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

Gérard Caudal (1)

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Using a two-dimensional empirical sea wave spectral model at full development, this paper performs an assessment of the compatibility of the energy and momentum budgets of sea waves over the whole spectral range. Among the various combinations of model functions for wave breaking and wind source terms tested, no one fulfilled simultaneously the energy and momentum balance of the transfer equation. Based on experimental and theoretical grounds, wave breaking is known to contribute to frequency downshift of a narrow-banded wave spectrum, when the modulational instability is combined with wave breaking. On those grounds, it is assumed that, in addition to dissipation, wave breaking produces a spectral energy flux directed toward low wavenumbers. I show that it is then possible to remove the energy and momentum budget inconsistency, and correlatively the required strength of this spectral flux is estimated. Assuming such a downward spectral flux permits to fulfill both energy and momentum balance conditions, while slightly reducing the consistency between source terms and empirical spectra, as estimated by a cost function K. Other tests were performed in which it was further assumed that wave breaking would also be associated with azimuthal diffusion of the spectral energy. This could allow a slight improvement of the cost function K, and might correlatively reduce the required downward spectral flux by a factor of 4, although it would not be able to remove it entirely.

Domaines: Océanographie

Gérard Caudal. Imbalance of energy and momentum source terms of the sea wave transfer equation for fully developed seas. Ocean Science, 2012, 8 (6), pp.1085-1098. ⟨10.5194/os-8-1085-2012⟩. ⟨hal-00732549⟩