AbstractA general formalism for computing the nonlinear interactions between triads of coastally-trapped gravity and vorticity waves is developed. An analysis of the linearized problem reveals that gravity (or edge) waves and vorticity (or shear) waves exist as members of the same non-Sturm-Liouville eigenvalue problem, with unstable shear waves representing the complex eigenvalue portion of the resulting spectrum. Interaction equations derived here cover resonant interactions between three edge waves, three shear waves, or a shear wave and two edge waves. Numerical examples are shown for the case of three edge waves on a planar beach in the absence of a longshore current. It is found that edge waves can exchange significant amounts of energy over time scales on the order of ten wave periods, for realistic choices of edge wave parameters.
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