Bore-driven swash on a mobile beach - Kelly, David M. (2009)
The problem of cross-shore beach face evolution in the swash zone is examined within the framework of the shallow water theory. A system comprising the shallow water and Exner equations is solved numerically using both uncoupled and fully coupled approaches. The uncoupled model assumes that changes in bed height have a negligible effect on the flow over a swash event, whereas the fully coupled model updates the hydrodynamic variables and beach profile simultaneously. In order to obtain accurate results over a single swash event several new numerical solvers based on the method of characteristics (MaC) and the MacCormack (1969) explicit finite-difference scheme are detailed. Particular attention is given to the treatment of discontinuities. A procedure for the explicit treatment of discontinuities, derived from techniques employed in gas dynamical problems, is developed and applied. Certain rather novel shock capturing approaches are also investigated. The shoreline boundary is discussed and a new robust algorithm for the treatment of this boundary on both fixed and mobile beds is presented. The resulting numerical models are used to simulate a variety of different swash events on an initially plane sloping mobile beach. Predictions of beach face evolution are made using the fully coupled approach and are compared with predictions made using an uncoupled analytical beach evolution model based on that of Pritchard and Hogg (2005). The fully coupled model leads to some interesting observations, in particular the possibility of local onshore sediment transport and the occurrence of a seaward facing sediment bore in the backwash. A characteristics based analysis is performed and reveals important differences in the flow structure of coupled and uncoupled swash events. The maximum wave run-up is also considered and it is shown that for the fully coupled system the run-up is significantly less than that predicted by the Shen and Meyer (1963) theory and motion of the leading edge can no longer be determined using simple ballistics concepts. Additionally, for verification purposes, new quasi-analytical solutions are constructed for the mobile bed dam-break problem using two distinct sediment transport formulae.