Steady debris flows over erodible bed

Abstract

Recently, Berzi & Jenkins (2008a, b) proposed a simple theory based on a linear rheology for the particle interactions, turbulent shearing of the fluid, buoyancy, and drag. They provided a complete analytical description of the steady, uniform flow of a granular-fluid mixture over either an erodible or a rigid bed contained between frictional sidewalls. They also used the theory to solve for the propagation of a granular-fluid wave moving at constant velocity over a rigid bed. Here, we extend this theory to the case of a granular-fluid wave moving at constant velocity over an erodible bed contained between frictional sidewalls. This is indeed a natural step in view of a realistic mathematical description of a real debris flow that propagates over mobile surfaces, where erosion/deposition phenomena are likely to occur. We make comparisons with the experiments performed with water and gravel and show that the theory is able to reproduce the wave front and body.