A, 5 • SURFACE ROUGHNESS AND WAVINESS 



in the boundary layer of a flat plate. In every case tried, the flow separated 

 from the surface of the roughness element but did not in every case lead 

 to immediate transition. The results of many experiments suggest that a 

 single roughness element must be comparable in height with the displace- 

 ment thickness in order to produce transition. In Liepmann's experiments 

 an element for which h = 0.765* did not produce immediate transition, 

 whereas elements for which k > 0.925* did produce immediate transition. 

 Certain experiments of Fage [13], when analyzed, show that the minimum 

 height to cause transition on a plate at certain definite locations down- 

 stream from the roughness element varies from 0.82 to 1.775* for smooth 



1. 



1.4 



I 

 O 



Xi.o 



CD 

 0.6 



0.2 



0.2 



0.4 



0.6 



0.8 



k/5^ 



Fig. A,5a. Effect of single cylindrical roughness element on the transition Reynolds 

 number of a plate. Original measurements of Tani, Hama, and Mituisi [15]. 



bulges, 1.44 to 1.625* for a smooth hollow, and 0.43 to 0.675* for a flat 

 ridge. The higher values are required to cause transition to approach the 

 roughness element ; the values to cause transition at the element as deter- 

 mined by extrapolation are 1.85*, 1.65* and 0.985*, respectively. Holstein 

 [14] has also found that roughness heights comparable to the displacement 

 thickness are required to move transition appreciably forward. 



In Fage's experiments it was found that a roughness element can 

 influence the position of transition far downstream, presumably because 

 it imposes a disturbance akin to turbulent fluctuations which slowly grow 

 until transition occurs. This effect was not observed in Liepmann's experi- 

 ments since observations were made only to a downstream distance of 

 6 inches. It is probable that, in the case in which Liepmann observed no 



<9 > 



