Waves impinging on beaches induce mean flows, such as longshore and rip currents. This nearshore circulation is of fundamental importance in the study of the transport of nearshore contaminants as well as littoral materials. Analytic models of this nearshore flow {see, e.g. 4, 9, 11, 12) have been constrained to be linear (in the governing equations) and simplistic in the bottom topography. Only recently have numerical models been developed to examine more complex situations. Steady state, finite difference models (1, 14), as well as a finite element model (10), have been proposed. The numerical model, developed by Birkemeier and Dalrymple (1), allowed for time dependency. Yet, in all of these cases, the governing equations have not included the nonlinear convective accelerations or lateral mixing terms. In this study, a nonlinear numerical model is presented based on a leapfrog finite difference scheme, which includes time dependency and eddy viscosity terms. Results are shown for a planar beach showing a comparison with the analytical longshore current models (with and without lateral mixing) of Longuet-Higgins (11, 12). The longshore current over a prismatic beach profile including an offshore bar is presented next, showing the effects of the bar on the velocity profile. The circulation set-up by a rip channel inset into a plane beach is then computed. A comparison is made to the linear model of Birkemeier and Dalrymple. Finally the model is applied to the case of synchronous intersecting wave trains (4). An interesting result occurs when the waves are of different amplitudes, which could provide an explanation of the formation of finger bars on a beach.
NUMERICAL MODELLING OF NEARSHORE CIRCULATION
