We note from figure 13 that T ' L < t t except for y* < 3. This is a bit differ- 

 ent than the case of many other physical properties in this region; it is found that 

 laminar and turbulent contributions to various transport and dissipation phenomena 

 are equal at y* £2 12, a common choice of boundary between a "wall layer" and the 

 "outer flow." It seems preferable to restrict the term "laminar sublayer" as designation 

 for the zone in which turbulent transport is actually negligible. 



Wall layer and laminar sublayer 



The physical picture of a wall neighborhood in which viscous effects are not 

 negligible has remained virtually unchanged since its description by Taylor in 1916 [22]. 

 He described it essentially as a Couette flow violently disturbed by the turbulence in 

 the main body of the shear zone, suggesting that it should therefore have a Reynolds 



U(s)e 

 number R e = roughly equal to the theoretical lower critical value for stability 



V 



of such a Couette flow, 150 to 200. 



This assumption permits engineering estimates of turbulent boundary layer and 

 channel flow (via the Karman integral relation, for example). As is well known, it 

 has since turned out to be quantitatively correct if we identify Taylor's layer as extend- 

 ing from the solid wall out to where laminar and turbulent shear are exactly equal. 

 As mentioned in the previous section, this occurs at y* zz 12 [23]. This is the "wall 

 layer." 



Because of the no-slip condition, there must be a non-inertial layer at the wall, 

 presumably characterized by a length made up of the characteristic ("friction") velocity 



nr 



U* = \l — and the kinematic viscosity : 



" P 



h = —■ (45) 



U* 



In this "laminar sublayer" [y* < 1], the direct turbulent transport is negligible. 



Recent hot-wire studies, like [7] and [23], have given information on r.m.s. 

 velocity fluctuation levels well inside the wall layer, and Klebanoff [7] has presented 

 a u' spectrum at y* — 3, virtually in the laminar sublayer. Still it seems likely that 

 more information will be necessary before a suitable theoretical picture can be 

 developed. 



By passing to the y = limits of the equations of motion and their derivatives, 

 it is possible to deduce some restricted relations. For example, it is well known that 

 the Reynolds equations reduce to Stokes flow, with only one appreciable component: 



d 2 U \ 1 / dP \ 



— ) =-(—)■ W 



dy 2 /o m \ ox /o 



The fluctuation momentum equations reduce to a simplified two-dimensional 

 Stokes flow: 



d 2 u • 1 dp 



— = , (47) 



dy 2 n dx 



d 2 w • 1 dp 



— = , (48) 



dy 2 n dz 



392 



