Jy. Sheng et Kr. Thompson, A MODIFIED GALERKIN-SPECTRAL MODEL FOR 3-DIMENSIONAL, BAROTROPIC, WIND-DRIVEN SHELF CIRCULATION, J GEO RES-O, 98(C4), 1993, pp. 7011-7022
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. Th
e basic idea behind Heaps' approach is to express the horizontal flow,
u(x, y, z, t), as a linear combination of vertical structure function
s, phi(r)(z), and then solve numerically for the temporally and horizo
ntally varying coefficients. To obtain an accurate representation of w
ind-driven flow, many phi(r) are often required. Following Lardner, we
reduce this number by subtracting from u an analytically defined flow
field, u(P), prior to its expansion in terms of the phi(r). Our choic
e of u(P) is steady Ekman flow in water of finite depth. This particul
ar choice includes, as a special case, the u(P) used by Lardner. Using
an idealized basin and time-harmonic wind forcing, we compare the con
vergence rate of the expansion of u - u(P) with u(P) taken to be (1) z
ero, corresponding to Heaps' approach, (2) flow with, constant horizon
tal shear stress through the vertical, corresponding to Lardner's rece
nt suggestion, and (3) steady Ekman flow. We find that removal of stea
dy Ekman flow generally leads to the most rapid convergence, particula
rly when the water depth is much greater than the Ekman depth, a condi
tion often found on the middle and outer continental shelf.