On the structure of granular jumps: the dynamical systems approach

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.

Automated summary

In this paper, jumps in granular chute flow are obtained as continuous solutions of the Saint-Venant equations. The internal structure of these jumps is elucidated through a dynamical systems approach, showing trajectories organized around the stable/unstable manifold of a fixed point. An analytic approximate expression for jump length is derived, with numerical experiments confirming jump stability.