Application of a Non-Linear Shallow Water Theory to Swash Following Bore Collapse on a Sandy Beach

Abstract

The non-linear shallow water theory is believed to be capable of describing many features of wave behaviour in the coastal zone. A set of solutions to the governing equations exists for swash following bore collapse on a hydraulically smooth and impermeable beach. These solutions predict that the maximum swash height is proportional to the square of the initial shoreline velocity, the locus of shoreline position through time is parabolic, the maximum swash depth at any position on the beach is a quadratic function of its distance from the initial shoreline position, the maximum swash depth at any position on the beach occurs before the time of maximum uprush, and a retrogressive bore forms in the backwash. All of these predictions have been observed in field data collected from a number of sandy beaches in southeast Australia. However, the theory consistently over-predicted the magnitude of the parameters measured. Evidence is presented to suggest that this discrepancy is due to the effects of friction and infiltration acting on the swash lens, which are not initially accounted for in the theory. If the available evidence is accepted, then the combined effects of friction and infiltration on a sandy beach serve to reduce the maximum swash height to approximately 65% of that expected from theory. Aside from the theoretical over-prediction of the magnitude of the swash parameters measured, the gross flow behaviour of the uprush on a rough and permeable beach face appears to be successfully described by the inviscid theory. There is some promise, therefore, for successfully modelling the effects of friction and infiltration within the framework provided by the theory. Unfortunately the backwash stage of the swash cycle is not so well predicted. It seems that a better understanding of both the backwash bore and the behaviour of granular-fluid flows is required before the backwash is successfully modeled.