Pairwise balancing of forces in traveling granular waves

A survey is given of the forces at work inside traveling roll waves and monoclinal flood waves in dry granular matter. By numerically solving the generalized Saint-Venant equations for shallow granular flow, we find a hierarchy of pairwise near-balancing forces, which together are responsible for sustaining the shape of the nonlinear waves in question. The leading force pair is gravity vs. friction, followed by inertia vs. pressure, while the minor imbalance left by the aforementioned pairs is settled by a (small though essential) diffusive force.