Resonant excitation of trapped waves by Poincaré waves in the coastal waveguides

Abstract

After having revisited the theory of linear waves in the rotating shallow-water model with a straight coast and arbitrary shelf/beach bathymetry, we undertake a detailed study of resonant interaction of free Poincaré waves with modes trapped in the coastal waveguide. We describe and quantify the mechanisms of resonant excitation of waveguide modes and their subsequent nonlinear saturation. We obtain the modulation equations for the amplitudes of excited waveguide modes in the absence and in the presence of spatial modulation and analyse their solutions. Different saturation regimes are exhibited, depending on the nature of the modes involved. The excitation is proved to be efficient, i.e. the saturated amplitudes of the excited waves considerably exceed the amplitude of the generator waves. Back-influence of the excited waveguide modes onto the open ocean results in a phase shift of the reflected Poincaré waves and possible energy redistribution between them. A comparison of rotating and non-rotating cases displays substantial differences in excitation mechanisms in the two cases.