Abstract
The effect of nonlinearity on the evolution of free edge waves is investigated by solving numerically the nonlinear shallow water equations. The numerical scheme is the two-dimensional WAF method, originally developed by Toro [Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1997]. First, a simple beach geometry [J. Fluid Mech. 381 (1999) 271] is considered and the numerical results are validated against available analytical solutions for small amplitude edge waves. Then, results are obtained for edge waves of larger amplitude. Nonlinear effects are found to be relevant even for moderate values of the nonlinearity parameter a which is the ratio between the wave amplitude and the water depth. In particular a resonance phenomenon has been observed which causes a modulation in time of the ultra-harmonic components of the wavefield. Larger values of a lead to a complex time evolution.
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