Energy and dissipation spectra of waves propagating in the inner surf zone

Abstract

The spectral behaviour of random sawtooth waves propagating in the inner surf zone is investigated in this study. We show that the elevation energy spectrum exhibits a universal shape with an $\omega ^{-2}$ tendency in the inertial subrange and an exponential decay in the diffusive subrange ( $\omega$ being the angular frequency). A theoretical spectrum is derived based on the similarities between sawtooth waves in the inner surf zone and Burgers wave solutions. Very good agreement is shown between this theoretical spectrum and laboratory experiments covering a large range of incident random wave conditions. Additionally, an equation describing the universal shape of the dissipation spectrum is derived. It highlights that the dissipation spectrum is nearly constant in the inertial subrange, consistent with prior laboratory observations. The findings presented in this study can be useful to improve broken wave dissipation parametrizations in stochastic spectral wave models.