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.
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.
| Original language | English |
|---|---|
| Journal | Coastal Engineering |
| DOIs | |
| Publication status | Published - 3 Nov 2021 |