A,10 • TENTATIVE CONCEPTUAL PICTURE 



so small that viscosity quickly damps their motion, this theory of tran- 

 sition requires a progression of separations with formation of free shear 

 layers of successively smaller scale until the chain is broken by shear 

 layers of such small Reynolds number that turbulence is not generated. 

 This tentative conceptual picture of transition can hardly be said to be 

 firmly demonstrated, but such a picture may serve, at least for a time, 

 as a useful guide in the presentation of existing data and as a guide to 

 future more systematic study of the basic phenomena. 



Let us examine the observed experimental fact that transition is 

 greatly affected by exceptionally small disturbances in an otherwise 

 steady flow. Fluctuations with time of amplitude as small as one tenth 

 of one per cent of the mean velocity have measurable effects on the po- 

 sition of transition. Dryden [1] calculated the effect of a small sinusoidal 



1.36 



Fig. A, 10. Streamlines for flow in the boundary layer of a plate subjected to peri- 

 odically oscillating pressure variations beginning at distance Lo from the leading edge. 

 Amplitude of free stream velocity variation — | per cent of mean value. Wavelength 

 Lw equal to 0.072 times initial length Lo. 



variation of the free stream velocity with distance along the outer edge 

 of a boundary layer using the Karman-Pohlhausen approximate method 

 of solution of the Prandtl boundary layer equations. Separation of the 

 flow was found to occur after three complete cycles of a sinusoidal vari- 

 ation of amplitude two per cent of the mean velocity. A far more satis- 

 factory computation was made in Germany during the war by Quick and 

 Schroder [38] by a step-by-step procedure. A sinusoidal velocity variation 

 of one-half per cent of the mean velocity and of wavelength of the order 

 of the boundary layer thickness produced 15 to 20 per cent variations in 

 displacement thickness with a separation bubble during the third cycle 

 and complete separation at the fourth cycle. The streamlines for this case 

 are shown in Fig. A, 10. It is surmised from these considerations that 

 small disturbances from any source will lead to intermittent separation 

 and the formation of free shear layers in the fluid. If the Reynolds num- 

 bers of these shear layers are sufficiently high, small scale turbulence will 



(29 > 



