Large- and Very Large-scale Structures - Transport and Coherent Structures in Wall Turbulence - page 411

typically λ at a given position y + . The large- and very

large-scale motions of size

+

∝ 2 y

+

v

, which significantly
contribute to the local uu , can locally contribute to uv

+

α Λ

0

, if

−

α Λ

+

[6.9]

y

+

∝

0

2

for reasons of similarity of scale. The experiments conducted
by Guala et al . [GUA 06] in a circular pipe at

confirmed the existence of large-scale
structures of size

4, 000

<<

Re 8, 000

, which contain and transport
streamwise kinetic energy in the logarithmic sublayer, as
predicted by the results discussed in the previous section,
and those of [ALA 04], among others. These structures also
transport the Reynolds shear stress in the outer sublayer.
Figure 6.25 shows the streamwise length scale that
corresponds to half of the cumulative stress. This is defined
in the spectral domain by

16 Λ

0

k

x

()

∫

E kdk

uv x x

⎛ ⎞

2 π

γ k = = 1 −

0

⎜ ⎟

uv x

L

∞

⎝ ⎠

()

x

∫

E kdk

uv x x

0

We can see that the structures of mean size make

L

≈Λ

0

the most significant contribution to uv near to the wall, at −

in the
range of Reynolds numbers analyzed by Guala et al.
[GUA 06]. In ot her words, the buffer sublayer where
production uv U y

. This zone typically corresponds to

y +

y Λ< 0.1

≤ 300

0

reaches its peak is, once again, under
the influence of the local scales, and the dynamical effect of
the large-scale structures is marginal there. However, the
size of the structures transporting the Reynolds shear stress
in a sublayer delimited by

− ∂∂

reaches values as

0.2 <Λ< y / 0.3

0