The numerical simulation of wind-wave interaction

The Navier-Stokes equations for a two-layer flow are written in a curvilinear system of co-ordinates in which the height is measured from the interface. A technique for averaging the equations over an ensemble of wave surfaces which are not very different from each other is proposed. Moments which include deviations in the rate of surface displacement and in the slopes are dropped. It is assumed that the averaged equations describe the evolution of a large-scale velocity field. The moments of the turbulent velocity field are parameterized using the isotropic coefficient of turbulent viscosity, which, from dimensional considerations, is expressed in terms of the length scale growing linearly upwards and downwards from the interface and the turbulent kinetic energy. The equation defining the evolution of turbulent energy is derived without allowing for the curvilinearity of the system of co-ordinates. Laboratory experiments in a wind-water tunnel are simulated by integrating the equations numerically. The results are compared with measurements.