A Linear Balance Model of Wind-Driven, Midlatitude Ocean Circulation

Abstract

The Linear Balance Equations (LBE) are intermediate between the more familiar Quasi-geostrophic (QG) and Primitive Equations (PE) in both physical completeness and computational efficiency. We first present a consistent boundary-value problem for the LBE and its numerical implementation. Then we examine its solutions for equilibrium, adiabatic, wind-driven, midlatitude circulation in a rectangular ocean basin. They differ from analogous QG solutions in many respects, even for the moderately small Rossby number appropriate to this problem. The LBE solutions have 1) less total transport; 2) a broader, weaker, more surface-intensified mean Gulf Stream with sizable standing menders and a shorter penetration length into the basin interior; 3) an enhancement of the mean thermocline circulation and its associated mesoscale eddies in the subtropical gyre relative to the subpolar gyre; 4) an enhanced eddy generation rate by Reynolds stress work and a diminished generation rate by potential energy conversion; and 5) greater eddy energy in the Gulf Stream and neighboring recirculation zone but diminished eddy energy in the far field. These solution differences are due to the combined dynamical influences of both a more general form of the Coriolis force and the ageostrophic buoyancy advection in the LBE, with the former effect the more sizable in this problem. One can partially summarize the relations between LBE and QG solutions by stating that the dynamics of the former have an intrinsic meridional asymmetry, absent in the latter, which is the general source of many of the more specific differences.