Convective-Wave Solutions of the Richard–Gavrilyuk Model for Inclined Shallow-Water Flow

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 discontinuities 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.