A conceptual model for sheet-flow drawn from rapid granular flow theories

Abstract

This paper is aimed at presenting i) a simple, yet sound, conceptual model applicable to the simulation of erosion, deposition and transport of cohesionless sediment in stratified flows under high shear stresses and ii) numerical solutions in idealized unsteady flow non-equilibrium transport situations. The conceptual model for the granular phase comprises 2DV mass and momentum and energy equations and constitutive equations, all derived within the dense limit of the Chapman-Enskog kinetic theory. 1D shallow-flow conservation and closure equations are derived for the fluid-granular mixture. Formulas for the average velocity in the transport layers, the vertical net flux of sediment mass and the thickness of the transport layer are thus obtained. Numerical solutions for dam-break flows over cohesionless mobile beds in prismatic and non-prismatic channels are obtained and discussed.