Obliquely Incident Wave Reflection and Runup on Steep Rough Slope

Abstract

A two-dimensional, time-dependent numerical model for finite amplitude, shallow-water waves with arbitrary incident angles is developed to predict the detailed wave motions in the vicinity of the still waterline on a slope. The numerical method and the seaward and landward boundary algorithms are fairly general but the lateral boundary algorithm is limited to periodic boundary conditions. The computed results for surging waves on a rough 1:2.5 slope are presented for the incident wave angles in the range 0-80°. The time-averaged continuity, momentum and energy equations are used to check the accuracy of the numerical model as well as to examine the cross-shore variations of wave setup, return current, longshore current, momentum fluxes, energy fluxes and dissipation rates. The computed reflected waves and waterline oscillations are shown to have the same alongshore wavelength as the specified nonlinear incident waves. The computed variations of the reflected wave phase shift and wave runup are shown to be consistent with available empirical formulas. More quantitative comparisons will be required to evaluate the model accuracy.