### 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 Slnn 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 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 ∆Q = Qc- Q > 0
the flow can be unstable. For small values of ∆Q 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 ∆Q, 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 ∆Q 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 aiongshore 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 ∆Q. 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 ∆Q
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 ∆Q. The results show that topographic variability has
a significant influence on nearshore circulation.