Resonant generation of internal waves on the soft sea bed by a surface water wave

Abstract

The nonlinear response of an initially flat sea bed to a monochromatic surface progressive wave was studied using the multiple scale perturbation method. Two opposite-traveling subliminal internal ‘‘mud’’ waves are selectively excited and form a resonant triad with the surface wave. The amplitudes of the internal waves grow on a time scale much longer than the period of the surface wave. It was found that the sea bed response is critically dependent on the density ratio of water and soil, depth of water, and depth and viscosity of the saturated soil. The result of instability analysis is in qualitative agreement with the result of a wave flume experiment.