Simulation of wave breaking over complex bathymetries by a Boussinesq model

Abstract

A Boussinesq-type model is applied herein to study wave propagation and wave breaking over complex bathymetries reproducing common coastal features, namely plane and barred beaches, submerged bars and rip channels. A hybrid finite volume–finite difference numerical scheme solves a set of, in the horizontal plane, two-dimensional extended Boussinesq equations where both nonlinear and dispersive effects are relevant and nonlinear shallow water equations where nonlinearity prevails over dispersion. The shock-capturing features of the finite volume method enable an intrinsic representation of spilling wave breaking and runup. Comparisons with experimental data indicate that the numerical model adequately simulates wave transformation over submerged bars, correctly capturing wave breaking onset and termination including the related energy dissipation. The development of breaking-induced currents and their interaction with wave propagation are also well represented within the applicability range of the governing equations.

Keywords:

• Boussinesq equations
• nonlinear shallow water equations
• rip current
• shock-capturing
• submerged bars

Acknowledgement

The authors would like to thank Prof. Maarten Dingemans for kindly providing experimental data and for advising on further references.