Studies on the Motion of Viscous Flows— VI 



In considering the numerical value 67.94 assigned by Taylor to e^, there can 

 be two alternative interpretations of the relation in Eq. (18): 



(i) X = a/h is a constant with a definite value (67.94/658)^^"* which is 

 nearly equal to e^. 



(ii) £3 is a function of x and hence its numerical value will be different, 

 in general, from 67.94. 'V. ■:: '-: . ; ■ ' 



The first case would imply that the solute as described in Taylor's experi- 

 ments should penetrate to a depth equal to twice the radius of the tube, irre- 

 spective of the nature of the solute. If on the other hand the depth of penetra- 

 tion is found to be different from the diameter of the vertical tube, then the 

 numerical value of e^ must, in general, vary. 



Furthermore, if the present theory is appropriate to the experiments 

 described by Taylor, then we can obtain from Eq. (14) by writing dcp/dz = Cq/z 

 (following Taylor), 



1 c„ pp a z^ 

 ... ,.,, 658 ^ ... • ,.__ 



where c g is the concentration of the solute at top of the tube and z is the depth 

 of penetration of the solute. 



Equation (19) can then be used, following Taylor's reasoning, to determine 

 the diffusion coefficient D experimentally, whatever the depth of penetration z. 

 In the above expression we have used R^ = 658. If, however, rigid-free bound- 

 aries are more representative of a particular experimental arrangement, then 

 Rg = 1100 is appropriate. It remains to be decided experimentally whether Eq. 

 (18) holds in nature, and if so, by which of the two possibilities noted above as 

 cases (i) and (ii).* 



ACKNOWLEDGMENT 



The present paper is part of an overall investigation concerning the effects 

 of simultaneously impressed gradients of macroscopic- state parameters on hy- 

 drodynamic stability, which originated under the support of the General Electric 

 Co. MSVD (Lieber, 1957, 1959). The present work was initiated under support of 

 the National Research Council of Israel (Rintel, 1962) and completed with the 

 support of the Fluid Mechanics Branch of the Office of Naval Research. We are 

 also indebted to Dr. A. T. Wilson of Victoria University, Wellington, New Zea- 

 land for sending us unpublished measurements of temperatures and salinity in 

 Lake Vanda. 



*The senior author (P. Lieber) is entirely responsible for this interpretation of 

 the correspondence between Sir G. I. Taylor's work and a limiting case of the 

 present theory. This nnatter was first brought to his attention by personal 

 communication with Sir Geoffrey. 



701 



