Theory of Turbulent Flow Between Parallel Plates 



laminar flow, the gradient and the second derivative must be related. This dual 

 defines a region near the wall that can be identified as a boundary layer. (Ap- 

 proximately out to y* = 2 in the von Karman logarithmic presentation.) It is 

 in this region that vorticity is developed in the form of "acoustic" eddies that 

 radiate into the core region. The frequency range for these eddies can be esti- 

 mated by both a low frequency cut-off and a high frequency cut-off. The fre- 

 quency range seems to fit Laufer's measured spectrum of turbulence for paral- 

 lel plates. The high-frequency end seems compatible with his limiting eddy 

 size, and the low-frequency seems to fit what might be considered loosely to be 

 von Karman vortices, namely, an alternative relaxation, shedding, or intermit- 

 tency measure for the flow field. Turned around to estimate the critical Reyn- 

 olds number, a value of about 750 is computed, based on the plate separation 

 and center mean velocity. A magnitude of fluctuation velocity amplitude in the 

 range 1-10 percent is crudely computed. It is believed that some preliminary 

 modelling of processes pertinent to turbulence in such a field has been achieved. 

 Further, it would appear that the method of attack could be extended to other 

 turbulent fields. 



REFERENCES 



1. Lin, C, The Theory of Hydrodynamic Stability, Cambridge, 1966 



2. Rossini, F., Thermodynamics and Physics of Matter, Princeton, 1955 



3. Greenspan, M., "Combined Translational and Relaxational Dispersion of 

 Sound in Gases," J. Acoustic Soc. Amer. 26, 70, 1954; "Propagation of 

 Sound in Five Monatomic Gases," ibid. 28, 644, 1956; "Rotational Relaxa- 

 tion in Nitrogen, Oxygen, and Air," ibid. 31, 155, 1959 



4. Iberall, A., "Contributions Toward Solutions of the Equations of Hydrody- 

 namics. Part A: The Continuum Limitations of Fluid Mechanics." Con- 

 tractors Report to Office Naval Research, Wash. D.C., Dec. 1963 



5. Iberall, A., "Attenuation of Oscillatory Pressures in Instrument Lines," 

 J. Res. Nat'l. Bur. Stands., 45, 85, 1950 



6. Brown, F., "The Transient Response of Fluid Lines," J. Basic Eng. 84, 

 547, 1962 



7. Watts, G., "An Experimental Verification of a Computer Program for the 

 Calculation of Oscillatory Pressure Attenuation in Pneumatic Transmis- 

 sion Lines," Los Alamos LA-3199-MS, Clearinghouse Fed. Sci. Tech. 

 Info. Dept. Commerce, Springfield, Va., Feb. 1965 



8. Laufer, J., "Investigation of Turbulent Flow in a Two- Dimensional 

 Channel," NACA Rep. 1953, 1951 



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