ejection along the slit. Since this differed in different photographs it is probably due to 

 the local fluctuations in skin friction and static pressure forces. 



A rather intermittent structure of the wall layer has been shown clearly by an 

 oscillogram of Ruetenik [24]. which is here reproduced as figure 16. As is to be 

 expected, the "bursts" containing higher frequencies are always accompanied by an 

 increase in velocity; this is "'turbulent" fluid coming in to y* = 5 from the outer part 

 of the wall layer. 



Independent observations on the intermittent character of this region have en- 

 couraged Einstein and Li [26] to propose a periodically growing and collapsing laminar 

 "Rayleigh model." Although proper adjustment of constants enables this model to give 

 encouraging agreement with measurements of some flow properties, it appears to suffer 

 from the basic ailment of an infinite r.m.s. skin friction fluctuation. 



It seems likely that a "Stokes model" of the sublayer, with sinusoidal rather 

 than sawtooth periodicity, would overcome this difficulty. However, a model of the 

 entire wall layer must doubtless be three-dimensional, as we see from the photographs. 



Fluctuations in skin friction and surface static pressure 



Since u — ' y near y = 0, it may be possible to interpret Klebanoff's w'-spectrum 

 at y* = 3 [7] as a spectrum of skin friction fluctuations. This possibility is encouraged 

 by the properties of a Couette flow with fixed wall at y — and moving wall (at y zzh), 

 having mean velocity U plus sinusodal oscillation u sin M t in its own plane. The 

 solution of this problem gives 



V 



h / cosh 2 Py — cos 2 Py 



—, (53) 



u \ V " cosh 2 ph - cos 2 ph 

 f 



1 ih 

 where ( — ) = — — — and p = \l — . (54) 



U /;, V 2 b\ 



This gives at the fixed wall 



u' 



£' /o V 2ah 



r 



V cosh 2 ah — cos 2 a/l 



(55) 



h 



If w is identified as an average frequency of the "shear-carrying eddies," i.e. 



w = „.(fci)«. • Uy^t « 100 sec" 1 , (56) 



and if h is chosen such that ~ 3, i.e. h ~ .008 cm, we find ah ~ 0.15. Hence 



\77/o 



— ) , and we conclude that at v* — 3 the relative longitudinal velocity 

 L7/o \XJ L 

 fluctuations have reached their boundary value. 



Klebanoff's power spectrum, though plotted in terms of wave number, was 

 actually measured in time, and in figure 17 is the Fourier transform, essentially the 



395 



