Analysis of stability of a thin layer of granular material moving on an inclined plane

The stability of a layer of a granular medium on an inclined plane has been studied within the framework of the model of a non-Newtonian fluid with an index of 2, which ensures the experimentally found quadratic dependence of the shear stress on the shear rate. It is shown analytically and numerically that these flows are stable or unstable depending on the value of the generalized Reynolds number relative to the critical value equal to 5 $\operatorname{ctg}\alpha$.