General Points - Transport and Coherent Structures in Wall Turbulence - page 9

which is the sum of the viscous stress and the Reynolds
stress. We introduce the friction velocity u τ

2

ρ u

τ

= τ [1.15]

0

and the internal length scale

ν

[1.16]

l =

ν

u

τ

The values rendered dimensionless by the wall units u
τ

+ . The dimensionless form of
equation [1.14] in inner variables is

()

and l
ν

are indicated by

∂ U

+

y

+

+

[1.17]

τ

+

= − uv = 1 −

tot

+ +

∂ y h

Figure 1.2. Reynolds stress in wall units as a function of the distance to
the wall. The solid line represents the total stress. These results are
obtained on the basis of direct numerical s imulations in a fully developed
turbulent channel flow for

hu

τ

. (From [DOC 06])

Re

ν ==

180

τ

Thus, the total stress varies linearly with the distance
from the wall. Relation [1.17] is exact. Figure 1.2 shows the