Numerical modeling of downslope flows of different rheology

Abstract

Naturally occurring flow along a long homogeneous slope is numerically simulated. It is taken into account that the flow is able to capture the slope material and to entrain it into motion. The flow depth and velocity increase with time at the expense of the capture. The medium in motion is simulated using different rheological models including those of Herschel & Bulkley and Cross, as well as the power-law fluid model. For all the models the time dependences of the total depth and the mean flow velocity are obtained. The slope inclination effect on the dynamic flow parameters is studied. For the Herschel–Bulkley model the yield strength effect is also investigated. On the basis of the numerical calculations some assumptions are made and then used to derive asymptotic formulas for the bottom material entrainment rate at large times from the entrainment onset for all the above-listed rheological models.