B,10 • TRANSPORT OF PROPERTIES IN A TURBULENT FLUID 



For a velocity distribution given by Fig. B,9e, the curve in Fig. B,9d 

 shows the distribution of T^/Tl given by Eq. 9-12 when it is assumed as 

 a rough approximation that a = 1. On the same figure are shown the 

 measurements of Lobb, Winkler, and Persh [18]. Fig. B,9e shows the 

 measurements of van Driest [19] and Spivack [20]. Both figures suggest 

 that T^/Tl passes through a maximum value in excess of unity, the indi- 

 cation of this being most pronounced in Fig. B,9e. This phenomenon 

 cannot be explained from the above considerations unless a proper dis- 

 tribution of r{y) is taken into account. 



1.01 



1.00 



0.99 

 11 



JO 



0.98 



0.97 



0.96 



01234 56 7 8 



y, mm 



Fig. B,9e. Total temperature profile across turbulent boundary layer at free stream 

 Mach number 2.8. The data are from Spivack [20] with an axial distance from throat 

 of 12.96 inches. 



B,10. Phenomena of Transport of Properties in a Turbulent 

 Fluid. Up to the present we have dealt with the mean turbulent flow 

 and certain simple relationships between mean quantities. For the latter, 

 analogies were employed rather than procedures based on a mechanism 

 of turbulence. Since the superficial nature of this approach is apparent, 

 it becomes advisable to look into the physical transport processes of tur- 

 bulence which are embodied in transport terms like uv, p'v, T'v, etc., of 

 the fundamental equations obtained in Art. 8. They represent the mean 

 rate of transfer of u, p', and T" respectively, across a unit area perpen- 

 dicular to y. One of the major aims of turbulent theory is to find a method 

 of calculating these transport terms directly from the hydrodynamic equa- 

 tions governing the turbulent motion (Eq. 4-3, 4-4, and 6-1). At present 

 the difficulties of the theories make such a program not yet possible. 



< 97 > 



