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

Abstract

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations 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 superharmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. The 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.

Unified analytical solution for group-induced infragravity waves based on Green's function

“…(1982) and Schäffer (1993) adopted the saturated breaking model assuming the wave height is proportional to local depth to model the forcing term and then solved equation (2.14), but no satisfactory verification against experiment has been reported. Using numerically modelled flow field to calculate the radiation stress, Rijnsdorp, Smit & Guza (2022) showed that the linearised equation (2.14) remains adequate in the outer surf zone. Furthermore, Rijnsdorp et al.…”

“…Furthermore, Rijnsdorp et al. (2022) demonstrated that the nonlinearity of infragravity wave itself starts to become important only in the inner surf zone over a mildly sloping beach of bottom slope 1/100. Liu et al.…”

“…For breaking waves in the surf zone, Symonds et al (1982) and Schäffer (1993) adopted the saturated breaking model assuming the wave height is proportional to local depth to model the forcing term and then solved equation (2.14), but no satisfactory verification against experiment has been reported. Using numerically modelled flow field to calculate the radiation stress, Rijnsdorp, Smit & Guza (2022) showed that the linearised equation (2.14) remains adequate in the outer surf zone. Furthermore, Rijnsdorp et al (2022) demonstrated that the nonlinearity of infragravity wave itself starts to become important only in the inner surf zone over a mildly sloping beach of bottom slope 1/100.…”

“…Using numerically modelled flow field to calculate the radiation stress, Rijnsdorp, Smit & Guza (2022) showed that the linearised equation (2.14) remains adequate in the outer surf zone. Furthermore, Rijnsdorp et al (2022) demonstrated that the nonlinearity of infragravity wave itself starts to become important only in the inner surf zone over a mildly sloping beach of bottom slope 1/100. Liu et al (2023) showed that fully nonlinear analysis of the infragravity wave energy budget is required for reef topography where the depth sharply reduces when offshore waves propagate over the foreslope into the reef flat.…”

Modeling Significant Wave Heights for Multiple Time Horizons Using Metaheuristic Regression Methods

“…Hence, proper estimation of wave properties is a challenge in coastal and offshore engineering. Various factors represent the wave characteristics, of which significant wave height (HSW) is the most important property [2][3][4].…”