The Tropospheric Circulation 633 



profile, a determination of the density and velocity distribution in the final state can 

 be made by taking 



P = p,(l + Iko) and p, = p,{\ + 2k), (XIX.44) 



where Ps is the surface density and p,, is the deep water density. For a uniform initial 

 stratification (subscript 0) it follows that 



With the continuity requirement, the basic equation gives as a good approximation 



Further when o^^j^ — 1 one obtains 



D I 3«2 \i/3 „ 3 m\ 



It follows that the current must become shallower and the bottom layer will increase 

 in thickness whenever Wq falls below the critical value, Mo.crit defined by 



Wo < "o.orit - J^^\ (XIX.48) 



The end of the adjustment process can be illustrated by means of a numerical example. 

 Initially the upper moving layer extends down to 600 m (Z)o = 600) and 

 Wq = 0-75 m sec"^ In the Gulf Stream region an adequate value of the total range 

 in CT< is 4-5 so that to a close approximation Ik = 4-5. 



Thus D results to 300 m and for u^ one obtains 2-25 m sec~^ Figure 297 shows a 

 graphical representation of this case. 



It is clear that the dimensionless quantity F defined by 



P - IT \i X n (XIX.49) 



{(pb - Ps)/pb}gDo 



has the form of a Froude number in which the gravitational acceleration is reduced in 

 proportion to the total percentage density range of the fluid. It can be seen that this 

 new number determines the nature of the baroclinic movements of a current subject to 

 momentum losses due to frictional influence. If the "internal Froude number" is less 

 than a certain critical value (in the above case ^) the current will be concentrated in the 

 lighter top layers. 



Apparently, oceanic currents usually have subcritical values of F. They then have a 

 tendency to develop a strong shearing motion with increasing velocity and increasing 

 stability near the sea surface and decreasing velocity and stability lower down. 



In the Straits of Florida and in the Gulf Stream region as far as Cape Hatteras the 

 range in CT( is smaller than it is further downstream and there is no homogeneous deep 

 water to facilitate a separation of the current from the bottom. After the current leaves 

 Cape Hatteras, however, the momentum it gains due to direct action of the wind on the 

 narrow strip exposed at the atmosphere is presumably incapable of balancing the losses 



