Dynamics of avalanches along general mountain slopes

A continuum dynamical hydraulic model for the flow of a finite mass of cohesionless shallow granular material down an inclined plane was proposed by Savage and Hutter (SH) in 1989. This model consists of depth-averaged equations for the time and space evolution of the velocity profile and the avalanche depth. Their model was generalized to incorporate more complicated topography in which the coordinate lines in the downhill direction are curved but not twisted. We present recently developed model equations by Pudasaini and Hutter for free-surface geophysical gravity-driven flows (e.g.avalanches, debris and pyroclastic flows) down complicated realistic mountain terrain generated by arbitrary space curves with slowly varying curvature and torsion. These are very important extensions to the successful SH theory, which incorporate curvature and torsion effects of the sliding surface. Shock-capturing numerical schemes are used to integrate the hyperbolic conservation system of equations. The physical significance of the numerical solutions is discussed