Riemann wave description of erosional dam-break flows

Abstract

This work examines the sudden erosional flow initiated by the release of a dam-break wave over a loose sediment bed. Extended shallow-water equations are formulated to describe the development of the surge. Accounting for bed material inertia, a transport layer of finite thickness is introduced, and a sharp interface view of the morphodynamic boundary is adopted. Approximations are sought for an intermediate range of wave evolution, in which equilibration of the sediment load can be assumed instantaneous but momentum loss due to bed friction has not yet been felt. The resulting homogeneous hyperbolic equations are mathematically tractable using the Riemann techniques of gas dynamics. Dam-break initial conditions give rise to self-similar flow profiles. The wave structure features piecewise constant states, two smoothly varied simple waves, and a special type of shock: an erosional bore forming at the forefront of the wave. Profiles are constructed through a semi-analytical procedure, yielding a geomorphic generalization of the Stoker solution for dam-break waves over rigid bed. For most flow properties, the predictions of the theoretical treatment compare favourably with experimental tests visualized using particle imaging techniques.