141 research outputs found
Predicting the breaking onset of surface water waves
Why do ocean waves break? Understanding this important and obvious property of the ocean surface has been elusive for decades. This paper investigates causes which lead deep-water two-dimensional initially monochromatic waves to break. Individual wave steepness is found to be the single parameter which determines whether the wave will break immediately, never break or take a finite number of wave lengths to break. The breaking will occur once the wave reaches the Stokes limiting steepness. The breaking probability and the location of breaking onset can be predicted, properties of incipient breakers measured. Potential applications to field conditions are discussed
High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind
The paper describes the numerical experiments with a three-dimensional phase-resolving model based on the initial potential equation of motion with free surface at deep water in the periodic domain written in the surface-following nonstationary curvilinear nonorthogonal coordinate system. The numerical scheme is based on Fourier-transform method. The vertical velocity on surface is calculated by solving the three-dimensional Poisson equation for the velocity potential. The velocity potential is represented as a sum of linear and nonlinear components. The linear component is described by Laplace equation. The nonlinear component is calculated by solution of the three-dimensional Poisson equation with the iterated right-hand side. The model includes some algorithms for calculation of the energy input from wind as well as for calculation of breaking and high-frequency dissipation. Initially, the conditions are assigned as a set of small waves corresponding to JONSWAP spectrum at high wave number. In response to waves’ growth, the spectrum shifts to lower wave numbers. The evolution of spectrum is generally in an agreement with the observed data. The wave spectrum and the spectra of different rates of energy transformation as well as the statistical characteristics of wave field for different stages of development are described
Fine scale inhomogeneity of wind-wave energy input, skewness, and asymmetry
Analysis of measured sea and lake wind wave data reveals large variability of the wind energy input, as well as the waves skewness and asymmetry. The spatial and temporal third moments alternate in sign over a few wave periods and over a few wavelengths, respectively. Simulation through a 2D Wave Boundary Layer model in which the air flow is modeled by 2nd order Reynolds equations (Chalikov, 1998) conforms to these findings and exposes a rich structure. We found clear correlation of the variations of the skewness and the asymmetry with the wind input
Advanced wave modeling, including wave-current interaction
The paper outlines principles of phase-resolving and phase-average wave models, with emphasis on the state of the art of wave-current interaction physics. We argue that these interactions are the least well-developed part of such models. Linear and nonlinear dynamics of waves on currents are discussed; depth-integrated and depth-varying approaches are described. Finally, examples of numerical model performance for waves on currents in realistic oceanic scenarios are presented
Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation
New parameterizations for the spectra dissipation of wind-generated waves are
proposed. The rates of dissipation have no predetermined spectral shapes and
are functions of the wave spectrum and wind speed and direction, in a way
consistent with observation of wave breaking and swell dissipation properties.
Namely, the swell dissipation is nonlinear and proportional to the swell
steepness, and dissipation due to wave breaking is non-zero only when a
non-dimensional spectrum exceeds the threshold at which waves are observed to
start breaking. An additional source of short wave dissipation due to long wave
breaking is introduced to represent the dissipation of short waves due to
longer breaking waves. Several degrees of freedom are introduced in the wave
breaking and the wind-wave generation term of Janssen (J. Phys. Oceanogr.
1991). These parameterizations are combined and calibrated with the Discrete
Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the
nonlinear interactions. Parameters are adjusted to reproduce observed shapes of
directional wave spectra, and the variability of spectral moments with wind
speed and wave height. The wave energy balance is verified in a wide range of
conditions and scales, from gentle swells to major hurricanes, from the global
ocean to coastal settings. Wave height, peak and mean periods, and spectral
data are validated using in situ and remote sensing data. Some systematic
defects are still present, but the parameterizations yield the best overall
results to date. Perspectives for further improvement are also given.Comment: revised version for Journal of Physical Oceanograph
Surface gravity waves in deep fluid at vertical shear flows
Special features of surface gravity waves in deep fluid flow with constant
vertical shear of velocity is studied. It is found that the mean flow velocity
shear leads to non-trivial modification of surface gravity wave modes
dispersive characteristics. Moreover, the shear induces generation of surface
gravity waves by internal vortex mode perturbations. The performed analytical
and numerical study provides, that surface gravity waves are effectively
generated by the internal perturbations at high shear rates. The generation is
different for the waves propagating in the different directions. Generation of
surface gravity waves propagating along the main flow considerably exceeds the
generation of surface gravity waves in the opposite direction for relatively
small shear rates, whereas the later wave is generated more effectively for the
high shear rates. From the mathematical point of view the wave generation is
caused by non self-adjointness of the linear operators that describe the shear
flow.Comment: JETP, accepte
The effect of breaking waves on a coupled model of wind and ocean surface waves. Part I : mature seas
Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 2145–2163, doi:10.1175/2008JPO3961.1.This is the first of a two-part investigation of a coupled wind and wave model that includes the enhanced form drag of breaking waves. In Part I here the model is developed and applied to mature seas. Part II explores the solutions in a wide range of wind and wave conditions, including growing seas. Breaking and nonbreaking waves induce air-side fluxes of momentum and energy above the air–sea interface. By balancing air-side momentum and energy and by conserving wave energy, coupled nonlinear advance–delay differential equations are derived, which govern simultaneously the wave and wind field. The system of equations is closed by introducing a relation between the wave height spectrum and wave dissipation due to breaking. The wave dissipation is proportional to nonlinear wave interactions, if the wave curvature spectrum is below the “threshold saturation level.” Above this threshold the wave dissipation rapidly increases so that the wave height spectrum is limited. The coupled model is applied to mature wind-driven seas for which the wind forcing only occurs in the equilibrium range away from the spectral peak. Modeled wave height curvature spectra as functions of wavenumber k are consistent with observations and transition from k1/2 at low wavenumbers to k0 at high wavenumbers. Breaking waves affect only weakly the wave height spectrum. Furthermore, the wind input to waves is dominated by nonbreaking waves closer to the spectral peak. Shorter breaking waves, however, can support a significant fraction, which increases with wind speed, of the total air–sea momentum flux.This work
was supported by the U.S. National Science Foundation
(Grant OCE-0526177) and the U.S. Office of Naval
Research (Grant N00014-06-10729)
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