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

Abstract

Abstract. 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 i 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 i 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.

Modeling the SAR Signature of Nonlinear Internal Waves

“…This model was selected for the following reasons: it was derived based on physical principles and measurements and has been used in many studies in radar remote sensing research. Also, at low wavenumbers, the DP model is identical to spectral model of Kudryavtsev et al( 1999), which is used in a subsequent part of this effort. The DP spectrum employs the same source terms and action modulation framework for computing SW-IW interactions as the LB model, but is more physically realistic.…”

“…This approach uses the innovative spectral model of Kudryavtsev et al (1999) and includes an action source term associated with the generation of parasitic capillary waves produced from the IW-SW interaction. An illustration of this spectral model is provided in Figure 5, for the same conditions (wind speed and direction) used to illustrate the DP model (Figure 4).…”

An Improved Spectrum Model for Sea Surface Radar Backscattering at L-Band

“…To be consistent with the in situ observations of gravity-capillary waves, Apel [23] and Elfouhaily et al [21] proposed a full wavenumber spectra based on the developed spectra. Kudryavtsev et al derived a physical model of the short wind wave spectrum by analyzing the input and dissipation of sea wave energy based on the propagation theory of the spectral energy density [29]. Including scattering theory and radar data, the precise retrieval of short-wave spectral properties was implemented with active microwave observations [22,25,26,30].…”

Interaction of waves, surface currents, and turbulence: the application of surface-following coordinate systems

“…This effect was subsequently used to calculate the "back-effect" of a wave field with a continuous Fourier spectrum, for which there is thus a continuous range of critical levels, on the mean flow field itself (Janssen, 1989;Jenkins, 1993;Makin and Kudryavtsev, 1999;Kudryavtsev et al, 1999;Kudryavtsev et al, 2001). …”