| Geophysical flows such as avalanches, rock slides and debris flows are
a major hazard in many mountainous region. Accurate, physically based
models are important for the design of defensive structures and hazard
zoning. Such flows contains particles of many sizes and the vertical
distribution of these particles can significantly influence the
dynamics. We introduce a new class of shallow-water granular flow
models that includes equations for the vertical distribution of the
different particle types. We compare this model with Discrete Element
Method simulations and show that they are in excellent agreement with
the theory. |