A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



transition, transition did in fact occur earlier when the roughness element 

 was present than when it was absent. 



Systematic experiments by Tani, Hama, and Mituisi [15] have clarified 

 the effect of a two-dimensional roughness element. Their experiments 

 were made on a flat plate with zero pressure gradient in a wind tunnel 

 in which Re^, was about 1.7 X 10^ with cylindrical wires as roughness ele- 

 ments. In the original paper the data were analyzed according to the con- 

 cept suggested by Schiller [16, pp. 189-192] that a roughness element 



300 



260 



220 



Re. 



180 



140 



100 



0.4 



0.8 



1.2 



Ret X "1 0~^ 



1.6 



2.0 



Fig. A,5b. Relation between Reynolds number of roughness element and transition 

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



induces transition when the Reynolds number of the element itself reaches 

 a definite critical value at which vortices appear in its wake. Dryden [17] 

 reanalyzed the data and showed much better agreement with the concept 

 that Re^ is a function of /c/5* where k is the height of the roughness ele- 

 ment and 6* is the displacement thickness of the boundary layer at the 

 location of the roughness element. Fig. A, 5a shows Re^ as a function of 

 k/b* whereas Fig. A, 5b shows the relationship between Re^, and Rek. 



Tani and Hama presented additional results in a later paper [18]. 

 They are plotted in Fig. A, 5c. As the roughness height is increased, the 

 position of transition moves forward from the smooth plate position until 

 it reaches the position of the roughness element. Re^, is a function of k/b* 



{ 10 ) 



