Nonlinear Infragravity Waves

A general dynamical equation for the full mixed edge-leaky spectrum over a laterally uniform beach was derived based on Hamiltonian formalism [Zakharov, 1968, 1999b]. The introduction of canonical variables in this formalism significantly simplifies the complicated derivation of the nonlinear interaction coefficient in the previous work. The subharmonic resonance mechanism for edge-wave excitation [Guza and Davis, 1974] is retrieved from the model equation as a special case. The effects of dissipation induced by bottom friction are included using a perturbation approach. A kinetic equation for Zakharov’s canonical variables can also be derived. The process of determining exact and near resonant triads has been automated by transforming the resonance condition into an algebraic system of equations. The resonance conditions are investigated for plane and exponential beaches. A numerical adaption of the dynamical equation was developed and tested for isolated edge-wave triads in the absence of leaky waves.