Large-Wave Simulation of Spilling Breakers Over Constant-Slope Bed

Abstract

A subgrid scale model is presented for the large-wave simulation (LWS) of spilling breaking waves over bottom of arbitrary shape and finite depth. According to LWS formulation, large velocity and free-surface scales are fully resolved, while subgrid scales are accounted for by an eddy viscosity model, similar to large-eddy simulation (LES). The LWS-based model is applied on the two-dimensional wave propagation over a constant-slope bed. Fluid motion is described by the Euler equations for inviscid but rotational flow, subject to the fully non-linear free-surface boundary conditions. The application of LWS is facilitated by a boundary-fitted transformation, which introduces free-surface elevation terms in the Euler equations and simplifies the numerical implementation. Subgrid velocity scales are modeled similarly to LES, while the effect of free-surface subgrid scales are modeled by wave SGS stresses model. The resulting equations are solved numerically by a two-stage fractional time-step scheme, while an absorption zone is placed in the outflow region to minimize reflection by the outgoing waves. The simulation is carried out for the propagation and breaking of waves over a flat bed with constant slope 1/35 and results are compared to available experimental data. The numerical predictions for the breaking height, the breaking depth and the free-surface elevation dissipation in the surf zone agree very well with the corresponding measurements. The model predicts the vorticity generation in the breaking face of the wave and the appearance of the undertow current in the surf zone. The predicted shear of the undertow current is higher than the measured one.