Nonlinear Theories — Inertial 123 



meander instability. One is tempted to speculate, therefore, that the Gulf 

 Stream automatically reaches the condition given by equation (35) at the 

 latitude of maximum wind curl, and that it acts in much the same way as 

 an ordinary open-channel transition (weir, overfall, and so on) to control 

 the over-all depth of the thermocline in the North Atlantic Ocean. 



One of the most gratifying features of the inertial theory of the Gulf 

 Stream is that it does not contain an arbitrary parameter such as the 

 viscous boundary-layer theory does. A disconcerting feature is the absence 

 of a well-defined countercurrent to the east of the Stream. Formally this is 

 accounted for by the lower-order derivatives in the inertial boundary-layer 

 theory. Too much emphasis should not be placed upon this apparent 

 advantage of the viscous over the inertial theory, because there is a bit of 

 confusion among various investigators over the countercurrent to the east 

 of the Stream: there are two ' counter currents ' of widely different nature. 

 The first kind is apparently associated with the warm core. It is evidently 

 a dynamical necessity resulting from advection of warm water from lower 

 latitudes (see fig. 33). The simple two-layer model treats the upper layer as 

 uniform, so of course it cannot show this feature. Since this countercurrent 

 has a width similar to that of the main Gulf Stream, I assume it is the 

 countercurrent which the Munk theory attributes to lateral friction. 



The countercurrent of the second kind is a much deeper, broader feature 

 of the circulation. It shows up somewhat in fig. 11 , as indicated by the close 

 spacing of the 800 and 1000 m. contours of the 27-0 cr^ surface along the 

 30° N. latitude circle. It is much too wide to be part of the boundary layer, 

 and there is no feature of the wind-stress distribution which can account 

 for it in the interior. Perhaps this countercurrent of the second kind reveals 

 some fundamental discrepancy between theory and reaHty; just what it is, 

 I do not know. 



Whereas Morgan's treatment (1956) shows quite clearly the role of the 

 various physical parameters in the determination of the Stream profile, it 

 is not aimed at giving a detailed representation of the actual Gulf Stream. 

 Charney's (1955) study constructs a two-layer ocean model with a choice of 

 D and \Jr on the outer edge of the boundary layer as near to what actually 

 occurs in nature as is possible. The two studies thus supplement each other. 



Charney's formulation makes use of the BernouUi equation (21) and the 

 equation of potential- vorticity conservation, equation (5). If we make use 

 of the fact that in the boundary layer, [ dv*ldx \ > \du*ldy \ , and use the de- 

 finition v*D* = drJr*ldz, the potential-vorticity equation is of the following 

 form: 



D* 



^F{ijr*). (36) 



