Peregrine's system revisited
For coastal engineers and modelers, this provides a numerically stable variant of a classic model for wave run-up, though the improvement is incremental.
The paper modifies the classical Peregrine Boussinesq model for long waves in shallow water to preserve an additional symmetry of the full water wave problem, resulting in well-conditioned dispersive terms in the swash zone that enable efficient and stable run-up computations.
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.