Dynamically consistent entrainment laws for depth-averaged avalanche models

摘要: The bed entrainment rate in a gravity mass flow (GMF) is uniquely determined by the properties of and flow. In depth-averaging, however, critical information on variables near lost empirical assumptions usually are made instead. We study interplay between assuming perfectly brittle bed, characterized its shear strength ${\it\tau}_{c}$ , erosion along bottom surface flow; frontal neglected here. brittleness assumption implies that stress at cannot exceed . For quasi-stationary flows simplified setting, analytic solutions found for Bingham frictional–collisional (FC) fluids. Extending this theory to non-stationary requires some velocity profile. fluid, profile ‘proxy’ eroding used; rheological parameters chosen match instantaneous shear-layer depth FC two-parameter family functions closely profiles obtained depth-resolved numerical simulations assumed; boundary conditions determine parameter values allow computation rate. Preliminary tests with formula incorporated simple slab model indicate matches asymptotically, but differs start-up phase. formulae valid only up limit (and if there Coulomb friction). This appears mark transition another regime – be described different where chunks material intermittently ripped out gradually entrained into