eliassen-Palm (EP) theorem. The EP theorem states that the proper wave-mean flow interaction, defined as the EP flux divergence, vanishes for waves that are linear, conservative, and steady. In the real atmosphere, this theorem is violated mainly due to wave breaking and turbulence. The resulting EP flux divergence then drives a residual circulation which causes the observed substantial deviations from some hypothetical radiatively determined state. With regard to this dynamical control we discuss the different contributions of Rossby waves and gravity waves. Recapitulation of Lindzen’s theory of gravity-wave saturation allows us to interpret various phenomena in the upper mesosphere such as interhemispheric coupling or modulations of the gravity-wave driven branch of the residual circulation by solar proton effects and thermal tides. In addition we discuss the relative importance of changes in radiative transfer and tropospheric gravity-wave sources on the long-term temperature trends in the summer mesosphere.

Spectral Energy Dissipation due to Surface Wave Breaking

Abstract: A semiempirical determination of the spectral dependence of the energy dissipation due to surface wave breaking is presented and then used to propose a model for the spectral dependence of the breaking strength parameter b, defined in the O. M. Phillips’s statistical formulation of wave breaking dynamics. The determination of the spectral dissipation is based on closing the radiative transport equation for fetch-limited waves, measured in the Gulf of Tehuantepec Experiment, by using the measured evolution of the directional spectra with fetch, computations of the four-wave resonant interactions, and three models of the wind input source function. The spectral dependence of the breaking strength is determined from the Kleiss and Melville measurementsofthebreakingstatisticsandthesemiempiricalspectralenergydissipation,resultinginb 5b(k,cp/u * ), where k is the wavenumber and the parametric dependence is on the wave age, cp/u * . Guided by these semiempirical results, a model for b(k, cp/u * ) is proposed that uses laboratory data from a variety of sources, which can be represented by b 5 a(S 2 S0) n ,w hereS is a measure of the wave slope at breaking, a is a constant, S0 is a threshold slope for breaking, and 2.5 ,n ,3isapowerlawconsistentwithinertialwavedissipationscalingand laboratory measurements. The relationship between b(S) in the laboratory and b(k) in the field is based on the relationship between the saturation and mean square slope of the wave field. The results are discussed in the context of wind wave modeling and improved measurements of breaking in the field.

Comparison of bounce‐averaged quasi‐linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations

Abstract: [1] Quasi-linear bounce-averaged diffusion coefficients for interactions between electrons and parallel propagating whistler waves in a dipole field are compared with test particle simulations. We solve equations of motion for a large number of electrons interacting with waves with a Gaussian distribution of wave power. For broadband and small amplitude waves, which are assumed by the quasi-linear analysis, our test particle simulation results agree well with quasi-linear theory predictions. We then demonstrate the effect of the wave amplitude on diffusion coefficients. We show that as the amplitude increases, the bounce-averaged quasi-linear diffusion coefficients become invalid. Critical wave amplitudes for the breakdown of the bounce-averaged diffusion coefficients for a range of energies and pitch angles are calculated for the set of wave parameters we used. Finally, we investigate the effect of wave bandwidth on bounce-averaged diffusion coefficients. Consistent with a previous theoretical prediction, bounce-averaged quasi-linear diffusion coefficients are still valid for narrowband waves, as long as the wave amplitude is small. When the amplitude of the narrowband wavefield increases, nonlinear effects such as phase-bunching and trapping become dominant and correspondingly quasi-linear theory becomes invalid. Our results demonstrate the validity of applying quasi-linear theory to interactions between electrons and small amplitude plasma waves in the radiation belt.

Detection of Rossby wave breaking and its response to shifts of the midlatitude jet with climate change

Abstract: [1] A Rossby wave breaking identification method is presented which searches for overturning of absolute vorticity contours on pressure surfaces. The results are compared to those from an analysis of isentropic potential vorticity, and it is demonstrated that both yield similar wave breaking distributions. As absolute vorticity is easily obtained from most model output, we present wave breaking frequency distributions from the ERA-Interim data set, thirteen general circulation models (GCMs) and a barotropic model. We demonstrate that a poleward shift of the Southern Hemisphere midlatitude jet is accompanied by a decrease in poleward wave breaking in both the barotropic model and all GCMs across multiple climate forcing scenarios. In addition, it is shown that while anticyclonic wave breaking shifts poleward with the jet, cyclonic wave breaking shifts less than half as much and reaches a poleward limit near 60 degrees S. Comparison of the observed distribution of Southern Hemisphere wave breaking with those from the GCMs suggests that wave breaking on the poleward flank of the jet has already reached its poleward limit and will likely become less frequent if the jet migrates any further poleward with climate change.

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity

Abstract: A nonlinear Schrodinger equation for the envelope of two dimensional surface water waves on finite depth with non-zero constant vorticity is derived, and the influence of this constant vorticity on the well-known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. At third order, we have shown the importance of the nonlinear coupling between the mean flow induced by the modulation and the vorticity. Furthermore, it is shown that these plane wave solutions may be linearly stable to modulational instability for an opposite shear current independently of the dimensionless parameter kh, where k and h are the carrier wavenumber and depth, respectively.

Vorticity generation by short‐crested wave breaking

Abstract: [1] Eddies and vortices associated with breaking waves rapidly disperse pollution, nutrients, and terrestrial material along the coast. Although theory and numerical models suggest that vorticity is generated near the ends of a breaking wave crest, this hypothesis has not been tested in the field. Here we report the first observations of wave-generated vertical vorticity (e.g., horizontal eddies), and find that individual short-crested breaking waves generate significant vorticity [O(0.01 s−1)] in the surfzone. Left- and right-handed wave ends generate vorticity of opposite sign, consistent with theory. In contrast to theory, the observed vorticity also increases inside the breaking crest, possibly owing to onshore advection of vorticity generated at previous stages of breaking or from the shape of the breaking region. Short-crested breaking transferred energy from incident waves to lower frequency rotational motions that are a primary mechanism for dispersion near the shoreline.