On the structure of granular jumps: The dynamical systems approach

Abstract

Jumps in granular chute flow are obtained as continuous solutions of the properly adapted Saint-Venant equations. We elucidate their internal structure via a dynamical systems approach and show that the jumps in phase space manifest themselves as trajectories organized around the stable/unstable manifold of the fixed point representing the uniform flow. Based on this, we derive an analytic approximate expression for the jump length. The paper concludes with a numerical experiment confirming the stability of the jumps.