Velocity moments in alongshore bottom stress parameterizations

The time-averaged alongshore bottom stress is an important component of nearshore circulation models. In a widely accepted formulation the bottom stress is proportional to < \(u) over right arrow\v >, the time average of the product of the instantaneous velocity magnitude \(u) over right arrow\ and the instantaneous alongshore velocity component v. Both mean and fluctuating (owing to random, directionally spread waves) velocities contribute to < \(u) over right arrow\v > Direct estimation of < \(u) over right arrow\v > requires a more detailed specification of the velocity field than is usually available, so the term < \(u) over right arrow\v > is parameterized. Here direct estimates of < \(u) over right arrow\v > based on time series of near-bottom currents observed between the shoreline and 8-m water depth are used to test the accuracy of < \(u) over right arrow\v > parameterizations. Common < \(u) over right arrow\v > parameterizations that are linear in the mean alongshore current significantly underestimate < \(u) over right arrow\v > for moderately strong alongshore currents, resulting in overestimation of a drag coefficient determined by fitting modeled (with a linearized bottom stress) to observed alongshore currents. A parameterization based on a joint-Gaussian velocity field with the observed velocity statistics gives excellent overall agreement with the directly estimated < \(u) over right arrow\v > and allows analytic investigation of the statistical properties of the velocity field that govern < \(u) over right arrow\v > Except for the weakest flows, < \(u) over right arrow\v > depends strongly on the mean alongshore current and the total velocity variance but depends only weakly on the mean wave angle, wave directional spread, and mean cross-shore current. Several other nonlinear parameterizations of < \(u) over right arrow\v > are shown to be more accurate than the linear parameterizations and are adequate for many modeling purposes.