B,28 • GENERAL FORM AND STRUCTURE 



can be transmitted to an irrotational flow only by tangential forces due 

 to viscosity. The layer in which this takes place is the laminar superlayer. 

 Corrsin and Kistler have shown that this layer must be very thin, partly 

 on the grounds that stabihty considerations would not permit it to be 

 otherwise, and partly on the grounds that the turbulent stretching of 

 vortex lines increases the vorticity and therefore sharpens up the velocity 

 gradient. The thickness has been estimated to be less than the dissipation 

 length X. The presence of the laminar superlayer cannot be detected ex- 

 perimentally, but the observed sharp demarcation between turbulent and 

 nonturbulent regimes tends to confirm the thinness of the layer. 



The spreading of the turbulent region therefore takes place by viscous 

 action at the immediate boundary, and the rate of encroachment depends 

 on the steepness of the laminar gradient and on the surface area, both of 

 which are increased by the larger-scale, eddy-diffusion process acting from 

 within. Viscosity is the vorticity-propagating agent, but it plays no con- 

 trolling role in the spread of the turbulent region. Corrsin and Kistler 

 point out that heat and matter are transported across the boundary in 

 exactly the same way; and if the Prandtl and Schmidt numbers are not 

 much smaller than unity, these scalar quantities should be transported 

 at the same rate as momentum. The processes at the immediate boundary 

 therefore do not explain why heat and matter spread faster than mo- 

 mentum. We shall return to this question in Art. 29. 



The phenomena just described require that the fluid everywhere be- 

 yond the boundary cannot have received any quantity by diffusion. If a 

 jet is hot, all of the heat is confined within the sharp boundary. The 

 same is true of all of the axial momentum. The only effect on the outer 

 fluid is a pressure-induced flow toward the jet and pressure-induced fluctu- 

 ations. Both are irrotational. The term, turbulence, cannot be applied to 

 these fluctuations. Relatively slow, potential-type velocity fluctuations 

 are in fact observed in the outer fluid. Jumps in mean velocity are also 

 observed in passing from turbulent to nonturbulent regions. Apparently 

 in some cases these are smaller than would be expected if free stream 

 velocity prevailed in the nonturbulent regions. Townsend proposes that 

 the fluid between two turbulent bulges is partially carried along as the 

 bulges move downstream, but there is some disagreement on this point. 

 Corrsin and Kistler find jumps in the intermittent region of a boundary 

 layer of about the order to be expected if the outer fluid is not carried 

 along. 



The sharp boundary is not to be confused with the limits as usually 

 expressed in terms of mean velocity distribution. It wiU be noted from 

 the 7 curves that the fluctuations in the sharp boundary generally ex- 

 tend beyond the mean velocity boundary. A bulge protruding far out 

 apparently carries so little mean velocity increment or defect that its 

 effect cannot be detected by the usual methods. 



'< 167) 



