Tulin and ^hwartz 



A comparison of experimental observations of rise 

 versus tim.e and radius versus height with theory (I) 

 lend strong support to the strong circulation theory 

 and suggest that ingested vorticity may be largely 

 annihilated. 



Based on these finding for homogeneous flows, a sim- 

 plified theory (II) for stratified media was developed 

 upon the assumptions: (i) the motion is deterrained 

 by conservation of volume, mass, and energy (neg- 

 lecting vorticity and momentum); (ii) complete simii- 

 larity (dR/dz = P, a constant). Good agreement was 

 found between the predictions of this theory and the 

 results of systematic experiments , and particularly 

 for the maximum rise of height. 



NOTATION 



a Density gradient in surroxonding fluid, a = (l/Pe)(dPe/dz) 



A Initial buoyancy parameter (theory) , Eq. (44) 



A, Vorticity mixing coefficient, Eq. (9) 



b Half distance between cores of vortex-pair 



B Stratification parameter (theory) , Eq. (45) 



c Constant 



Gp Energy dissipation coefficient 



D Energy dissipation parameter , Eq. (46) 



E Total energy of convected mass 



G Experimental buoyancy parameter , Eq. (44) 



j Geometrical parameter, j = for planar geometry, 

 j = 1 for axial symmetry 



k Virtual potential energy coefficient, Eq. (3 8) 



k^ Virtual mass coefficient 



K Virtual kinetic energy coefficient, Eq. (37) 



M_ Vertical component of total momentum 



ti Parameter defined by Eq. (47) 



T Radial distance from center of rising mass, r^ = | + r| + t, 



R Mean radius of rising mass 



R^ Non-dimensional mean radius of rising mass, R = R/Rq 



S Experimental density stratification parameter , Eq. (53) 



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