Run-up flow of a collapsing bore over a beach

The collapse of a 2D bore propagating shoreward on a sloping beach and the subsequent run-up from the shoreline and run-down are simulated using a Reynolds Averaged Navier–Stokes (RANS) model based on a Volume of Fluid (VOF) method. The results are compared with experimental results. The bore collapse phenomenon is first studied and the transition between bore collapse and run-up is characterized. Numerical results indicate that the bore collapse phenomenon is not completed at the shoreline. The transition is further upslope and the energy at the transition includes a significant part of potential energy unlike that predicted by the classical theory of Whitham. The swash flow is investigated, showing the dissymmetry between run-up and run-down. Taking into account the modeling of turbulence slightly reduces the run-up height and allows recovering the value experimentally recorded. The bottom shear stress variations were computed from the results of numerical simulations. The maximum bottom shear stress is at any time found in the vicinity of the bore head. It is maximum at the transition between bore collapse and run-up flow and decreases while the run-up flow climbs on the beach.