Coupled Numerical Modelling of Wind and Waves and the Theory of the Wave Boundary Layer

Abstract

The description of a coupled wind and wave model in conformal coordinates is given. The wave model is based on potential equations for the flow with a free surface, extended with the algorithm of breaking dissipation. The wave boundary-layer (WBL) model is based on the Reynolds equations with the K − e closure scheme with the solutions for air and water matched through the interface. The structure of the WBL and vertical profiles of the wave-produced momentum flux (WPMF) in a long-term simulation of the coupled dynamics are investigated and parameterized. The shape of the β function connecting elevation and surface pressure is studied up to high nondimensional wave frequencies. The errors of a linear presentation of the surface pressure are estimated. The β function and the universal shape of the WPMF profile obtained in coupled simulations allow a formulation of the one-dimensional theory of the WBL, and the carrying out of a detailed study of the WBL structure including the dependence of the drag coefficient on the wind speed. It is shown that a wide scatter of the experimental data on the drag coefficient can be explained, taking into account the age of waves. It is suggested that a reduction of the drag coefficient at high wind speeds can be qualitatively explained by the high-frequency wave suppression.