Surface Roller Model for the Numerical Simulation of Spilling Wave Breaking over Constant Slope Beach

Abstract

A surface roller model, which captures incipient breaking and postbreaking behavior, is presented for the numerical simulation of spilling breakers. It is based on the corresponding model used in conjunction with Boussinesq-type equations and is applied on the two-dimensional, inviscid but rotational, free-surface flow resulting from the propagation and breaking of regular waves over constant slope beach. The numerical solution of the Euler equations, subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions, is facilitated by a hybrid finite differences and spectral method scheme. Results are presented for beach slope values of 1/50, 1/35, and 1/20, and corresponding Irribaren numbers of 0.12, 0.20, and 0.30, respectively. Breaking depth d b , breaking wave height, and free-surface elevation envelope results are in very good agreement with available experimental measurements and indicate that empirical formulas underpredict both breaking wave height and breaking depth. At the breaking point, wave speed is equal to 1.2(gd b ) 1/2 , while the local Froude number increases with increasing Irribaren number. During postbreaking, the surface roller model generates appropriate vorticity at the breaking face of the wave but overestimates the undertow current in the surf zone.