106 Nonlinear Theories — Inertial 



To carry the argument much further becomes difficult, because one has to 

 allow for the possibility that changes in the stratification affect the mixing 

 length in some way about which we can only guess. Since we do not know 

 what these laws actually are, we may easily be led astray. Rossby (1936 a) 

 is led to argue that there should be a countercurrent on the inshore side of 

 the Gulf Stream, but none on the Sargasso Sea side. In fact, the counter- 

 current observed on the inshore side is very much weaker than the pro- 

 nounced countercurrent on the Sargasso Sea side. Rossby's treatment of 

 the dynamics of the countercurrents, in the wake-stream model, has been 

 very stimulating. We shall use the same dynamical equations later in this 

 chapter, when we come to discuss the Stream as a stream of uniform 

 potential vorticity. 



LATERAL MIXING 



The Rossby wake-stream theory and the finear theories discussed in the pre- 

 ceding chapter all depend heavily upon the existence of large-scale turbu- 

 lence: lateral mixing and the associated lateral-eddy viscosity. Whenever 

 we attempt to frame a hydrodynamical problem in terms of eddy viscosity 

 we must prescribe a certain scale of motion, to divide motions into what we 

 will regard as mean motions and turbulent motions. Our dynamical equations 

 are expressed expUcitly in terms of the mean motions only; the turbulent 

 motions are lumped statistically into one parameter: the lateral-eddy 

 viscosity. It is clear that in a medium in which all scales of motion are 

 present the distinction between mean motion and turbulence is purely 

 arbitrary, but that it is of utmost importance to have a clear mental picture 

 of the scale of motion which divides the two forms of motion in every 

 theoretical discussion. Thus, as we have seen, the actual Gulf Stream 

 meanders; a space and time average over several months would doubt- 

 less look rather hke the gradual fanning out past Cape Hatteras that both 

 Munk and Rossby seem to have in mind. Individual eddies and meanders 

 would be statistically averaged out as turbulence; we may speak of the 

 mean motion in this situation as the climatological-mean Gulf Stream. The 

 pertinent scale of motion which separates mean motion from turbulent 

 motion in this case is about 100 km., the half wavelength of meanders. As 

 I have shown (Stommel, 1951, 1953), it seems hkely that the eddies which 

 break off from the Stream (for example, that represented in fig. 30) carry 

 enough momentum to produce lateral shearing stresses of the order which 

 Munk has postulated. But this is true only if we regard Munk's theory as 

 applying to the climatological-mean Gulf Stream. 



Actually, of course, we are not satisfied with such a coarse statistical 

 description of the Stream as the one to which the 100 km. scale of averaging 



