Nonlinear shear instabilities of alongshore currents over barred beaches

Abstract

The nonlinear dynamics of finite amplitude shear instabilities of alongshore currents in the nearshore surf zone over barred beach topography are studied using numerical experiments. These experiments extend the recent study of Allen et al. [1996], which utilized plane beach (constant slope) topography by including 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 specified using a model formulated by Thornton and Guza [1986] (T-G). Distinct classes of flows develop depending on the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value Q(C) the flows are linearly stable. For ΔQ = Q(C) - Q > 0 the flow is unstable. For small values of ΔQ, equilibrated shear waves develop that propagate alongshore at phase speeds and wavelengths that are in agreement with predictions from linear theory for the most unstable mode. At intermediate values of ΔQ, unsteady vortices form and exhibit nonlinear interactions as they propagate alongshore, occasionally merging, pairing, or being shed seaward of the sandbar. At the largest values of ΔQ examined, the resulting flow field resembles a turbulent shear flow. A net effect of the instabilities at large ΔQ is to distribute the time-averaged alongshore momentum from local maxima of the T-G forcing, located over the sandbar and near the shore, into the region of the trough. The across-shore structure of the time-averaged alongshore current is in substantially better qualitative agreement with observations than that given by a steady frictional balance with T-G forcing. The results point to the possible existence in the nearshore surf zone of an energetic eddy field associated with instabilities of the alongshore current.