Numerical modelling of turbulent airflow over water waves

A nonlinear numerical model is developed for turbulent boundary-layer flow over a train of water waves of finite amplitude or slope. The airflow is assumed to be steady, two-dimensional, and neutrally-stratified. The wave surface is assumed to be aerodynamically rough and flow conditions at the wave surface are prescribed. The numerical model used in this study adopts three turbulence closure schemes with different degrees of physical completeness. Two of these are second-order schemes, which are believed to describe turbulent flow more completely than the simpler closures used in most previous studies. Although models with all turbulence closures agree qualitatively in the prediction of the amplitude of the surface normal stress perturbation, the lower- and higher-order closures differ significantly in predictions of phase, and hence the form drag and energy transfer rate between wind and waves. Our model results are in reasonable agreement with field and laboratory measurements, although predicted energy transfer rates are generally at the low end of the range of experimental values. Cases with airflow at various angles to the wave direction are also considered.