Tulin and Shwartz 



A., the constant appearing in the relation for circulation change, 

 and which depends in part on the way in which vorticity is ingested 

 into the vortex pair. In fact, the asymptotic behavior of the vortex 

 pair changes radically as Ai varies around the value unity. This 

 is demonstrated in the table below. 



Asymptotic Behavior (ijj » 1) 



4^ 



We/ Wi, 



A, > 1 



A, = 1 



A. < 1 



A, = 



_A, 

 |jlR ' 



Aj^'K, 



R(K2A'K,) 



R(K2A'K|) 



K.R ' 



K, /h. + Kj 



K /K 



r 2 



K ,/K 



\/"2 



K.R-^ 



_-2 



K.R 



K,/K.-R 



K /K • R 



r 2 



l/(U2/A,) 



.1/3 



l/(2*A,) 



.t'/2 



For values of A, > 1, the velocity ratio is seen to decline, 

 so that the strong circulation assumption must eventually become 

 invalid. The case Aj = i yields results qualitatively similar to 

 the weak circulation case. In the case where A| < 1, however, the 

 velocity ratio increases to the asymptotic value shown and, most 

 interesting, the added momentum coefficient (K| - Kgijj) vanishes 

 asymptotically, so that the motion becomes determined by volume, 

 vorticity, and energy balances alone. Finally, in the case where 

 A, « 1 (effective annihilation of ingested vorticity), then asympto- 

 tically the motion becomes determined by volume and energy balances 

 cilone, yielding z ~ t . 



III. COMPARISON WITH EXPERIMENT (HOMOGENEOUS MEDIA) 



In Figs. 5 and 6 are shown data from actual experiments on 

 two-dimensional vortex pair motions in homogeneous fluids. Most 

 of the data shown were obtained in experiments carried out in our 

 own laboratory. Suffice it here to show a schematic of the facility 

 which was used. Fig. 7, and to show Table 1, in which the properties 

 and characteristics of the experimental vortex pairs are listed. 



336 



