Harmonic-induced wave breaking due to abrupt depth transitions

Abstract

Abrupt depth transitions (ADTs) have been shown to induce the release of bound waves into free waves, which results in spatially inhomogeneous wave fields atop ADTs. Herein, we examine the role of free-wave release in the generation and spatial distribution of higher-harmonic wave components and in the onset of wave breaking for very steep periodic waves upon interaction with an ADT. We utilise a Smoothed Particle Hydrodynamics (SPH) model, making use of its ability to automatically capture breaking and overturning surfaces. We validate the model against experiments. The SPH model is found to accurately reproduce the phase-resolved harmonic components up to the sixth harmonic, particularly in the vicinity of the ADT. For the cases studied, we conclude that second-order free waves released at the ADT, and their interaction with the linear and second-order bound waves (beating), drive higher-order bound-wave components, which show spatial variation in amplitude as a result. For wave amplitudes smaller than the breaking threshold, this second-order beating phenomenon can be used to predict the locations where peak values of surface elevation are located, whilst also predicting the breaking location for wave amplitudes at the breaking threshold. Beyond this threshold, the contributions of the second-order and higher harmonics (second-harmonic amplitudes are up to 60% and sixth-harmonic up to 10% of the incident amplitude) cause breaking to occur nearer to the ADT, and hence the wave breaking onset location is confined to the region between the ADT and the first anti-node location of the second-order components. Counter-intuitively, we find that, at the point of breaking, steeper incident waves are found to display reduced non-linearity as a result of breaking nearer to the ADT.