28 



constant. For a value of ic equal to 5 cm^/s the change in Rosshy number 

 would correspond to a change in the north-south temperature contrast from 

 9° to 36°- Note that this large change does not appear to have a corres- 

 pondingly large effect on the nondimensional heat transport. The three 

 solid curves in Figure 2 are for the cases in which R^^ is equal to 1000. 

 The dotted curve represents a single test calculation made for R^ equal to 

 2x10-5 and Rj equal to 100. The total depth, D, appears only in R-l. The 

 test calculation shows that beyond a certain point, the purely thermal 

 solution is insensitive to the total depth. A similar result has been 

 obtained previously in the thermocline calculations of Stommel and Webster 

 (1962). 



Figure 3 shows vertical sections made for a zonal and meridional plane 

 cutting the basin. The temperature has been normalized by dividing it by 



Ae* • Note that the isotherms are fairly flat over most of the basin. 

 Exceptions occur near the western boundary in a narrow zone, and in the 

 northern part of the basin. The upturned isotherms near the western wall 

 are associated with an intense, northward moving boundary current. A much 

 slower, but deeper compensating current moving southward exists below. This 

 western boundary current differs from that of the wind-driven ocean theories 

 (stommel, 19^+8) in that the net, vertically integrated mass transport is 

 zero. This 1ype of boundary current associated with the thermohaline circula- 

 tion has been anticipated by Stommel (1958, page 157) in his prediction of 

 an undercurrent in the vicinity of the Gulf Stream. Analytic solutions have 

 been obtained only from a simplified linear model by Takano (1962). 



Another set of calculations similar to those shown in Figure 2 indicate 

 that h/E* depends markedly on the Reynolds number only in the range 

 < Rg < 10. For larger Reynolds numbers horizontal mixing plays a rather 

 small role in the poleward heat flux. Through an extrapolation of the 

 results, it is estimated that the equilibrium value of E/H* for very large 

 values of Reynolds numbers would be approximately .2, assuming that R-j^= 100 

 and the Rossby number is in the geophysical range. The oceaxiographic 

 interpretation of this result is shown in Figure h. Assuming that E/E* is 

 0.2, the total poleward heat flux is given as a function of the vertical 

 diffusion coefficient, < , and the total meridional temperature difference 

 imposed at the surface . The Atlantic Ocean is known to have a direct 

 thermal-haline circulation. For a rough comparison of heat transport in 

 the model with observ9.tions we note from Figure 1 that the poleward flux 

 at 1+5° latitude in the North Atlantic is about 2x10 cal/s. Allowing for 

 the effect of salinity, a north-south virtual temperature difference of 

 l8°C is in best agreement with surface temperature data. From Figure U we 

 see that a vertical diffusion of 5, cm /s would be required for the model to 

 have a poleward heat flux of 2x10*'-^ cal/s. This is a reasonable value of 

 K , since independent empirical estimates based on water mass analysis are 

 all of the order of unity (Robinson and Stommel, 1959) • 



In the lower part of Figure k the strength of the thermohaline circula- 

 tion is plotted, also based on an extrapolation of the numerical results to 

 the case of very high Reynolds numbers. The total rate of overturning in 



