Self -Conv eating Flows 



practical way for determining a priori the values of D and K/k. 

 These latter parameters can be determined only by comparing 

 certain sets of experimental results with corresponding theory, 



A series of experiments on the motion of vortex-pairs in a 

 homogeneous medium of the same density, Series III (see Table 1), 

 where the parameters G and S (and therefore also A and B) are 

 identically equal zero, may be used for determining the dissipation 

 parameter D. The rise of the vortex-pairs in this case is predicted 

 by Eq. (51) and is graphically depicted in Fig, 9 (with A = 0). 

 The actual predicted rise of the convected mass depends on the 

 numerical value of the parameter D (or n) . 



In Fig. 6 are shown a comparison between experimental and 

 theoretical results on the rise of impulsively started masses in a 

 uniform medium of the same density. In a log- log plot, the slope 

 of the trajectory for large values of (Wot/zg) should be equal, 

 according to our analysis, to i/(2 +D), and it can be used therefore 

 for determining the value of the dissipation parameter D associated 

 with the motion of the rising mass. Included in Fig, 6 are the 

 experimental results of Richards [ 1965] , on the rise of two- 

 dimensional puffs in homogeneous surroundings. The best agree- 

 ment with cill experimented results is obtained when we choose 

 D = 0.2. 



The numerical value of K/k enters into the analysis only 

 when there is an initial difference between the rising and surrounding 

 fluid densities or when the surrounding fluid is stratified. This 

 veilue will be also determined from a comparison of some experi- 

 mental and theoretical results. For a vortex-pair convected in a 

 density- stratified medium we found earlier that, for sufficiently 

 small values of the parameters A, B and D, the time it takes the 

 mass to reach its maximum height is inversely proportional to the 

 Vaisala frequency and is given by 



(tmaxV^)-yill (61) 



This value decreases only very gradually as the value of B (or S) 

 so that Eq. (61) is very useful for the experimental determination 

 of K/k. 



In Fig, 11 the value of the product (tj^^s^g), as measured 

 in the experiments of Series I and II, is presented as a function of 

 the stratification parameters S; the initial conditions for each 

 experiment presented in the Figure are included in Table 1, There 

 are certain inherent inaccuracies in the experimental determination 

 of tmax which explain the scatter. Also shown in Fig. 11 are the 

 asymptotic solution for the ma:ximum rise time, Eq. (60), and the 

 exact solution, according to Eq, (43), with D = 0,2 and G/S = -0.715, 



351 



