Quasi-linear Theory of Wind-Wave Generation Applied to Wave Forecasting

Abstract

The effect of wind-generated gravity waves on the airflow is discussed using quasi-linear theory of wind-wave generation. In this theory, both the effects of the waves and the effect of air turbulence on the mean wave profile are taken into account. The main result of this theory is that for young wind sea most of the stress in the boundary layer is determined by momentum transfer from wind to waves, therefore, resulting in a strong interaction between wind and waves. For old wind sea there is, however, hardly any coupling. As a consequence, a sensitive dependence of the aerodynamic drag on wave age is found, explaining the scatter in plots of the experimentally observed drag as a function of the wind speed at 10-m height. Also, the growth rate of waves by wind is found to depend on wave age. All this suggests that a proper description of the physics of the momentum transfer at the air–sea interface can only be given by coupling an atmospheric (boundary-layer) model with an ocean-wave prediction model. Here, results are presented of the coupling of a simple surface-layer model with a third-generation wave model. First, results obtained with a single gridpoint coupled model are discussed, and the evolution in time of wave height, wave stress, and the aerodynamic drag is investigated. Next, results obtained from a hindcast with the coupled model on the North Sea are discussed. In both cases, the wave-induced stress is found to have some impact on the results for wave height, while the impact on the stress in the surface layer is significant.