A nonlinear, nondispersive energy balance for surfzone waves: infragravity wave dynamics on a sloping beach.

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the non-linear shallow water equations (NLSWE) to study the nearshore dynamics of infragravity waves. Based on simulations of waves on a relatively moderate and mild beach slope with a non-hydrostatic wave-flow model (SWASH), the new theory shows that spatial gradients in the infragravity energy flux are nearly completely balanced by the combined effect of nonlinear triad interactions and (smaller) bottom stresses. The new balance confirms many features of weakly nonlinear theories used previously to study infragravity waves, and yields an improved description in the inner surfzone where the wave motions become highly nonlinear. The gain of infragravity energy flux throughout the shoaling region and the outer surf zone is driven by triad interactions between infragravity waves and sea-swell wave groups. The infragravity energy flux decreased in the inner surfzone, primarily through an energy cascade towards super-harmonic frequencies (in the sea-swell band) where the wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. Infragravity wave breaking, characterized by triads between two infragravity and one sea-swell harmonic (or three infragravity harmonics) became only significant deep inside the surfzone of the mild slope. Even though infragravity waves were breaking on the mild slope, non-linear interactions between infragravity waves and sea-swell wave groups were responsible for at least half of the net IG flux loss.