General Points - Transport and Coherent Structures in Wall Turbulence - page 37

These distributions attain their asymptotic form with
universal constants within the limit of large Reynolds
numbers, in the zone with no viscous effect, where the total
stress is reduced to the Reynolds stress - in other words, in
the logarithmic sublayer delimited by 3

+
≤≤

Re y 0.15 Re

τ τ

[EYI 08, KLE 09, MAR 13]. The coefficient u A is then 1.26
[M AR 13]. Figure 1.16 shows the experimental profiles of
()

+ across a wide range of large Reynolds numbers.
The emergence of the logarithmic distribution with a
“universal” constant

2

uu u y

τ

u A is clearly visible.

Figure 1.16. Distributions of the turbulent intensity of the streamwise
velocity for

(A), 98,190 (B), 68, 780 (C), 18, 010 (D).
The vertical dotted lines delimit the zone 3

Re

τ =

628, 000

. Rey e

τ

≤≤

+

0.15

τ

This figure is adapted from [MAR 13]

Various semi-empirical corrections can be made to
relations [1.51], in particular to take account of the viscous
effects with lower Reynolds numbers [TAR 11a, TAR 11b].