Modulation of short wind waves in the presence of strong internal waves: The effect of growth-rate modulation

A model is proposed for the modulation of centimeter surface waves in the field of strong internal waves. The modulation mechanism is considered to be due to growth-rate modulation caused by variation in the wind-speed profile over the water surface at which a nonuniform current produced by internal waves is specified. The growth rate is calculated on the basis of the quasi-linear model of modulation of short wind waves by turbulent wind. A current produced on the surface by strong internal waves is described by the model based on the modified Korteweg-de Vries equation. The parameters of internal waves are taken from the Coastal Ocean Probe Experiment. The wind-induced growth rate is calculated as a function of the phase of the wave train for different values of the wind friction velocity and the surface wavelength. The calculations are carried out for the cases when the direction of internal-wave propagation is aligned with the wind and opposed to it. The calculation results are in qualitative agreement with experimental data.