Chapter Nine 



MEANDERS IN THE STREAM 



Very little is really knouTi about the meanders of the Gulf Stream. They 

 have been observed only a few times; beyond their wavelength, the 

 direction of propagation, and the fact that they may grow into detached 

 eddies, nothing is known. There are no detailed data on their structure as 

 a function of depth, especially below the 900 ft. level commonly reached by 

 the bathythermograph. However, because they are essentially wavelike 

 they are tempting theoretically, and attempts have been made to treat them 

 by Unearized perturbation equations. 



THE APPLICATION OF THE PERTURBATION METHOD 



The perturbation method has been eminently successful in the classical 

 theories^ of sound waves, of tides, of gravitational water waves, and of the 

 Benard-type thermal-convection cells. Most of these problems are peculiarly 

 suited to the perturbation method because they involve very simple models: 

 the fluid is at rest, or in uniform motion, and the coefficients of the pertur- 

 bation equations are constants. Helmholtz (1868) first investigated the 

 following unstable system. Two homogeneous currents move, one above the 

 other, with uniform (but different) velocities, under the influence of gravity . 

 The upper layer is less dense than the lower. The shear at the common 

 boundary tends to produce instability; gravity tends to produce stability. 

 Short waves on the common boundary are shown to be unstable; long waves 

 are stable. 



Kelvin (1871) apphed the perturbation technique to the problem of wind 



^ This historical section is after Queney (1950). 



