Numerical modeling of slope flows entraining bottom material

Entrainment of bottom material has a substantial influence on the dynamics of slope flows such as snow avalanches and debris flows, and should therefore be taken into account by mathematical models. An approach based on the assumption that the entrainment takes place when the bed shear stress is equal to the shear strength of the bottom material was proposed by Issler and Pastor Pérez (2011). In this paper, this approach is applied to model laminar flows of Bingham and Herschel–Bulkley fluids as well as turbulent flows with entrainment. Full (not depth-averaged) equations are used to calculate the flow parameters including the shear stress at the bottom, the velocity profile and the flow depth variation with time due to entrainment. The paper focuses on studying of qualitative features of motion with basal entrainment. Modeling of real flows from start to stop is not considered here. shown that in entraining flows moving down long constant slopes the flow velocity increases. The velocity profiles in laminar flows described by Bingham and Herschel–Bulkley models at large time become almost linear except in a relatively narrow layer near the upper flow surface and the entrainment rate tends to a constant value. This value depends on the coefficients describing the flow material properties, the shear strength of the bottom material, and the slope angle. Asymptotic formulae for the entrainment rate and the shear rate in the linear part of the velocity profile are derived analytically and confirmed by numerical calculations.