On the modelling of short and intermediate water waves

TL;DR

This paper develops a nonlinear, nonlocal model for short and intermediate water waves in finite depth, extending beyond the long-wave KdV regime, with implications for numerical analysis.

Contribution

It introduces a new Hamiltonian-based model for water waves of finite depth that captures short and intermediate regimes, not covered by traditional long-wave models.

Findings

Derivation of a nonlinear, nonlocal wave model

Discussion on numerical solution implications

Extension beyond the KdV long-wave approximation

Abstract

The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.