A modified galerkin-spectral model for three-dimensional, barotropic, wind-driven shelf circulation

Abstract

The authors describe an efficient numerical scheme for calculating wind-driven currents on the continental shelf. Our scheme is based on the spectral approach introduced by Heaps and subsequently modified by Lardner. The basic idea behind Heaps' approach is to express the horizontal flow, u(x, y, z, t), as a linear combination of vertical structure functions, Phi sub(r)(z), and then solve numerically for the temporally and horizontally varying coefficients. To obtain an accurate representation of wind-driven flow, many Phi sub(r) are often required. Following Lardner, we reduce this number by subtracting from u and analytically defined flow field, u sub(p), prior to its expansion in terms of the Phi sub(r). Our choice of u sub(p) is steady Ekman flow in water of finite depth. This particular choice includes, as a special case, the u sub(p) used by Lardner. Using an idealized basin and time-harmonic wind forcing, we compared the convergence rate of the expansion of u-u sub(p) with u sub(p) taken to be zero, corresponding to Heaps' approach, flow with constant horizontal shear stress through the vertical, corresponding to Lardner's recent suggestion, and steady Ekman flow. We find that removal of steady Ekman flow generally leads to the most rapid convergence, particularly when the water depth is much greater than the Ekman depth, a condition often found on the middle and outer continental shelf.