﻿Lord Rayleigh on ^Eolian T( 



ones. 



437 



" Pour une vitesse suffisante, au-dessous de laquelle il n'y a 

 pas de tourbillons (cette vitesse limite croit avec la viscosite 

 et decroit quand Fepaisseur transversale des obstacles aug- 

 mente), les tourbillons produits periodiquement se detachent 

 alternativemeni a droite et a gauche du remous d'arriere qui 

 suit le solide; ils gagnent presque immediatement leur emplace- 

 ment dejinitif] de sorte qu'a Varrih'e de V obstacle se forme 

 une double rangee alter nee d'entonnoirs stationnaires s ceux 

 de droite dextrogyres, ceux de gauche levogyres, separes par 

 des inter valles egaux." 



The symmetrical and unsymmetrical processions of vor- 

 tices were also figured by Mallock* from direct observation. 



In a remarkable theoretical investigation f Karman has 

 examined the question of the stability of such processions. 

 The fluid is supposed to be incompressible, to be devoid of 

 viscosity, and to move in two dimensions. The vortices are 

 concentrated in points and are disposed at equal intervals (I) 

 along two parallel lines distant h. Numerically the vortices 

 are all equal, but those on different lines have opposite 

 signs. 



Apart from stability, steady motion is possible in two 

 arrangements (a) and (b), fig. 1, of which (a) is symmetrical. 



Fiff. 1, 



<» — * 



4 



* 



(*) 



^t 



$ 



3 



3 



(b) 



L 



Karman shows that (a) is always unstable, whatever may be 

 the ratio of A to I ; and further that (b) is usually unstable 

 also. The single exception occurs when cosh Qrrh/l) =\/2, or 

 /yZ = 0-283. With this ratio of h/l, (b) is stable' lor every 

 kind of displacement except one, for which there is neutrality. 



* Proc. Roy. Soc. vol. lxxxiv. A. p. 490 (1010 s ). 



t Gqttingen Nachrichten, 1912, Heft 5, 8. 547: Kannan and 

 Rubach, Pht/sik. Zeitschrift, 1912, p. 49. I have verified the more 

 important results. 



