Large- and Very Large-scale Structures - Transport and Coherent Structures in Wall Turbulence - page 397

( )

small domains of calculation, of dimension in

the streamwise and spanwise directions, and then in a large
domain

πΛΛ , 2

0 0

( )

in order to determine the effects of
large-scale motions on transport. Figure 6.19 shows the
contours of the premultiplied cospectral density of the
Reynolds shear stress. The solid-line contours correspond to
the small domain of calculation, and we can see the cutoff
due to the limited dimensions of the computational domain.
The structures whose size is

8, 4 πΛΛ

0 0

transport (i.e.
contain) nearly 50% of the Reynolds shear stress beyond the
inner sublayer - particularly in the logarithmic sublayer.
Their effect is lesser in the inner sublayer in accordance with
the concept of active and passive structures mentioned in
[TOW 76], which suggests that the impermeability of the
wall limits the large-scale motions by the effect of blocking of
the wall-normal velocity. These observations are not entirely
new, and can be traced back to Blackwelder and Kovasznay
[BLA 72] who showed that the large-scale structures
contained 50% of the turbulent energy and 80% of the
Reynolds shear stress in the outer sublayer. The
aforementioned studies and other more recent ones,
including [KRO 92, LIU 01, ALA 03, GUA 06, WU 12,
BAL 13], confirmed the results of these investigations.

L

Λ> 3

0

Figure 6.19. The premultiplied cospectral density of the Reynolds shear
stress as a function of the wavelength and the distance from the wall,
according to [ALA 04]. Two series of DNS are conducted by the authors,
with . The solid-line contours correspond to the small domain of

calculation and the shaded areas correspond to the large domain

Re

τ =

950