Self-Conveoting Flows 



48" 



-56"- 



HOMOGENEOUS OR LINEARLY 

 DENSITY-STRATIFIED FLUID 



APERTURE 0.75" WIDE 



PISTON DISPLACEMENT, L 



Fig. 7, Experimental facility for studying vortex-pair motion 



suggests a small value. In this case, 



(aK.) 



[^] =^nR.f^[R-l] 



(24a) 



The trajectory according to Eq. (24a) with Kg/p. = 1/2 and 



Qf'K|/ix = 0.38 is shown in Fig. 4. A fair fit with the experiments has 



been achieved, and noticeably better than is possible with any linear 



trajectory. 



The strong circulation theory thus explains the two important 

 features of vortex pair behavior which cannot be explained by the 

 usual theory of complete similarity. These features are: (i) the 

 tendency for forced vortex trajectories (homogeneous flow) to more 

 nearly follow the law z ~ t rather than z ~ t '^^, and (ii) the ten- 

 dency for the entrainment coefficient (dR/dz) to grow during the 

 initial phase of the motion. These results suggest that in vortex 



339 



