B,2 • NATURE OF TURBULENT FLOW 



lar ones, when they occur, are readily accounted for in terms of pressure 

 gradients resulting from the curvature of the main flow, usually imposed 

 by the shape of the boundaries. Irregular ones, called turbulence, are by 

 far the more common, and their direct cause is less obvious. Their occur- 

 rence does not depend on the shape of the boundaries, but hke all second- 

 ary flows, they must depend on a generating mechanism which produces 

 motions in directions other than that of the applied shear. We must look 

 for this mechanism within the flow itself. Our inquiry can be divided into 

 two parts, the first having to do with how the motions begin, and the 

 second being concerned with how the motions maintain themselves. 



To consider the first part, it is necessary to recall the transition prob- 

 lem treated in Sec. A. In many important cases a shear flow is laminar 

 over the initial part of its course and then becomes turbulent and re- 

 mains so for the remainder of its course. According to present evidence 

 the initial onset of turbulence occurs suddenly by a breakdown of the 

 laminar flow in localized regions. The cause of the breakdown is attributed 

 to instability of the laminar flow under the action of disturbances. While 

 conditions may be altered by the roughness of a surface or pressure gradi- 

 ent, a characteristic feature is the completeness of the turbulent state in 

 the patches which grow following the breakdown. It is now well known 

 that turbulence is convected downstream in the manner of any other fluid 

 property, and, except in special cases where the flow is impeded to such a 

 degree that turbulence can hold its position, it is washed away from the 

 point where it originates and is followed by laminar flow. Repeated break- 

 downs are therefore generally required to maintain a continuous supply 

 of turbulence, and instability of laminar flow is an essential part of this 

 process. 



For the second part of the inquiry we turn our attention to some 

 section downstream where all isolated patches have grown together and 

 the flow is continuously turbulent. We now observe that turbulence which 

 is convected on downstream is followed by other turbulence from up- 

 stream. A steady state is maintained if the turbulence leaving is as vigor- 

 ous as that arriving. The question now is whether instability plays a 

 similar role in this sustaining process as it played in initiating the turbu- 

 lence originally. Evidently it does not if turbulent motions already present 

 can reinforce themselves to counteract the damping action of viscosity. 

 Since turbulent motions produce frictional stresses against which the 

 mean flow does work, a mechanism does exist by which turbulent motions 

 capture kinetic energy from the mean flow. This is expressed by the 

 well-known production term in the energy equations, consisting of the 

 turbulent shear stress times the mean local velocity gradient. In short, 

 turbulence carries with it the mechanism for sustaining itself, and this is 

 sufficient to balance losses or gains by diffusion and convection and losses 

 by viscous damping and still maintain a steady state at each point. 



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