Tulin and Shwavtz 



interior is created, and is pulled down around the bottom of the 

 rising mass toward the plane of symmetry. To the extent that the 

 ingested vorticity remains on its own side of this plane, the vorticity 

 within the interior will be steadily reduced; of course, ingested 

 vorticity of opposite sign does have a chance to mix and thus to 

 annul itself, depending on the efficiency of mixing. Should effective 

 annihilation of ingested vorticity occur, then the initial total vor- 

 ticity within one side of the pair would be conserved in time. 



As for the kinetic energy implicit in the motion of the vortex 

 pair, it must be continuously reduced with time due to turbulent 

 dissipation, 



Self-Similarity in Vortex-Pair Motions . It is a striking 

 characteristic of free turbulent flows in homogeneous media at 

 sufficiently high Reynolds numbers that, under similar circumstances, 

 the flows at different points in space or time can usually be reduced 

 from one to another upon normalization by an appropriate length 

 and velocity scale (self- similarity) . This is true, for example, of 

 the flow at different downstream sections of turbulent jets and wakes. 

 It is therefore natural to expect that a turbulent vortex-pair exhibits 

 complete self- similarity during its life time, and this assumption 

 has been made in all theoretical treatments of the subject, starting 

 with Morton, Taylor, and Turner [ 1956] . Two important consequences 

 of this complete similarity are: (1) conservation of the ratio of 

 internal and external velocity scales, W/W , during the motion; 

 (2) linearity of the length scale of the convected mass with the dis- 

 tance traveled from a virtual origin. 



This latter result, predicting that the traces of the side 

 boundaries of the convected mass form a wedge, is independent of 

 the dynamics of the motion and serves to provide a check on self- 

 similarity. In fact, a number of previous experiments on self- 

 convecting masses claim to confirm this behavior to a reasonable 

 approximation, see, e.g.. Scorer [1958] , Woodward [1959] and 

 Richards [ 1965] . 



It is oUvious to ask whether a "natural" value of the velocity 

 ratio W/W , or the same thing, of the constant P = dR/dz is ob- 

 served, independent of the original circumstances giving rise to the 

 convected mass. The answer seems to be no. In the present experi- 

 ments , two distinctly different ranges of value of dR/dz differing 

 by a factor 2, have been repeatedly measured; these correspond to 

 two different stroke lengths in the apparatus used to originate the 

 vortex motions. Furthermore, although the present data may be 

 claimed to correspond "in a reasonable approximation" to a constant 

 value of dR/dz, yet quite consistent deviations from linearity exist 

 between the traces of pair radius and distance traveled, see Fig. 4. 

 These deviations are such that dR/dz seems actually to increase 

 throughout the observed motions. 



328 



