Theory of Turbulent Flow Between Parallel Plates 



y - 1 



7 - 1\ / 7-1 



1 + ;=- + 1 + q + 



1 + 



^2^ 



i.e., when the numerator in ? vanishes. 



(This may be checked independently by letting s = in the solutions. 

 The result is the same.) 



Thence, 



1 + 



y - 1 



V2 



1 + 



y - 1 



1 + q + 



7 - 1 



= 4.8 X 10" , 

 f = 43 Hz . 



It is impossible, at the present state of development, to assign a precise 

 meaning to this estimate. It marks the end at which a mechanism for the self- 

 generated formation of eddies can be found. In magnitude, their size is of the 

 order of the characteristic dimension. One suggestive connection may be pro- 

 posed between the low-frequency cutoff and the onset of nonlinear phenomena 

 found in the von Karman vortex street. 



Goldstein [13], (Fig. 149, Vol. 11) represents the von Karman vortex fre- 

 quency for a circular cylinder in a wind tunnel by its Strouhal number, as a 

 function of increasing Reynolds number. It is clear that a "noise" spectrum, 

 associated with turbulence, appears "suddenly" at a critical Reynolds number 

 (near "the" critical Reynolds number). As an approximation, it then appears 

 that the Strouhal number is essentially constant. For the cylinder in a wind 

 tunnel, it is experimentally shown that 



Df 



0. 16 



D = cylinder diameter 



If the two walls in parallel plate flow were similarly viewed as alternating 

 sources of vorticity then a Strouhal number of nominal magnitude 



2hf 



0.16 



might be correspondingly assigned. This leads to 



f = 92 Hz . 



727 



