In equations 3 and h the unit vectors I and J are directed toward 

 the east and north respectively, so that the equations are the equations 

 of motion in the two directions. 



The increment of energy associated with the displacement may be repre- 

 sented as 



Substituting the values of %r and -~ from equations 3 and ': gives 



This development is a special application to incompressible fluids of the 

 more general exposition by Van Meighem (I95l)« Equation 6 contains the 

 criterion for stability. Assuming flow from west to east (so that the 

 only perturbations will be in the y-direction), the Inst two terms of the 

 equation will drop out, and the stability depends on the sign of the first 

 factor. 



If !^3<> r £ LU« r '^he perturbed energy of the 



Sy "t>0 or -g& >/, 



*^ Li f* 



system is increasing and the system is unstable; if ~sff ^ T » 



•J 

 system is stable. Therefore, the equilibrium condition is attained when 



5u " J " 2,6JSin«p., Since the latitude of Operation ST.a MDRTTLT.. was 33°3VN, 



sin Cp is 0.553;» and the equilibrium or inertia"!, period is therefore 2)> 

 hours divided by 2 times 0.553 > or 21.7 hours. 



Equation 6 may be used to show that the maximum possible velocity gradi- 

 ent toward the right-hand side of a west-to-east flow must be smaller than the 

 Coriolis Parameter (f) or else the flow becomes unstable and eddies form. 

 On the left-hand side of the current, however, an increase in shear merely 

 adds to the stability. Two illustrations show how the Gulf Stream system 

 conforms to these principles. -Figure 5, taken from VJorthington (l955).j is 

 , a velocity section across the Gulf Stream off Woods Hole, Mass. This figure 

 clearly indicates the spreading out of the current toward the right, which 

 is necessary to prevent instability, whereas the left side of the current 

 shows the packing of the jet. 



dy the 



