Dispersion-improved fully nonlinear shallow water model

Abstract eng:
We propose a variant of the fully-nonlinear weakly-dispersive Serre–Green–Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. Contrary to other models of this kind found in the literature, the one proposed here conserves the energy, thanks to the approximation procedure based on a variational principle. In addition to improved dispersion properties, the new model admits limiting waves with angular crests. Numerical comparisons with the Euler equations show that the new model is substantially more accurate than the classical Serre equations, specially for long time simulations and for large amplitudes.

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