The effect of breaking waves on a coupled model of wind and ocean surface waves. Part II : growing seas

Abstract

This is the second part of a two-part investigation of a coupled wind and wave model that includes the enhanced form drag of breaking waves. The model is based on the wave energy balance and the conservation of air-side momentum and energy. In Part I, coupled nonlinear advance–delay differential equations were derived, which govern the wave height spectrum, the distribution of breaking waves, and vertical air side profiles of the turbulent stress and wind speed. Numeric solutions were determined for mature seas. Here, numeric solutions for a wide range of wind and wave conditions are obtained, including young, strongly forced wind waves. Furthermore, the “spatial sheltering effect” is introduced so that smaller waves in airflow separation regions of breaking longer waves cannot be forced by the wind. The solutions strongly depend on the wave height curvature spectrum at high wavenumbers (the “threshold saturation level”). As the threshold saturation level is reduced, the effect of breaking waves becomes stronger. For young strongly forced waves (laboratory conditions), breaking waves close to the spectral peak dominate the wind input and previous solutions of a model with only input to breaking waves are recovered. Model results of the normalized roughness length are generally consistent with previous laboratory and field measurements. For field conditions, the wind stress depends sensitively on the wave height spectrum. The spatial sheltering may modify the number of breaking shorter waves, in particular, for younger seas.