Abstract
Analysis of the wind waves dispersion relation becomes complicated if drift current is present. In general, this relation is derived from the Rayleigh equation, which does not have an analytical solution for an arbitrary velocity profile. In the limiting case, when the gravity-capillary wavelength is small compared to the typical flow depth, the simple Doppler approximation can be used. But in general, this approximation is not valid, and it necessary to take into account the vertical profile of horizontal velocity up to the depth, which corresponds to the considered wavelength. The velocity profile of the drift current is determined using Particle Image Velocimetry. High-resolution spatiotemporal spectra of the waves are obtained with color schlieren technique. Small addition of sodium dodecyl sulfate enabled us to estimate the influence of soluble impurities on the structure of the drift current and modification of the ratio between the drift current depth and the gravity-capillary wavelength. In the present work, an algorithm for numerical calculation of the dispersion relation for a given velocity profile is proposed. It is shown that the dispersion relation for a wind channel is adequately described by Rayleigh equation and the angle between the wave propagation direction and the wind, which is introduced in geophysics for correction of the dispersion relation, may be actually related to different values of the ratio between the wavelength and the drift current depth.
Published Version
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