A surface density and wind‐driven model of the thermocline

Abstract

A simple analytical model is used to determine the density and flow fields in the subtropical gyre. The flow, which is taken to be steady, nondiffusive, and in geostrophic balance, is driven by a vertical velocity induced by the overlying convergent Ekman layer and a specified surface density field. The thermocline region, in which the density increases continuously with depth, overlies a stagnant homogeneous layer. It is shown that if the surface density increases monotonically to the north along the eastern boundary, where the zonal transport is taken to vanish, then the thermocline depth increases monotonically to the north; this implies westward flow (outflow) at the eastern boundary near the thermocline base with compensating inflow occurring higher in the water column. Although the model is formulated for a general specified surface density field, some general conclusions are reached for surface density fields which vary with latitude alone. It is shown that in this case the simplest and possibly the only choice of the potential vorticity is a function of density divided by the Bernoulli function. For this potential vorticity function, density profiles are similar at each latitude, and the potential vorticity is a minimum at the core of recirculating regions. A specific surface density field is then considered, and a solution is obtained in terms of Bessel functions for the density and pressure field. The results show that for submerged surfaces there is a transfer of water from the eastern to the western boundary along the southern boundary of the gyre, with a clockwise recirculating gyre elsewhere. For outcropped isopycnal surfaces, downwelling into the western boundary is the primary transport mode, with recirculation and east to west transport playing secondary roles. Finally, the relation of this model to layered models is discussed.