Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems

TL;DR

This paper derives a non-hydrostatic shallow water model from Navier-Stokes equations, compares it with Saint-Venant and Boussinesq systems, and discusses different approximation levels for fluid pressure.

Contribution

It introduces a new non-hydrostatic model for shallow waters and compares it with existing Saint-Venant and Boussinesq models, highlighting differences based on pressure approximation.

Findings

Derived two formulations of the non-hydrostatic model.

Compared the new model with Boussinesq systems.

Analyzed the impact of pressure approximation levels.

Abstract

From the free surface Navier-Stokes system, we derive the non-hydrostatic Saint-Venant system for the shallow waters including friction and viscosity. The derivation leads to two formulations of growing complexity depending on the level of approximation chosen for the fluid pressure. The obtained models are compared with the Boussinesq models.