Simulation of Depth-Limited Breaking Waves in a 3D Fully Nonlinear Potential Flow Model

Abstract

Extending an earlier two-dimensional (2D) implementation, a novel method is introduced for both detecting the onset of wave breaking and simulating the resulting energy dissipation in limited water depth, in a three-dimensional (3D) fully nonlinear potential flow (FNPF) model. Breaking onset is identified using a universal criterion, based on the ratio of the horizontal particle velocity at the crest to the crest phase velocity. The breaking-induced energy dissipation is based on the nondimensional breaking strength parameter and is implemented in the model as an absorbing surface pressure. The 3D-FNPF solves Laplace’s equation using a higher-order boundary element method based on Green’s second identity and marches the solution forward in time. The implementation of wave dissipation due to breaking is carried out in three steps: (i) a nondimensional breaking strength parameter is calculated based on a previous 2D unified depth-limited dissipation model; (ii) the instantaneous power to be dissipated is computed using this parameter and energy dissipation is modeled as a damping pressure specified in a region around the breaking crest; and (iii) the dissipation process of each breaking wave is terminated using a criterion calibrated through a comparison of the free surface elevation with experimental data from the literature. The new 3D model is experimentally validated for regular spilling and plunging breaking waves propagating over a 3D submerged bar and an elliptical shoal. Future work will extend this model to irregular 3D breaking waves.