Interactions between Steady Won-Uniform Currents and Gravity Waves with Applications for Current Measurements

Abstract

Interactions between steady non-uniform currents and gravity waves are generalized to include the case of a random gravity wave field. The Kitaigorodskii-Pierson-Moskowitz frequency spectrum is used as the basic spectral form for zero current condition. Modified spectral functions in both wavenumber and frequency spaces under the influence of current are found by using energy conservation and kinematic wave conservation laws. The relative importance of the current-wave interaction was measured by the nondimensional parameter U/C0, with U as the current speed and C0 the phase speed of a wave under no current. As a result of the current-wave interaction, the magnitude and the location of the energy peak in the spectrum is altered. Since the phase speed of gravity waves is a monotonically decreasing function of wavenumber and frequency, the influence of current will be predominant at the higher wavenumber range. Furthermore, the contribution from the higher wavenumber range dominates the surface slope spectrum; the current conditions changes the surface slope pattern drastically. This phenomenon is studied by use of Phillips' equilibrium range spectrum in wavenumber space. It was found that the rms surface slope is extremely sensitive to the change of current conditions especially for the case of adverse current, but eventually becomes saturated at a high positive value. The surface slope data together with a generalized dispersion relation offer a possible current measurement technique which appears ideally suited for remote sensing devices such as stereoscopic photography and radar scattering.