Continuum description of avalanches in granular media

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation, which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes [A. Daerr and S. Douady, Nature (London) 399, 241 (1999)]: layer bistability, and transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propagating uphill for larger angles.