Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics

TL;DR

This paper introduces a modified Serre-Green-Naghdi model with a free parameter to enhance dispersion accuracy while conserving energy, outperforming classical equations in long-term and large-amplitude wave simulations.

Contribution

A novel energy-conserving variant of the Serre-Green-Naghdi equations with adjustable dispersion properties for improved shallow water wave modeling.

Findings

Enhanced dispersion characteristics with the new model.

Significantly better accuracy in long-term simulations.

Conservation of energy in the modified equations.

Abstract

For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. The novelty here consists in the fact that the new model conserves the energy, contrary to other modified Serre's equations found in the literature. 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.