General Points - Transport and Coherent Structures in Wall Turbulence - page 24

Figure 1.9 shows the von Kárman constant deduced from
the measurements taken by O sterlund et al. [OST 00] and
Nagib and Hites [NAG 95]. The maximum Reynolds number
attained in these experiments is approximately

3

.
The von Kárman constant was determined in the inner layer
delimited by 50

Re

θ =×

28 10

+ +

≤≤ y 0.15 δ . We have expressed as the

κ

value predicted by the renormalization group κ = 0.37 ,

RNG

and represent the data as a function of 1ln Re
θ

. In spite of
an inherent dispersion, we note that the von Kárman
constant increases with 1ln Re
θ

. A linear regression suggests

the variation κκ ∝ 5ln Re

θ

. According to the results

RNG

presented in

Figure 1.9, the von Kárman constant reaches its value
0.37

3

- a limit beyond which it should,
in theory, remain constant.

κ = at Re

θ =×

50 10

RNG

Figure 1.9. The von Kárman constant expressed as its value obtained by
the renormalization group as a function of the Reynolds number.
Experimental data harvested from [OST 00] and [NAG 95].
This figure is adapted from [TAR 11b]