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

TL;DR

This paper develops a nonlinear, nondispersive energy balance model for surfzone waves, revealing the dominant role of triad interactions and bottom stresses in infragravity wave dynamics on sloping beaches.

Contribution

It introduces a new nonlinear energy balance based on NLSWE that improves understanding of IG wave behavior in the surfzone, especially near the shoreline.

Findings

Spatial gradients in IG energy flux are balanced by bottom stresses and triad interactions.

IG energy flux increases during shoaling and outer surfzone due to triad interactions.

IG wave breaking and energy dissipation are significant only deep inside the surfzone.

Abstract

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations (NLSWE) to study the nearshore dynamics of infragravity (IG) 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 IG energy flux are nearly completely balanced by the combined effect of bottom stresses and predominantly nonlinear triad interactions. The new balance confirms many features of existing weakly nonlinear theories, and yields an improved description in the inner surfzone where waves become highly nonlinear. A gain of IG energy flux throughout the shoaling and outer surfzones is driven by triad interactions between IG waves and pairs of sea-swell (SS) waves. The IG energy flux decreased in the inner surfzone, primarily through an energy cascade to the swell-band and super-harmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. IG wave breaking, characterized by triads between three IG or two IG waves and one SS wave, was significant only deep inside the surfzone of the mild slope. Even though IG waves broke on the mild slope, nonlinear interactions between IG waves and pairs of SS waves were responsible for at least half of the net IG flux loss.