Peregrine's system revisited

TL;DR

This paper revisits Peregrine's long wave model, proposing an invariantized modification that enhances stability and symmetry, improving computational efficiency for wave run-up simulations.

Contribution

It introduces an invariantized modification of Peregrine's system that maintains asymptotic similarity and improves numerical stability in shallow water wave modeling.

Findings

The modified system preserves key symmetries of the water wave problem.

It has well-conditioned dispersive terms in the swash zone.

Enables efficient and stable run-up computations.

Abstract

In 1967 D. H. Peregrine proposed a Boussinesq-type model for long waves in shallow waters of varying depth. This prominent paper turned a new leaf in coastal hydrodynamics along with contributions by F. Serre, A. E. Green \& P. M. Naghdi and many others since then. Several modern Boussinesq-type systems stem from these pioneering works. In the present work we revise the long wave model traditionally referred to as the Peregrine system. Namely, we propose a modification of the governing equations which is asymptotically similar to the initial model for weakly nonlinear waves, while preserving an additional symmetry of the complete water wave problem. This modification procedure is called the invariantization. We show that the improved system has well conditioned dispersive terms in the swash zone, hence allowing for efficient and stable run-up computations.