The Wind-Driven Shelf and Slope Water Flow in Terms of a Local and a Remote Response

Abstract

Clarke and Van Gorder suggest that many coastally trapped wave modes are needed to describe the wind­ driven shelf and slope water alongshore velocity field. Calculations with an harmonic wind forcing confirm this and show that, for example, the alongshore velocity field is usually underestimated by using only three coastally trapped wave modes. This is a serious drawback in the forced-wave mode method since it is difficult to calculate the many needed higher order modes. Fortunately large mode-number coastally trapped wave asymptotics also suggest that these higher order modes are effectively generated by just the local wind. Both computationally and physically, it is therefore convenient to regard the velocity field as being due to a two dimensional “local” solution which depends only on local winds and a “remote” solution driven by the alongshore pressure gradient and depending on non-local wind stress. To compute such a “Local Plus Remote” solution at a given coastal cross section, the alongshore pressure gradient forcing must be known. It can be accurately estimated by the forced coastally trapped method with a few lower order modes because the alongshore pressure gradient is due to nonlocal effects and the higher order modes are primarily locally determined. For illustrative purposes, calculations were carried out for a very wide shelf (the West Florida shelf) and a much narrower shelf (the Coastal Ocean Dynamics Experiment shelf off California). Although the theory can be applied directly for general large-scale wind forcing, for ease of illustration sinusoidal wind forcing was used. Results for these markedly different shelves confirmed the ability of the Local Plus Remote method to accurately estimate the alongshore velocity field using a pressure gradient force estimated with only coastally trapped wave modes I, 2, and 3. For accurate pressure, it was necessary to include mode 0, the barotropic deep-sea nondivergent Kelvin wave.