A Model of Wind- and Buoyancy-Driven Ocean Circulation

Abstract

A layered model of steady geostrophic ocean circulation driven by wind stress and buoyancy flux at the surface is derived. Potential vorticity, or thickness, of the two near-surface layers is driven by Ekman pumping and buoyancy pumping. The latter is represented as a flow of mass proportional to the modified buoyancy flux, across the first submerged layer interface. This mass flux is modified by the advection of buoyancy in the wind-driven Ekman layer. Though diffusive diapycnal buoyancy flux across deeper layers is neglected at lowest order, it is essential for the global balance of the buoyancy budget. The global buoyancy balance requirement determines such parameters as the midocean outcrop latitudes of layers that outcrop in the subtropical gyre, and the depths of interfaces at the eastern boundary of layers that do not. These parameters control the mean thicknesses of the layers and, with the diapycnal diffusivity, the mean diffusive flux of buoyancy through each active layer. In this way the area-mean stratification is determined by the wind-driven circulation and the surface buoyancy flux. Model solutions were computed for two idealized runs differing only by the amplitude of buoyancy forcing In run A, the surface buoyancy flux was chown to give a meridional buoyancy transport equivalent to 0.15 PW (1 PW = 1 petawatt) across the subtropical-subarctic gyre boundary. In run B, the buoyancy forcing was adjusted to give an intergyre meridional buoyancy transport equivalent to 0.51 PW. In both runs diapycnal diffusivities in the layers were held at O(10?4 m2 s?1). These two runs gave density contrasts over the active layers of 8 kg m?3 (run A) and 18 kg m?3 (run B). The latter is an extremely large figure compared to the maximum density contrast across the ocean pycnocline observed in nature. The author concludes that the ocean cannot accomplish meridional buoyancy transport equivalent to O(1 PW), while diapycnal diffusivities are O(10?4 m2 s?1) and density gradients across the pycnocline are ?O(4 kg m?3/1000 m). It is necessary for global buoyancy and heat balance that there are regions in the oceans with far larger diapycnal diffusivities than O(10?4 m2 s?1). Likely candidates for such regions are the upper layers of the ocean, where extremely powerful mixing can be driven by surface wind stirring and convection, and the high-energy zones of the western boundary currents.