Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 80

The situation is more complex in the inner layer. The
viscosity is dominant in and below of the buffer sublayer.
Consequently, the scale governing the terms of the balance
should be u
τ

. Figure 2.6, reproduced from [HOY 08],
shows the different transport terms in the inner scales at
2, 000

4

ν

Re

τ =

. Unlike the outer layer, where the local scale

3 adequately describes the transport, [HOY 08] observed
significant differences between the profiles for different
Reynolds numbers, in particular for the dissipation and the
pressure-linked components

y / u

τ

π i d defined in equation
[2.4]. Production is relatively spared from this discordance.
The maximum difference between the production profiles for
different Reynolds numbers is two times smaller than the
difference in the dissipation distributions. Indeed, the
dissipation at the wall increases with the Reynolds number
under the influence of the passive structures, in accordance
with the earliest analyses performed by Bradshaw [BRA 67].

π i s and

The large-scale passive structures contribute to the
streamwise and spanwise turbulent intensities, but affect
the Reynolds stress relatively little or not at all, which is in
line with the original concept of active structures advanced
by Townsend [TOW 76]. However, we will see in the final
chapter that the large structures con tr ibute not only to the
turbulent intensities but also to

uv in the logarithmic
sublayer, where they play a highly active role. 9 Structures as
large as 5

−

Λ 0 transport the majority of the Reynolds stress,
typically at y

0.3 [GUA 06]. The size of these structures
decreases near to the wall, and is

Λ 0 >

Λ 0 in the inner layer,
where production reaches its peak. One simple way of
reconciling the pioneering concept of [TOW 76] with the
recent advances is to specify that the length scale
characteristic of the active structures depends on y + and Re .

τ

9 The very large structures only appear when the Reynolds number is
high, i.e. Re τ > 1,800 (see Chapter 6).