Tulin and Shwartz 



Vb z^= sinfsin' Vb"+ zVbT] (57) 



where we have normalized the time t according to 



t= ^^5^ (58) 



Equation (5 7) is particularly useful for the approximate deter- 

 mination of the maximum rise of a mass convected in a stratified 

 medium and the time at which this maximum height is reached, 

 *max« ^o^ the maximum height we find 



/ 1 n'/"^ 



and the time required to reach this height is given by 



W = ^-4 (60) 



This last result is especially interesting. In experiments on 

 convected masses of fluid moving through a density stratified 

 mediuna it was frequently observed that the time it takes the mass to 

 reach its maximum height is inversely proport ion al to the Vaisala 

 frequency of the stratified medium, i.e. , ^mai^^g - const. Equation (60) 

 is just a statement of this same f act for smal l v ailues of B (as usually 

 exist in nature) , since tnwDcVB = /2k/5iC (t-gVag). 



V. COMPARISON OF EXPERIMENTAL AND THEORETICAL 

 RESULTS (STRATIFIED MEDIA) 



In our experimental investigation we have studied the motion 

 of impulsively started rising masses (or vortex-pairs) in both 

 uniform and density- stratified surroundings. According to the 

 theoretical considerations presented in theprevious section, the 

 time-histories of these motions, expressed in appropriate non- 

 dimensional terms, are determined by three parameters. A, B 

 and D, i.e. , for given values of these parameters the rise and 

 growth of the convected mass as a function of time can be predicted. 

 A and B are determined by G and S and by a third parameter 

 which is the ratio of the virtual kinetic and potential energy coef- 

 ficients , K/k,' according to Eqs. (44) and (45). 



While the parameters G and S are determined in each case 

 by the initial conditions of the rising vortex-pair, there is no 



350 



