Green-Naghdi and related models for shallow water waves (Mathematical Analysis in Fluid and Gas Dynamics)

Abstract

We develop a systematic procedure for extending the two-dimensional Green-Naghdi (GN) model to include higher-order dispersive effects, and present various model equations for both flat and uneven bottom topographies. We derive the linear dispersion relation for the extended GN models to explore the well-posedness of the linearized problem. Last, we show that these models permit the same Hamiltonian formulation as that of the original GN model.