Imbalance of energy and momentum source terms of the sea wave transfer equation for fully developed seas

Ocean Science

G. V.Caudal¹ 

DOI  :  10.5194/os-8-1085-2012

学科分类：海洋学与技术

来源: Copernicus Publications

【 摘 要 】

In the concept of full development, the sea wave spectrum is regarded as anearly stationary solution of the wave transfer equation, where source andsink terms should be in balance with respect to both energy and momentum.Using a two-dimensional empirical sea wave spectral model at fulldevelopment, this paper performs an assessment of the compatibility of theenergy and momentum budgets of sea waves over the whole spectral range. Amongthe various combinations of model functions for wave breaking and wind sourceterms tested, not one is found to fulfill simultaneously the energy andmomentum balance of the transfer equation. Based on experimental andtheoretical grounds, wave breaking is known to contribute to frequencydownshift of a narrow-banded wave spectrum when the modulational instabilityis combined with wave breaking. On those grounds, it is assumed that, inaddition to dissipation, wave breaking produces a spectral energy fluxdirected toward low wavenumbers. I show that it is then possible to removethe energy and momentum budget inconsistency, and correspondingly therequired strength of this spectral flux is estimated. Introducing such adownward spectral flux permits fulfilling both energy and momentum balanceconditions. Meanwhile, the consistency between the transfer equation andempirical spectra, estimated by means of a cost function K, is eitherimproved or slightly reduced, depending upon the wave breaking and windsource terms chosen. Other tests are performed in which it is further assumedthat wave breaking would also be associated with azimuthal diffusion of thespectral energy. This would correspondingly reduce the required downwardspectral flux by a factor of up to 5, although it would not be able to removeit entirely.

【 授权许可】

Unknown