2000 Alongshore currents over variable beach topography

Abstract. The nonlinear dynamics of unstable alongshore currents in the nearshore surf zone over variable barred beach topography are studied using numerical experiments. These experiments extend the recent studies of Allen et al. [1996] and SImm et al. [1998], which utilized alongshore uniform beach topographies by including sinusoidal alongshore variation to shore parallel sandbars. The model involves finite difference solutions to the nonlinear shallow water equations for forced, dissipative, initial value problems and employs periodic boundary conditions in the alongshore direction. Effects of dissipation are modeled by linear bottom friction. Forcing for the alongshore currents is provided by gradients in the radiation stress, which are specified using linear theory and the dissipation function for breaking waves formulated by Thornton and Cuza [1983]. Distinct flows develop depending on the amplitude c and wavelength A of the topographic variability and the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value Qa the flows are linearly stable. For Q =- Q> 0 the flow can be unstable. For small values of Q the effect of increasing is t