B • TURBULENT FLOW 



Comparing the boundary layer and free flow, it is seen that the region of 

 intermittency occurs where the velocity is not much different from that 

 of the free stream in the case of the boundary layer, whereas it pene- 

 trates more deeply into the jet and wake flows. The range of mean ve- 

 locities occurring in the region covered by the various instantaneous po- 

 sitions of the boundary is therefore much less for the boundary layer than 

 for jets and wakes; and while the boundaries may appear superficially 

 similar in all cases, the bulges and hollows involve the greater portion 

 of the mean velocity field in free flows. This applies particularly to the 

 wake. 



According to Townsend [1] free flows contain large eddies which have 

 a relatively small amount of energy, but which nevertheless serve to con- 

 vect the fluid about in large bulks. He postulates a double structure con- 

 sisting of the large eddies containing little turbulent energy and a smaller 

 scale of eddies containing most of the turbulent energy. This would seem 

 to be a reasonable picture in view of the freedom of motion in the absence 

 of a wall, but, to the degree that the outer boundary of a wall flow is 

 also free, the same picture might also apply to the outer region of a 

 boundary layer. 



A statistical measure of the width of the intermittent zone is the 

 standard deviation of the instantaneous boundary from its mean position 

 given by [(F — F)^]*, where Y is the instantaneous position and Y is the 

 average position. 



From Townsend's point of view the standard deviation is determined 

 primarily by the large eddies. Corrsin and Kistler [117] were able to pre- 

 dict the observed behavior (not the absolute magnitude) of the standard 

 deviation in the boundary layer, jet, and wake on the basis of Lagrangian 

 diffusion by continuous movements (Taylor [119]). However, this required 

 only the assumption of similarity of velocity and length scales to one 

 another and to the main flow, and therefore does not rule out a possibly 

 predominant part played by the large eddies. It seems evident that the 

 contour of a marked surface completely within the turbulent region would 

 be qualitatively hke that of the free boundary, but that its coarseness 

 would depend on the scale of the eddies in the neighborhood and on the 

 presence of turbulence on both sides. The boundary is therefore a marker 

 which gives us a picture of the eddy diffusion at the extreme limits. 



The next question of considerable interest has to do with the mecha- 

 nism by which the turbulence spreads into fluid which was originally non- 

 turbulent. This spreading and enveloping of new fluid is the only means 

 by which the average position of the boundary can migrate laterally. 

 Given that the outer flow is irrotational, it must become rotational when 

 it crosses the boundary into the turbulent region. Corrsin and Eastler 

 have concluded that the change takes place suddenly and wholly within 

 a very thin laminar superlayer "plastered" over the boundary. Vorticity 



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