A,9 • BREAKDOWN OF LAMINAR FLOW VS. TRANSITION 



bubbles vary from 600 to 2000 for the bubbles near the leading edge and 

 are of the order of 2000 to 3000 for those near midchord. 



It is obvious that there is room for much additional research, but the 

 turbulence of the air stream and the pressure gradient must be varied and 

 measured if progress is to be made in understanding the phenomena. 



A,9. Breakdown of Laminar Flow vs. Transition. Transition is 

 often regarded as synonomous with the breakdown of laminar flow but 

 wider experimental experience shows that finer distinctions must be made. 

 Breakdown of laminar flow may be followed by a flow varying periodically 

 with time, exhibiting regular vortex patterns. Such flows can be described 

 without the introduction of the random element characteristic of that 

 type of flow for which the name "turbulent" should be reserved. The 

 more familiar examples of flows of this type for which theoretical treat- 

 ments are available are (1) the Karman vortex street behind a circular 

 cylinder ; (2) the Taylor three-dimensional vortex cells between two con- 

 centric rotating cylinders; (3) the Gortler vortices near a concave surface; 

 and (4) the vortex cell pattern in a thin layer of fluid heated from below. 

 These periodic patterns are well defined and mainly laminar in their 

 motion only at Reynolds numbers not too far above that for flow break- 

 down. In the case of the cylinder, for example, the beautiful pictures of 

 Karmdn vortices can be obtained only at Reynolds numbers based on a 

 cylinder diameter of a few thousand. 



Turbulent flow is characterized by the presence of irregular and ran- 

 dom velocity fluctuations of relatively high frequency, but the experi- 

 mental detection and measurement of the velocity fluctuations require 

 equipment not widely available because of its complexity and cost. Tur- 

 bulent flow is most readily detected by the very high rate of diffusion of 

 momentum, heat, vapor, and material particles as compared with the 

 molecular diffusion present in laminar flow. Some of the very large num- 

 ber of techniques of determining the occurrence of transition based on 

 diffusion phenomena are described in IX, F. A familiar method used by 

 Osborne Reynolds depends on the diffusion of dye particles in water, or 

 of smoke particles in air. In laminar flow, filaments maintain their identity 

 over great distances whereas in turbulent flow the dye or smoke is dif- 

 fused laterally very rapidly, destroying the filament. 



In many flows, as for example that behind a circular cylinder at 

 Reynolds numbers from a few thousand to a few hundred thousand, the 

 flow is of mixed character. The flow in the wake shows a periodic character 

 with definite frequency but the rapid diffusion of smoke in the wake 

 shows that the flow there is turbulent. The laminar boundary layer is 

 shed periodically and alternately from the two sides but immediately be- 

 comes turbulent on separation. The vorticity in the layers which roll up 

 into Karman vortices at lower Reynolds numbers is now rapidly diffused 



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