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

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A physical model of the short wind wave spectrum in the wavelength range from 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 wave spectrum. It is assumed that in this range the spectrum shape is determined 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 between generation of capillaries and their viscous dissipation. The short gravity wave spectrum results through the balance between wind input and dissipation due to wave breaking. A parameterization of wind input is obtained in part 1 of the present paper. To describe the dissipation due to wave breaking, 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 ratio 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 viscous sublayer, which affects the energy losses by wave breaking. To obtain 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 wave 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 omnidirectional and up‐wind spectra, their wind speed dependence and angular spreading, and the wind speed dependence of integral mean square slope and skewness parameters, are well reproduced by the model. Also the model well reproduces the measured wind speed dependence of the drag coefficient and of the coupling parameter.