  In the present study we discuss several modeling issues of powder-snow
avalanche flows. We take a two-fluid modeling paradigm. For the sake of
simplicity, we will restrict our attention to barotropic equations. We begin
the exposition by a compressible model with two velocities for each fluid.
However, this model may become non-hyperbolic and thus, represents serious
challenges for numerical methods. To overcome these issues, we derive a single
velocity model as a result of a relaxation process. This model can be easily
shown to be hyperbolic for any reasonable equation of state. Finally, an
incompressible limit of this model is derived.
