The Richard Gavrilyuk model refines the familiar Saint Venant model by the addition of internal vorticity effects, correcting from first principles overshoot phenomena observed in the 60's by Brock. This adds technical complications however, both to existence and stability analyses as we discuss here. Most important perhaps is a subtle instability in a special limit of parameter space, that appears relevant to physically observed ``toe oscillations'' in hydraulic jumps or weirs.