Modeling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

TL;DR

This paper introduces two novel methods to model wave breaking within a fully nonlinear free-surface potential flow framework, validated through numerical simulations and experimental comparisons.

Contribution

It presents two innovative approaches for wave breaking modeling in Hamiltonian potential flow, extending existing methods with energy dissipation and momentum conservation.

Findings

Both methods successfully simulate wave energy dissipation.

Numerical results align well with experimental data.

The approaches improve the realism of wave breaking simulations.

Abstract

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al (2000)'s eddy-viscosity approach originally developed for Boussinesq-type wave models. In this approach, an extra term, constructed to conserve the horizontal momentum for waves propagating over a flat bottom, is added in the dynamic free-surface condition. In the second method, a pressure distribution is introduced at the free surface that dissipates wave energy by analogy to a hydraulic jump (Guignard and Grilli, 2001). The modified Hamiltonian systems are implemented using the Hamiltonian Coupled-Mode Theory, in which the velocity potential is represented by a rapidly convergent vertical series expansion. Wave energy dissipation and conservation of horizontal momentum are verified numerically. Comparisons with experimental measurements are presented for the propagation of a breaking dispersive shock wave following a dam break, and then incident regular waves breaking on a mildly sloping beach and over a submerged bar.