Tutin and Shwartz 



applies only to an idealized vortex-pair in which each vortex has a 

 highly concentrated core which is set into motion only by the influence 

 of the other vortex. Such an ideal vortex-pair moves through the 

 surrounding fluid in a direction perpendicular to the plane joining 

 the vortex cores and with a velocity W determined only by the pair 

 separation, 2b, and the circulation about a single vortex, F, 

 according to the relation 



A unique feature of this idealized vortex-pair motion is the 

 existence of a closed streamline and a finite captured mass, as 

 indicated by the oval in Fig. 2a. Thomson [ 1867] calculated the 

 semi-axes of the oval-shaped captured mass to be 2.09b and 1 . 73b 

 so that the cross-sectional area is approximately 3,62'n-b and the 

 ratio of width to thickness is 1.21. 



Under certain circumstances it is entirely possible that 

 carefully balanced vortex-pairs, approximating Thomson's ideali- 

 zation, can be formed. The motion around the vortex centers must 

 be affected by viscosity in a real fluid, but as long as the viscous 

 cores do not extend close to the bounding closed streamline, the 

 flow within and without this streamline may be so closely matched 

 that no large shearing motions or accompanying drag are associ- 

 ated with the motion of the captured mass. In fact, nearly ideal 

 vortex-pairs are sometimes found in the wakes of lifting surfaces. 

 Fig. la, and are known as "contrails," see Scorer [ 1958] and 

 Spreiter and Sachs [ 1951] . Of course, the concentrated vorticity 

 in the vortex cores tends to diffuse, and does so rapidly when the 

 flow in the core is turbulent. 



Turbulent Vortex-Pairs . The probable short lifetime of 

 ideal vortex-pairs under turbulent conditions gives special impor- 

 tance to vortex-pairs whose behavior is governed by turbulent 

 entrainment; indeed, it is these kinds of motions which are most 

 commonly observed in nature, as in the case of a mass of fluid 

 forced out rapidly through an aperture. Fig. lb, or in the convection 

 of isolated masses in nature. Fig. Ic, or in the bent-over and rising 

 chimney plume. 



Turbulent vortex-pairs are characterized by the fact that the 

 interior motion does not match the outer flow at the boundary of the 

 captured mass, so that a region of high shear exists there, accom- 

 panied by the production of vorticity and by turbulent entrainment. 

 In other words, these vgrtex-pairs move with a velocity W not 

 equal to the velocity W derived from Thomson's model, Eq, (1). 



We may, in principle, generalize Thomson's model to con- 

 sider those cases where the velocity of translation, W, has a more 



324 



