Chapter Eight 



NONLINEAR THEORIES OF 

 THE GULF STREAM 



This chapter records attempts to include the effect of the nonlinear inertial 

 terms in theoretical explanations of the Gulf Stream. From a historical 

 point of view it is important that mention be made of the wake-stream 

 theory advanced by Rossby. Rossby's theory of the Gulf Stream assigns 

 a very important role to lateral friction, just as the linear theories dis- 

 cussed in the preceding chapter do, but does not take into account the 

 effect of the variation of the CorioHs parameter with latitude. Next, we 

 shall consider some of the more recent nonUnear theories in which lateral 

 friction is assumed to play only a minor role. We therefore reexamine 

 the question how large lateral mixing and viscosity really are, and we 

 find that although a definite answer cannot be given, there are grounds 

 for supposing that lateral friction may actually be small as compared to 

 inertial terms. 



We shall derive a principle of conservation of a quantity called ' potential 

 vorticity ' in order to incorporate the inertial terms in a convenient manner, 

 and then make a vorticity analysis of a Gulf Stream section. After a few 

 preliminary remarks about certain very simple potential-vorticity models, 

 we shall proceed to a study of the recent * inertial boundary-layer ' theories 

 of Morgan and Charney. Finally, reference will be made to Rossby's 

 concept of 'critical' flow as applied to the left-hand edge of the Gulf 

 Stream. 



