  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.
