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bursts of high-frequency fluctuations which are associated with intermittent separations of the 

 laminar flow herald the arrival of the more random fluctuations characteristic of fully devel- 

 oped turbulent flow. The transition just described, which depends on the amplification of van- 

 ishingly small disturbances, may be termed self-excited transition. 



Disturbances of greater amplitude arising from free-stream turbulence or rough surfaces 

 tend to hasten the decomposition of the laminar boundary layer into a turbulent boundary layer. 

 Taylor 1^ has developed the concept of momentary separations arising from momentary adverse 

 pressure gradients as the mechanism instigating turbulent motion. In accordance with Taylor's 

 analysis both the scale and intensity of the free-stream turbulence have been shown experi- 

 mentally^ to have a marked bearing on the position of transition. 



The studies of Liepmann^*'^' on the stability of laminar boundary layers on ciu-ved 

 surfaces have shown the ToUmien-Schlichting type of stability to exist on surfaces convex to 

 the flow and the Gortler type of stability involving vortices to exist on concave surfaces. Con- 

 vex surfaces have a greater stabilizing effect and concave surfaces a lesser stabilizing effect 

 than flat surfaces. 



The presence both of large boundary-layer Reynolds numbers and of adverse pressure 

 gradients tends to promote transition by increasing the instability of the laminar boundary 

 layer and by accelerating the amplification of the ToUmien-Schlichting waves. 



Under special circumstances transition is hastened when the laminar boundary layer 

 separates from the body and reattaches itself as a turbulent boundary layer. Such separation 



may be caused by sharp adverse pressure gradients ^ ^on bodies at large angles of attack or by 



1 9 

 sharp adverse pressure gradients induced by large single roughnesses obstructing the flow. 



Quantitative criteria for establishing the transition points on smooth bodies of revolu- 

 tion will be considered here for two technically important flow situations which are character- 

 ized by the absence or presence of significant amounts of turbulence in the main flow stream. 

 Zero or low-turbulence condition exists in specially constructed low-turbulence wind tunnels 

 while a condition of various degrees of turbulence is present in most wind tunnels and flow 

 facilities. The flight of aircraft is considered a case of low turbulence on the basis of tests 

 by Jones^° who concluded that the scale of turbulence in the atmosphere is such as to have 

 no effect on transition. A a'tnilar low-turbulence condition may be assumed in the case of 

 bodies moving in the depths of the oceans where currents are absent. 



Transition in the low-turbulence case may be considered to be of the ToUmien- 

 Schlichting type wherein vanishingly small disturbances are amplified in the boundary layer 

 to the castastrophic point of resulting turbulence within the boundary layer. The stability 

 analysis of laminar boundary layers shows the existence of a point of neutral stability where- 

 in the immediate neighborhood upstream disturbances of all frequencies are damped out. 

 Mangier^ ^ has prepared a chart, partly reproduced in Figure 3, which specifies the neutral 

 stability point in terms of the critical value Rq ^ of boundary-layer Reynolds number Rq 

 where 



