Modeling of Breaking and Nonbreaking Long-Wave Evolution and Runup Using VTCS-2

Abstract

We present a variable grid finite-differences approximation of the characteristic form of the shallow-water-wave equations without artificial viscosity or friction factors to model the propagation and runup of one-dimensional long waves, referred to as VTCS-2. We apply our method in the calculation of the evolution of breaking and nonbreaking waves on sloping beaches. We compare the computational results with analytical solutions, other numerical computations and with laboratory data for breaking and nonbreaking solitary waves. We find that the model describes the evolution and runup of nonbreaking waves very well, even when using a very small number of grid points per wavelength. Even though our method does not model the detailed surface profile of wave breaking well, it adequately predicts the runup of plunging solitary waves without ad-hoc assumptions about viscosity and friction. This appears to be a further manifestation of the well-documented but unexplained ability of the shallow water wave equations to provide quantitatively correct runup results even in parameter ranges where the underlying assumptions of the governing equations are violated.