  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.
