Self-Conveating Flows 



or. 



This result suggests how to estimate the dimensionless quantity n 

 (or D) through the analysis of the trajectories of rising masses in 

 this specicd case, 



2. A mass with initial density difference rising in a 

 homogeneous medium; i.e. , B = 0. Then 



(^) = b - (1 ^2D) ]^""'^[ (l ^2D) ]^"' <52) 



If A > 0, then no maximum height is reached, but if A < 0, 



z„„. _r i.2DHA| -|'^"'^°' 



^0 L |A| -I ' ' 



The predicted rise of the mass as a function of time and the 

 maximum rise of the mass for a range of values of A (< 0) and D, 

 as obtained from Eqs . (52) and (53), are presented in Figs. 9 and 

 10, These figures demonstrate clearly the effect of the (negative) 

 initial buoyancy and energy dissipation parameters on the time 

 history of an impulsively started rising mass moving through a 

 uniform surrounding fluid of smaller density. 



2a. The same case as above but for Wq = cind A > 0, 

 First of all, (43) may be rewritten: 



^ "'o k z / (i + 2D)K V Pe L\ z J (1 + 2D)K \ p^ / 



z 



or in this case 



3. A mass with no initial buoyancy rising in a stratified 

 medium, i.e., A = 0, Then, 



347 



