Nonlinear Infragravity–Wave Interactions on a Gently Sloping Laboratory Beach

Abstract

A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy transfers to investigate energy flows within the spectra. Energy flows are identified by dividing transfers into four types of triad interactions, with triads including one, two, or three infragravity-frequency components, and triad interactions solely between short-wave frequencies. In the shoaling zone, the energy transfers are generally from the spectral peak to its higher harmonics and to infragravity frequencies. While receiving net energy, infragravity waves participate in interactions that spread energy of the short-wave peaks to adjacent frequencies, thereby creating a broader energy spectrum. In the short-wave surf zone, infragravity-infragravity interactions develop, and close to shore, they dominate the interactions. Nonlinear energy fluxes are compared to gradients in total energy flux and are observed to balance nearly completely. Overall, energy losses at both infragravity and short-wave frequencies can largely be explained by a cascade of nonlinear energy transfers to high frequencies (say, f . 1.5 Hz) where the energy is presumably dissipated. Infragravity-infragravity interactions seem to induce higher harmonics that allow for shape transformation of the infragravity wave to asymmetric. The largest decrease in infragravity wave height occurs close to the shore, where infragravity-infragravity interactions dominate and where the infragravity wave is asymmetric, suggesting wave breaking to be the dominant mechanism of infragravity wave dissipation.

Transfer and dissipation of energy during wave group propagation on a gentle beach slope

“…The analysis presented in this paper is therefore consistent with previous studies [ Van Dongeren et al ., ; de Bakker et al ., ; Battjes et al ., ] suggesting lf wave breaking as the mechanism behind the sharp reduction in ILW amplitude. In Van Dongeren et al .…”

“…The nonlinear wave interactions can be studied to the second order on the basis of high‐order spectral (HOS) energy balance [ Hasselmann et al ., ; Elgar and Guza , ; Herbers et al ., ; de Bakker et al ., , among others]. In these studies, the transport of energy associated with a frequency f is presented as a balance between the cross‐shore gradient of the energy flux spectrum F f , a nonlinear source computed by bispectral analysis and a dissipation term that includes energy losses such as wave breaking: …”

The role of the reef-dune system in coastal protection in Puerto Morelos (Mexico)

“…This numerical model solves the nonlinear shallow water equations, including the terms for non-hydrostatic pressure, which make it suitable for simulating wave transformation as a result of nonlinear wave-wave interactions in the surf and swash regions. The model is also capable of simulating wave-current interaction, wave breaking (Smit et al, 2013;de Bakker et al, 2015), wave 20 transformation on reefs (Torres-Freyermuth et al, 2012;Zijlema et al, 2012), and wave-runup (e.g., Brinkkemper et al, 2013;Ruju et al, 2014;Guimarao et al, 2015;Medellín et al, 2016). For further details, including model equations see (Zijlema et al, 2011).…”

Experimental studies of the local reflection of long waves from an underwater slope

“…⎯The local reflection coefficient at the offshore boundary of the underwater slope depends on the steepness of the incident waves and normalized bot tom slope and can be determined from formula (5).…”

“…The experiments that are related to the studies of the ability of an underwater slope to create reflection are extremely rare. Among the works of this type that were carried out in the recent years we have to note unique laboratory experiments that studied the reflection of IGWs during wave transformation over a sloping bot tom [5,8]. As a result of these experiments it was established that infra gravity waves can also be sub jected to the process of their energy dissipation as gravity wind waves.…”