Alongshore currents over variable beach topography
Authors: Slinn Donald N. , Allen J. S. , Holman R. A. 
Published: February 2004

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 Slinn 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 Guza [1983]. Distinct flows develop depending on the amplitude ∈ and wavelength λ 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 QC the flows are linearly stable. For ΔQ = QC ‐ Q>0 the flow can be unstable. For small values of ΔQ the effect of increasing ∈; is to stabilize or regularize the flows and to cause the mean flow to approximately follow contours of constant depth. Equilibrated shear waves develop that propagate along the mean current path at phase speeds and wavelengths that are close to predictions for the most unstable mode from linear theory applied to alongshore‐averaged conditions. At intermediate values of ΔQ, unsteady vortices form and exhibit nonlinear interactions as they propagate along the mean current path, occasionally merging, pairing, or being shed seaward of the sandbar. Eddies preferentially form in the mean current when approaching alongshore troughs of the sandbar and break free from the mean current when approaching alongshore crests of the sandbar. At the largest values of ΔQ examined the resulting flow fields resemble a turbulent shear flow and are less strongly influenced by the alongshore variability in topography. As the amplitude of the alongshore topographic variability increases, alongshore wavenumber‐frequency spectra of the across‐shore velocity show a corresponding increase in energy at both higher alongshore wavenumbers and over a broader frequency range with significant energy at wavenumbers of topographic variability and harmonics. Across‐shore fluxes of mass and momentum generally increase with increasing topographic amplitude and increasing ΔQ. Time‐ and space‐lagged correlations of the across‐shore velocity show that correlation length scales decrease as topographic perturbation amplitudes increase. Terms from the vorticity equation show that the alongshore variation of the radiation stresses and the value of ΔQ are of importance to the flow behavior. Hybrid experiments separating effects of spatially variable forcing and the dynamic influence of topography on time‐averaged currents show that the effects are generally comparable with the relative importance of each effect a function of ΔQ. The results show that topographic variability has a significant influence on nearshore circulation.