2k 



A definition of V* axid d inay be obtained by combining these two 

 relationships . 



Scale analysis indicates that there are only three completely independ- 

 ent variables in the problem. A convenient formulation of these three 

 dimensionless variables is given below. An estimate of their approximate 

 magnitude in the case of the real ocean is also indicated. 



R = V*d2/(icL) '^ 100 



^e = V*L/A '\' 10 - 1000 



R = V*/2fiL "^ 10 



<-]_ ana k^ ' 



and horizontal, respectively. R^ is a Rossby number. The estimate of the 

 magnitude of the Rossby number is for the ocean interior. Much larger 

 values would be appropriate for the type of flow in the western boundary 

 current . 



A useful nondimensional form of the total poleward heat transport in 

 the basin is obtained by normalizing the calculated northward flux with 

 the amount of heat transferred down to greater depths from over an area, 

 L , through a vertical temperature gradient of Ae*/d. 



H/H* _ Poleward Heat Flux 

 icL2 Ae*/d 

 From general considerations 



H/H* = F (Ri, Rg, Rq, t) 



Numerical integrations of the model were performed to determine F as a 

 function of the independent parameters for which the model ocean 

 settled down to an equilibrium state . 



In most cases the initial conditions are a state of uniform strati- 

 fication and no motion. When a north-south density gradient is imposed 

 through the surface boundary condition, convection takes place in the 

 northern part of the basin. This in turn leads to the buildup of horizontal 

 density gradients in the main body of the fluid. As the parameter, R^, is 

 increased, the effective horizontal mixing decreases. This allows an 

 increasingly complex flow pattern to form. To resolve these complex patterns 

 a detailed numerical grid and a large amount of calculation are necessary. 

 The calculations of this study are therefore restricted to cases in which 

 Rq < 36. Within this range an equilibrium is usually obtained after a 

 numerical integration over the equivalent of a decade. 



The behavior of the heat transport as a function of time is shown in 

 Figure 2 for four different cases . These calculations show the effect of 

 a four-fold change in the Rossby number with the other parameters kept 



