A,27 • PRESENT STATUS AND FUTURE DIRECTION 



are usually of importance only when all other disturbances are exceed- 

 ingly small. As the free stream passes around the body under study it is 

 subjected to a single disturbance corresponding to the mean velocity dis- 

 tribution around the body. This pulse can be analyzed into a spectrum, 

 and if the body is of blunt shape yielding a sharp and large amplitude 

 pulse, there may be sufficient energy in the region of amplified oscillations 

 to be of importance. Similarly a single small roughness element yields a 

 single pulse, even though it generates no turbulence directly, which con- 

 tributes to the disturbance spectrum. Distributed roughness yields a ran- 

 dom disturbance which can be analyzed in terms of its spectrum. Insta- 

 bility of the highly curved flow near a stagnation point and vorticity 

 produced by intense shock waves at the leading edge also contribute to 

 the spectrum at supersonic speed. 



The region of spectrum which is amplified depends on the Reynolds 

 number of the boundary layer and on the mean velocity distribution as 

 discussed in IV,F. The linear theory then yields a growing disturbance. 

 According to experiment the next step is the appearance of turbulent 

 spots in the flow which grow in size. Since the disturbances arising from 

 free stream turbulence and distributed roughness have a random charac- 

 ter, these spots will appear at various points in the flow in a random 

 manner as described by Emmons [3] and transition will be intermittent 

 and extend over a considerable area. 



The transition process or the real instabiUty of the flow is the result 

 of the nonlinear character of the equations describing the motion. Be- 

 cause of the nonlinear character the effects of several disturbances cannot 

 be obtained by superposition, the concept of analysis into a spectrum is 

 of limited utility, and it is difficult to conceive a simple typical process 

 describing the essential features of the phenomenon. Munk [123] has tried 

 to describe transition as an interplay between the selective aggregating 

 action of shear flow on vorticity of one sign, the spreading-out of vorticity 

 of the opposite sign, and the nonselective diffusion of vorticity by vis- 

 cosity. Other pictures have previously been presented in Art. 10 in terms 

 of the rolling-up of shear layers arising in flow separation or of the pro- 

 duction of Gortler vortices in regions of highly curved streamlines. Betz 

 {12Jf\ has recently described the origin of vortices in a fluid of small vis- 

 cosity, pointing out several difficulties which can be avoided by assuming 

 that vortices are formed by the rolling-up of vortex sheets. Progress in 

 the development of a satisfactory conceptual picture and theory is de- 

 pendent on progress in the study of nonstationary solutions of the Navier- 

 Stokes equations. 



When the disturbances are large the intermediate stage describable 

 by linear theory is absent. Large disturbances in this sense are actually 

 quite small; in the case of initial turbulence of 0.25 per cent or more, 

 the laminar boundary layer oscillations are not observable, being masked, 



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