The effect of breaking waves on a coupled model of wind and ocean surface waves. Part I : mature seas

Abstract

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.