Granular flows in a rotating drum and on an inclined plane: Analytical and numerical solutions

Snow avalanches and debris flows can be characterized by dry granular and grain-liquid mixture flows down a slope. To describe such flows, we investigate a dry granular flow in a rotating drum that follows the sense of the flow down an infinitely long slope and a semi-infinite volume of the grain-liquid mixture flow down an inclined plane that is a simplified but helpful configuration for debris flows by means of analytical tools and direct numerical simulation. Particularly, a semi-exact solution at the steady state can be achieved in a dry granular flow in a rotating drum. Such a solution can provide intuitively reasonable results and can reproduce an asymmetry profile for the depth commonly observed in the experiment. A direct numerical simulation from a static initial state until the steady state is performed further by applying a high-resolution non-oscillatory scheme to investigate more complex transient behaviours and verify the semi-exact solution derived here. Furthermore, for the case of a grain-liquid mixture flow down an inclined plane, an analytical solution has been derived by combining characteristic method with similarity transformation. The phenomenon that the mass bodies of debris flows are constantly stretched can be accounted for by the analytical solution. Additionally, it is found that the elongated phenomenon is not affected by the granular bed friction angle, but it is affected by the slope angle. Furthermore, a direct simulation is performed as well to enhance understanding and verify the analytical solution.