On the advective and diffusive heat balance in the interior of a subtropical ocean

An exponential solution to the thermoeline equations is scaled and calibrated for the intermediate circulation in middle latitudes of the open ocean in accordance with the scaling and results of the more complete numerical models of Bryan & Cox. Evaluation of the average potential vorticity for a number of stations is a main feature of the calibration method. The results of tests on the calibrated model in which the wind stress parameter E is varied show good qualitative agreement with the published numerical results for the region in which the analytical model is valid.

The effects of varying the vertical thermal diffusion parameter K are investigated. A significant feature of the results is the lack of appreciable difference in temperature distributions for the cases when E = K = 1 (the reference case) and E = 1, K = 0 (the purely advective case). The relative sizes of terms in the heat-balance equation are investigated. It is shown that the dominant balance near the surface (but beneath the frictional layer) is between horizontal and vertical advection if the ratio E/KC > 1 where C is the dimensionless thermocline scale parameter evaluated from the potential vorticity equation. The value of the above ratio is approximately 5 in the reference case. For all values of the parameters it is shown that the ratio of horizontal advection to vertical diffusion is not less than one just beneath the surface layer in middle latitude regions of surface downwelling.