Non-Hydrostatic Dam Break Flows II: One-Dimensional Depth-Averaged Modeling for Movable Bed Flows

Abstract

The dam break flow over a movable bed is an important problem in fluvial flow processes. These flows are usually predicted by a one-dimensional (1D) approach based on a hydrostatic pressure distribution. Recent 3D non-hydrostatic simulations of dam break waves over movable beds based on the Reynolds-averaged Navier-Stokes (RANS) equations revealed that Saint Venant theory is not accurate predicting the flow dynamics within the scour hole developed. In this work a generalized 1D non-hydrostatic model for flow over movable beds is proposed assuming a linear, non-hydrostatic, pressure distribution. The new set of 1D equations account for the vertical acceleration, which is important in dam break waves over movable beds, given the instantaneous curved beds generated over the erodible terrain. These equations account for both the bed- and suspended-load transport modes. A high-resolution finite volume numerical scheme with a semi-implicit treatment of non-hydrostatic terms is developed to solve the governing equations, producing solutions that are in good agreement with 3D computational results and experimental data. The free surface profiles predicted by the new model show a significant improvement as compared to those obtained from the existing hydrostatic simulations. The unsteady non-hydrostatic simulations are further demonstrated to be convergent to steady flow solutions with non-hydrostatic pressure.