Solitary wave shoaling and breaking in a regularized Boussinesq system

TL;DR

This paper investigates solitary wave behavior over decreasing depth using a coupled BBM system, introducing a conservation law and breaking criterion, and employs numerical methods validated against existing models.

Contribution

It develops a new conservation equation and wave breaking criterion within a coupled BBM framework for water waves over sloping bottoms, validated by numerical simulations.

Findings

Good agreement with previous models by Grilli et al.

Different mild slope models are effective in their respective regimes.

Numerical simulations accurately capture wave shoaling and breaking.

Abstract

A coupled BBM system of equations is studied in the situation of water waves propagating over decreasing fluid depth. A conservation equation for mass and a wave breaking criterion valid in the Boussinesq approximation is found. A Fourier collocation method coupled with a 4-stage Runge-Kutta time integration scheme is employed to approximate solutions of the BBM system. The mass conservation equation is used to quantify the role of reflection in the shoaling of solitary waves on a sloping bottom. Shoaling results based on an adiabatic approximation are analyzed. Wave shoaling and the criterion of breaking solitary waves on a sloping bottom is studied. To validate the numerical model the simulation results are compared with those obtained by Grilli et al.[16] and a good agreement between them is observed. Shoaling of solitary waves of two different types of mild slope model systems in [8] and [13] are compared, and it is found that each of these models works well in their respective regimes of applicability.