The effect of breaking waves on a coupled model of wind and ocean surface waves

Understanding the role of breaking surface waves in air-sea exchange processes is integral to accurate weather and climate modeling. A coupled wind and ocean surface wave model is developed that includes the enhanced form drag of breaking waves. Breaking and non-breaking waves induce air-side fluxes of momentum and energy in a thin layer above the air-sea interface within the constant stress layer (the wave boundary layer). By conserving momentum and energy in the wave boundary layer and wave energy, we derive coupled nonlinear advance-delay differential equations, which govern four physical quantities critical to air-sea transfer processes: the vertical wind profiles of the speed and turbulent stress, the wave height spectrum, and the length distribution of breaking wave crests as a function of wave scale. Introduction of non-dimensional variables elucidates the parameters controlling the momentum fluxes into breaking and non-breaking waves. In order to understand better the coupled wind and wave system, analytic solutions are obtained for limiting cases with either wind input to only breaking or input to only non-breaking waves. To solve the full system of advance-delay differential equations, we developed a numerical method based on two nested iterations. Solutions indicate that the number of breaking waves strongly depends on the sea state. Furthermore, breaking waves may contribute significantly to the total air-sea momentum flux. The breaking wave contribution increases for younger, strongly forced wind waves. This new wind and wave model provides a powerful tool to gain insight into complex coupled wind-wave dynamics.