A model of the effect of breaking waves on the air-sea momentum flux

Above the air-sea interface, within the constant stress layer, the momentum flux partitions into turbulent and wave-induced components. Non-breaking surface waves induce a wave-like pressure perturbation in the air, while ahead of a breaking crest the airflow separates, causing a pressure drop on the leeside of the wave. Both pressure perturbations lead to energy and momentum fluxes from wind to waves. By conserving airside momentum and energy and also imposing the wave action balance, we derive coupled equations governing the turbulent stress, wind speed, wave spectrum, and breaking wave distribution (length distribution of breaking crests per unit surface area as a function of wave number). Furthermore, we assume that smaller scale breaking waves are sheltered from wind forcing if they are in airflow separation regions of longer breaking waves (spatial sheltering effect). The saturation spectrum and the breaking wave distribution approach constant values for large wave numbers. Our model also yields the normalized roughness length (Charnock coefficient), which is roughly consistent with earlier observations. Model results suggest that breaking waves can support a significant fraction of the momentum flux, especially for younger seas.