Self-Conveoting Flows 



general relation to the velocity W which characterizes the internal, 

 rotational motions of the vortex-pair. Two distinct cases suggest 

 themselves, in theory. In one case, W > W , and the convected 

 mass loses volume to the surrounding fluid and continually shrinks 

 in size; we denote this vortex-pair as "underdeveloped," see Fig. 

 2b. In the other case, W < W , and the "overdeveloped" vortex- 

 pair gains mass through the entrainment of exterior fluid, Fig. 2c. 

 Of these it is the latter motion which is most commonly observed in 

 nature and forms the main subject of this work. 



Within an overdeveloped motion, the velocity at the boundary 

 inside the vortex-pair, as seen by an observer moving with it, will 

 be larger than the velocity of the surrounding fluid just outside the 

 boundary of the pair. Accompanying the velocity gradients thus 

 created across this boundary, shear stresses are exerted by the 

 vortex-pair on the surrounding fluid, resulting in the entrainment of 

 outer fluid and a general increase in the volume of the convected 

 mass, see Fig. 3, Within the high shear zones at the boundary on 

 either side vorticity of sign opposite to that within the respective 



SHEAR AND ENTRAINMENT 

 LAYER 



INGESTED VORTICITY 

 MIXES HERE 



Fig. 3. Entraining vortex pair (W, > W^) 



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