Numerical Simulation of Nonlinear Wave Propagation and Breaking Over Constant-Slope Bottom

The numerical simulation of the two-dimensional free-surface flow resulting from the propagation of nonlinear gravity waves over constant-slope bottom is presented. The simulation is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. Wave breaking is accounted for by a surface roller model. The formulation includes a boundary-fitted transformation and is suitable for future extension to incorporate large-eddy and large-wave simulation terms. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:50, and three different inflow wave heights. Over the bottom slope, waves of small wave heights are modified according to linear theory. For nonlinear waves, wavelengths are becoming shorter, the free surface elevation deviates from its initial sinusoidal shape and wave heights increase with decreasing depth. Breaking is observed for the cases with the larger initial wave height and the smaller outflow depth.