General Points - Transport and Coherent Structures in Wall Turbulence - page 21

channel flow covering a range from small Reynolds numbers
/ Re = u h ν = 0 to moderate values Re τ = 1, 1 0 0 . Indeed, we

τ τ

()

can see a sublayer wherein which, apparently,

U

+

∝ ln y

+

begins at . A more detailed analysis, though, reveals

that the von Kárman constant

y + = 30

has not yet reached its
asymptotic value, because the Reynolds numbers in question
here are small, and the “logarithmic layer” is not entirely
free of viscous effects in the case shown in Figure 1.5. Let us
stress the highly restrictive nature of the numerous
hypotheses that have led us to relation [1.25], which, in
particular, requires that the viscous stress be negligible and
the Reynolds stress uv +

κ

be constant and equal to 1 in that
zone. However, rigorously speaking, these hypotheses are
valid only within the range Re τ

−

→∞ . Thus, in the range of

values considered here, the zone wherein the Reynolds
stress is constant and “approximately” equal to the stress at
the wall (though not exactly equal) is greatly restricted, as
shown by Figure 1.6.

Re τ

Figure 1.6. Profiles of the Reynolds stress in units wall in a fully
developed turbulent channel flow. The results are obtained by Bauer
[BAU 14] by direct numerical simulations in the range
180 to

Re

τ =

Re

τ =

1,1 0 0