86 LiNEAK Theories — Viscous 



means that other processes must act to counteract the negative-vorticity 

 tendency due to the wind alone. 



The Hnear theories involve two processes, the first of which is friction. 

 Since, as we have already seen, the ocean surface circulation does not seem 

 to be frictionally bound to the bottom, we inquire whether it is frictionally 

 bound to the ocean shores by horizontal eddies. Such a horizontal viscosity 

 would provide a positive- vorticity tendency over the ocean shown in fig. 52. 

 A numerical check, made using (i) values of lateral-eddy viscosity inferred 

 from the distribution of conservative properties, and (ii) a horizontal 

 oceanic circulation which looks like the -wind system, without any evidence 

 of asymmetry, requires a circulation many times as fast as the real ocean 

 circulation for lateral friction to produce a positive-vorticity tendency 

 strong enough to balance the ^vind-st^ess- vorticity tendency. 



The second process is the tendency of planetary vorticity. Regardless of 

 hemisphere, columns of water moving northward without convergence or 

 divergence have a negative-vorticity tendency, and those moving south- 

 ward have a positive-vorticity tendency. This foUows from the conservation 

 of angular momentum, or, to put it in other words, the variation of the 

 CorioUs parameter with latitude. Since the net meridional transport of 

 water across a parallel of latitude is zero (as much water moves north as 

 south), the planetary- vorticity tendency is positive for water in the eastern 

 part of the ocean presented in fig. 52, and negative for water in the western 

 part. Therefore the planetary- vorticity tendency alone is incapable of 

 balancing the \^ind-stress-vorticity tendency. In the steady state we must 

 have a zero over-all vorticity tendency, by definition. That is, at every point 

 in the ocean the wind-stress-, frictional-, and planetary- vorticity tendencies 

 must cancel out one another. 



The distribution of the A\ind-stress- vorticity tendency may be regarded 

 as fixed, let us say of an order of magnitude — 1 . If there were only a broad 

 current system without the asymmetry that is actually observed but with 

 a transport of water similar to the observed transport, the frictional- 

 vorticity tendency would be of a smaller order of magnitude, say + 0- 1 , and 

 the planetary- vorticity tendency would be of the order — 1 in the Avestern 

 and -fl in the eastern part of the ocean shown in fig. 52. Thus there would 

 be an approximate balance of tendencies in the eastern part of the ocean, but 

 the western part would not be in equihbrium; hence, for such an ocean as 

 this in a steady state of motion, a symmetrical current system is not 

 physically possible. The state of afi'airs for a symmetrical circulation is 

 summarized in table 2. 



If we let the current system be strongly asymmetrical, as it is in fig. 53, 

 we do not seriously affect the balance between the wind-stress- vorticity 

 tendency and the planetary- vorticity tendency in the eastern part of the 



