Large- and Very Large-scale Structures - Transport and Coherent Structures in Wall Turbulence - page 421

the large-scale structures is not di re ct i n the sublayer
80

( )

reaches its
maximum. These structures are irrotational, and the effect
they have, essentially, is to limit the length of the streaks to
values, which are multiples of the thickness

y +

, where the mean production

< − uv U y ∂∂

. This
limitation of the wavelength should lead to a spectral zone
where the one-dimensional spectrum

Λ

0

decreases in
the inner region. The results found by Hoyas and Jimenez
[HOY 06] and Jimenez et al . [JIM 04] show that

k β

−

E ∝

uu x

gives
an accurate depiction of the spectral behavior in a range of
wavelengths

β = 1

[ ]

+

L

= 500,10 Re

τ

. The velocity scale is u , and

τ

the integral of

u E within this range is

∝ Re ∝ Re

dk
uu Eku u e
k

τ τ

( )

2 2

∫

2

∫

2

= ∝

x

∝ ln

τ uu x τ τ τ

x

The turbulence in the inner sublayer organizes
autonomously by amalgamation of the packets of QSV s to
form long streaks. The mechanism is identical to that for the
formation of VLSM . The outer flow has no effect on the
length scales of the wall-normal velocity in the inner layer.
These length-scales are simply the length and diameter of
the individual QSV s, and are linked to the inner scales. The
long streaks, whose size ranges from 10 to , are

surrounded by active regions containing sites with large uv

20 Λ

0

.
The amalgamation of the wakes of the packets of vortex
structures gives rise to coherent organization on a large scale
in the direction of the flow. These structures transport a non-
insignificant percentage of the Reynolds shear stress, which
does not mean that the large-scale structures actively
produce turbulence. Turbulence production in the inner layer
is a phenomenon that is truly local. In closing, it should also
be borne in mind that the long tails observed in the

−