Resonant Interaction of Waves in a Beach Zone

Generation of edge waves on a uniformly inclined beach by an incoming swell is considered on the basis of the shallow water model. The subharmonic resonance mechanism of interaction is analyzed by using multi-scaled expansion asymptotic techniques. From the derived equations for the wave’s modulation, excitation of the edge waves within a constrained space (in alongshore direction) is analyzed. A dynamic space threshold for edge-wave generation is suggested and is defined by the intensity and the frequency of the incoming swell and the geometry of the shore. Applying spatial constrictions enables us to study the generation of an edge waves between wave breakers. Nonlinear non-stationary wave solutions for the envelope of interacting edge waves generalize the well-known Sine-Gordon model. An infinite set of exact solutions is obtained by using the Lamb method for the phase synchronism regime of wave interaction. KCI Citation Count: 1