Lumley 



Fig. 2 - Effect of profile change expressed in 

 terms of the ratio of displacement thickness 

 to momentum thickness, (from Lin (1955)). 



Figure 2 shows the lower critical Reynolds number versus a shape param- 

 eter, the ratio of displacement to momentum thickness. This parameter assumes 

 the value unity for a "square" profile, and increases as the rise to free stream 

 velocity becomes more gentle, reaching a value of roughly 3.5 at separation. 

 While the curve in Fig. 2 was computed specifically for profiles in the presence 

 of pressure gradients and heat transfer at the surface, it is only a slight gen- 

 eralization to speculate that the same curve will describe, at least qualitatively, 

 the effect of other conditions which work principally through a change in profile. 



In describing these stabilization methods, it should be remembered that 

 some of them, especially suction, in addition to changing the profile (in a direc- 

 tion to increase the lower critical Reynolds number) may also prevent boundary 

 layer growth, if applied with sufficient intensity. Thus a boundary layer per- 

 mitted to grow will eventually reach its critical Reynolds number (based on 



918 



