Cross-shore variation of water surface elevation and velocity during bore propagation

Abstract

In this study, we have investigated the hydrodynamics of a turbulent bore generated by removing a gate suddenly with water impounded on one side. This bore generation method was referred to a general dam-break problem. In order to perform the numerical simulation of the bore formation and propagation, we considered the incompressible flows of two immiscible fluids, liquid and gas, governed by the Navier-Stokes equations. The interface between the two fluids (air and water) was tracked by the volume-of-fluid (VOF) technique, and the M-type Cubic Interpolated Propagation (MCIP) scheme was used to solve the Navier-Stokes equations. It is known that the MCIP method is a low diffusive and stable scheme and is generally extended the original one-dimensional CIP to higher dimensions, using a fractional step technique. A Large Eddy Simulation (LES) closure scheme, which is a cost-effective approach to turbulence simulation, was employed to predict the evolution of quantities associated with turbulence. In order to verify the applicability of this numerical model to the bore simulation, the simulation results were compared to the laboratory experimental data. The numerical model for the bore formation and propagation based on the two-phase fully nonlinear Navier-Stokes equations was well verified by comparing with the analytic model based on the fully nonlinear shallow water wave equations and the laboratory experimental results.