Velocity moments in alongshore bottom stress parameterizations

The time-averaged alongshore bottom stress is an important component of nea rshore circulation models. In a widely accepted formulation the bottom stre ss 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 fluctuatin g (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 usuall y 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 ne ar-bottom currents observed between the shoreline and 8-m water depth are u sed 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 arro w\v > for moderately strong alongshore currents, resulting in overestimatio n of a drag coefficient determined by fitting modeled (with a linearized bo ttom 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 a rrow\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 alo ngshore 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 > a re shown to be more accurate than the linear parameterizations and are adeq uate for many modeling purposes.