The Tropospheric Circulation 



637 



The application of these equiHbrium conditions to the Gulf Stream requires an esti- 

 mate of the order of magnitude of the individual terms. These can be obtained 

 approximately from the "Atlantis" sections for concentrated boundaries of the current 

 and one obtains the following values given in the [cm g sec] -system: 



10- 



du 

 ex 



cu 



cz 



10 



da 

 dx ' 



8a 



Fz 



gda 



a dz 



10- 



10-^ to 10-8 



10-= 



/• 





f 



(f- a 



. 10-* 

 . 10-1* 

 . 10-8 



Introducing these values in equation (XIX. 59) shows that in the Gulf Stream, in spite 

 of always secured static stability and in spite of the almost always secured inertia 

 instability, hydrodynamic instability may still occur provided the vertical shear in 

 the flow reaches excessive values. 



This can be illustrated by an example taken from the "Atlantis" section shown in 

 Fig. 294. (Chesapeake Bay-Bermuda, April 1932). Along the left-hand side of the 

 Gulf Stream in the region of largest vertical and horizontal shear (depth 220 m) one 

 obtains 



du cu 



— ==0-47 X 10-2sec-i; ^ 



cz ox 



0-33 X lO-^sec-i and 



cz 



0.33 X 10-«. 



With these values and with/ = 0-85 x 10-* 



[fj^^ =0•16xl0-l^ 



while 



' CxJ a CZ 



The current and density stratification is thus, of course, hydrodynamically stable as 

 could be expected since at this part of the Gulf Stream the current shows no tendency 

 to meander. Hydrodynamic instability would only occur if the vertical shear in the 

 flow would reach values four times larger. Further to the north, in the section between 

 Cape Hatteras and the Newfoundland Banks, conditions might be diff'erent and may 

 readily be so that the current system becomes hydrodynamically unstable; these small 

 horizontal wave formations will soon grow into large meanders and finally lead to the 

 formation of vortices. Strong vertical current shear and low static stability are required 

 for this. It can be understood that a strong acceleration of the flow in the top layers of 

 the Gulf Stream caused by the direct action of a strong westerly wind acting on the 

 sea surface will provide the necessary vertical current shear to give rise to hydro- 

 dynamic instability in the current system and to lead to the formation of meanders. 



Haurwitz and Panofsky (1950) in a study of the stability and meandering be- 

 haviour of the Gulf Stream have attempted to show that especially favourable con- 

 ditions for the development of unstable waves occur when the Gulf Stream is not too 



