Dam-break reflection

Abstract

Summary The unsteady reflection of dam-break flow along a horizontal channel by a remote barrier is modelled using the nonlinear shallow water equations. The interaction generates an upstream moving bore that connects the collapsing reservoir of fluid to a rapidly deepening fluid layer adjacent to the barrier. These motions are modified when the fluid is released into a channel containing a pre-wetted layer, because the oncoming flow is itself headed by a bore that alters the initial reflection. Solutions for these flows are calculated using quasi-analytical techniques that utilise the method of characteristics and the hodograph transformation of the governing equations, and the results are validated by comparison with direct numerical integration of the shallow water equations. The analytical solutions enable the precise identification of dynamical features in the flow, including the onset and development of discontinuous solutions that are manifest as bores, as well as their long term behaviour, the rate at which energy is dissipated, and for flows generated from the release of a finite reservoir, the maximum depth of the fluid layer at the barrier.