General Points - Transport and Coherent Structures in Wall Turbulence - page 35

i rro tational and contribute to uu , vv (to a lesser degree) and
ww , but not to the Reynolds s tress uv

− . 9 Thus, the effect of

()
max

the Reynolds number on is lesser, and reflects the

− uv

simple fact that the constant shear stress sublayer must
emerge with high Reynolds numbers. Panton [PAN 07]
suggests

⎛ ⎞
−

uv 2

[1.49]

∝ 1 − for Re ∞

⎜ ⎟
⎝ ⎠

τ

2

u

κ Re τ

τ

max

and

Re

y

+
−

∝

τ

for Re → ∞ [1.50]

τ

uv ,max

κ

for the position at the wall where the Reynolds stress
reaches its maximum value. Figure 1.15 recaps the
experimental results analyzed by Fernholz and Finley [FER
96], and compares these measurements with the estimation
[1.49] (the von Kárman constant used for the estimation is
0.37 ). We note a non-insignificant dispersion of the

experimental results around

κκ = =

RNG

3

. On the other hand,
the measurements are indeed grouped around relation [1.49]
at

Re

θ =

10

Re

θ ≥×

410

3

.

9 We will see, in particular in the last chapter, that structures with large
scales are, in reality, not totally passive and transport significant amounts
of Reynolds shear stress in a limited area of the logarithmic sublayer, at
large Re values. In this chapter, however, we will content ourselves with

highlighting the lesser sensitivity of uv

τ

to Re
τ

in comparison to that of

−

the ii uu , and presenting the classical points of view, without lingering on

the topic of the recent advances, which will be discussed in subsequent
chapters.