Nonlinear Theories — Inertial 



121 



limit of the interior region of the model indicated by curve 2 a is at the 

 equator (5 = 0), curve 2a corresponds to a model very much like the real 

 Gulf Stream. Morgan finds the width of the Stream to be 150 km. Curve 2 c 

 represents the same situation with 5=1, that is, with the southern boundary 

 at approximately 15° N. latitude. 

 The shift of the southern bound- 

 ary produces a shghtly narrower 

 stream, but the effect is quite 

 smaU. The parameters chosen for 

 curve lb represent a homogene- 

 ous ocean with a depth equal to 

 that of the upper layer of model 

 2 a. One sees that the stratifica- 

 tion does not have much influence 

 on the shape of the stream. Com- 

 parison may also be made between 

 curve 2 a and curve 1 a. Curve 1 a 

 represents a homogeneous ocean 

 the depth of which is like that of 

 the real ocean; this is the stream 

 which would exist if the ocean 

 were homogeneous. It is even 

 narrower than the real Stream. 



A further indication of the 

 insensibility of the Stream to 

 density stratification shows up 

 by comparing curves 2 a and 2 b. 

 The density difference in the 

 latter is twice that in the former; 

 otherwise, all parameters are the 

 same. 



Curve 3 shows a very narrow 

 stream, the narrowness being due 

 to the increase in s. It applies 

 to inertial boundary layers that 



might be formed in connection with the pole-to-pole thermohaline 

 circulation discussed in Chapter XI. 



In fig. 68 the dimensionless transport per unit width, d\]f*jdx, is plotted 

 against x for each of the cases discussed above. The transport tends to 

 decrease monotonically with increasing x because of the decrease in velocity, 

 but this is partly offset by the small D* in the two-layer models very close 

 to a; = 0; thus in these cases the transport first increases and then decreases 



Fig. 68. Dimensionless plot of the trans- 

 port per Tinit width as a function of distance 

 from the western coast, according to Morgan 

 (1956). The numbers on the curves refer 

 to the same choice of parameters as those 

 shown in fig. 67. 



