A modified Galerkin‐Spectral model for three‐dimensional, barotropic, wind‐driven shelf circulation

Abstract

We 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, ϕr(z), and then solve numerically for the temporally and horizontally varying coefficients. To obtain an accurate representation of wind‐driven flow, many ϕr are often required. Following Lardner, we reduce this number by subtracting from u an analytically defined flow field, uP, prior to its expansion in terms of the ϕr. Our choice of uP is steady Ekman flow in water of finite depth. This particular choice includes, as a special case, the uP used by Lardner. Using an idealized basin and time‐harmonic wind forcing, we compare the convergence rate of the expansion of u − uP with uP taken to be (1) zero, corresponding to Heaps' approach, (2) flow with constant horizontal shear stress through the vertical, corresponding to Lardner's recent suggestion, and (3) 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.