Coupled sea surface-atmosphere model - 2. Spectrum of short wind waves

A physical model of the short wind wave spectrum in the wavelength range fr om a few millimeters to few meters is proposed. The spectrum shape results from the solution of the energy spectral density balance equation. Special attention is paid to the description of the capillary range of the short wa ve spectrum. It is assumed that in this range the spectrum shape is determi ned mainly by the mechanism of generation of parasitic capillaries. This is described as the cascade energy transfer from the gravity to the capillary waves. Thus the capillary wave spectrum results through the balance betwee n generation of capillaries and their viscous dissipation. The short gravit y wave spectrum results through the balance between wind input and dissipat ion due to wave breaking. A parameterization of wind input is obtained in p art 1 of the present paper. To describe the dissipation due to wave breakin g, the approach developed by Phillips [1985] is used. The spectral rate of energy dissipation is presented in the form of a power dependence of the ra tio of the saturation spectrum to some threshold level. It is further shown that the threshold level depends on the drift current shift in the water v iscous sublayer, which affects the energy losses by wave breaking. To obtai n a short wave spectrum which is valid in the whole wavenumber domain, the capillary and the short gravity wave spectra are patched in the vicinity of the wavenumber corresponding to the minimum phase velocity. This short wav e spectrum is incorporated into the wind over waves coupled model developed in part 1 of the present paper. The measured statistical properties of the sea surface related to the short waves, such as the spectral shape of omni directional and up-wind spectra, their wind speed dependence and angular sp reading, and the wind speed dependence of integral mean square slope and sk ewness parameters, are well reproduced by the model. Also the model well re produces the measured wind speed dependence of the drag coefficient and of the coupling parameter.