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

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.