Convective-wave solutions of the Richard-Gavrilyuk model for inclined shallow water flow

TL;DR

This paper investigates convective-wave solutions in the Richard-Gavrilyuk model for inclined shallow water flow, revealing their role alongside hydraulic shocks in the structure of Riemann solutions.

Contribution

It introduces and analyzes convective-wave solutions in the Richard-Gavrilyuk model, extending classical shallow water equations to include vorticity effects.

Findings

Convective waves have constant fluid velocity equal to wave speed.

Fluid height and enstrophy vary across these waves.

They are crucial in the Riemann problem solution structure.

Abstract

We study for the Richard-Gavrilyuk model of inclined shallow water flow, an extension of the classical Saint Venant equations incorporating vorticity, the new feature of convective-wave solutions analogous to contact discontinuitis in inviscid conservation laws. These are traveling waves for which fluid velocity is constant and equal to the speed of propagation of the wave, but fluid height and/or enstrophy (thus vorticity) varies. Together with hydraulic shocks, they play an important role in the structure of Riemann solutions.