On the Interaction of Wind and Waves

We discuss the effect of wind-generated, gravity waves on the air flow. We study this example of resonant wave mean flow interaction using the quasi-linear theory of wind-wave generation (A. L. Fabrikant Izv. atmos. ocean. Phys. 12, 524 (1976); P. Janssen J. Fluid Mech. 117, 493-506 (1982)). In this theory both the effects of the waves and the effect of air turbulence on the mean wind profile is taken into account. For a given wave spectrum, results of the numerical calculation of the steady-state wind profile are presented. The main result is that for young wind sea most of the stress in the boundary layer is determined by the transfer of momentum from wind to waves, therefore resulting in a strong coupling between air flow and waves. For old wind sea there is, however, hardly any coupling. As a consequence, a sensitive dependence of the aerodynamic drag on the wave age is found, explaining the scatter in plots of the experimentally observed drag as a function of the wind speed at 10 m. Also, the growth rate of waves by wind is found to depend on wave age, reflecting the effect of the waves on the wind profile. All this suggests that a proper description of the physics of the momentum transfer from atmosphere to the ocean waves can only be given by coupling an atmospheric boundary-layer model with an ocean-wave prediction model. Here, we present the first results of the coupling of a simple surface-layer model with the third-generation wave model. The wave-induced stress is found to have a significant impact on the results for the wave height and the stress in the surface layer.