TRANSITION FROM LAMINAR TO TURBULENT FLOW 



measure of the pressure gradient, and the kinematic viscosity v. To these 

 must be added the free stream turbulence, and the radius of curvature r 

 and roughness k of the surface at the selected location. There is no obvi- 

 ous reason for omitting higher derivatives of u^ or the complete distribu- 

 tion of velocity within the boundary layer. If, however, the quantities 

 listed are sufficient, dimensional reasoning yields the result that 



(We A 



_ „ . 5^ dUe, b k L W 

 V dx r 8 8 u, 



In line with this approach to the problem, it has become customary 

 to state the location of transition in terms of the local boundary layer 



3000 



2000 



Reg 



1000 



100 



i- (U'2 + v'2 + W'2) 



u^ 



Fig. A,6. Effect of intensity of free stream turbulence on the transition Reynolds num- 

 ber of a plate expressed in terms of displacement thickness of the boundary layer. 



Reynolds number rather than in terms of Xt in the hope that values for 

 bodies of different shape would be more nearly comparable. There is con- 

 siderable diversity of practice in selection of the particular boundary layer 

 thickness to be used. Since the velocity in the boundary layer approaches 

 asymptotically that outside, there is no accurately determinable value of 

 the actual thickness. The displacement thickness 5* is frequently used 

 and will be used hereafter. NACA writers have used the value of y for 

 which u/u^ = 0.707 as the thickness, because of the ease with which it 

 can be read from experimental curves and because it is approximately 

 proportional to 5*. Thus for the Blasius exact solution, the NACA value 



(20) 



