Abstract
We develop a model of transformation of the short surface wave spectrum in the presence of a nonuniform flow on a water surface, in which the modulation of wind-wave growth rate is taken into account. The model of a turbulent near-water atmospheric layer is used to calculate the modulated growth rate. In this model, turbulent stresses in the wind are described using a gradient approximation with model eddy viscosity specified with allowance for the known laboratory experiments. The examples of short-wave modulation in the presence of nonuniform flows on a water surface, originating from ripples and intense internal waves, are considered. It is shown that deformations of the wind-velocity profile and its long-wavelength perturbation due to the nonlinear interaction between the wind surface waves and the wind has a significant effects on the short-wave growth rate and its modulation. In the case of ripples, this deformation reduces to an increase in the roughness parameter of the wind-velocity profile and to a velocity-profile modulation with ripple period. The modulated growth rate is calculated within the framework of a quasi-linear model of surface-wave generation by a turbulent wind, in which the hypothesis of random phases of the wind-wave field is used. The amplitude and phase of the hydrodynamical modulation transfer function are calculated within the framework of the relaxation model. The calculation results are in reasonable agreement with the available experimental data. A model described by the combined Korteweg–de Vries equation is used to study a surface flow field generated by intense internal waves. The internal-wave parameters are takes from the results of the COPE experiment. We calculate the wind growth-rate dependences on the wave-train phase for the cases of downwind and upwind propagation of an internal wave. The calculation results agree qualitatively with experimental data.
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