Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 239

coexist with the active ones, and play an increasingly
dominant role, within the bound h + . The velocity scale,

which is c ha racteristic of these structures, is then identical
to that of uu . Hence, we can write

→∞

uu

() (

*

+

[4.27]

uu y ≡

P P

)

PP

u αα
τ

2 −

c

[PAN 07] supposes that t he active contribution, which is
directly responsible for

uv , is indep en dent of the outer
velocity scale, and is solely governed by u

−

. Therefore

τ

uu

()

*

[4.28]

+

uu y ≡

AA

AA

u τ

2

The interaction u A u P depends simultaneously on u and

τ

U c . Thus, it accepts a composite characteristic scale

2 − β U c β

u τ

with a priori , so that β ≠ α

2

uu − u

() (

*

+

[4.29]

uu y ≡

A P

=

A

) ( )

AP

2 − β β 2 − β β

uU uU

τ c τ c

Equation [4.25], when expressed in mixed scales, becomes

α α − β

⎛⎞ u ⎛⎞ u

* + *

()

+ 2

uu = u u

τ

− 2 u

τ

+ u u [4.30]

⎜⎟ ⎜⎟

A A A P P

U U

⎝⎠ ⎝⎠

c c

0
adequately describe the results found by [DEG 00] and
[MET 01]. The veloci ty scale of the passive structures,
therefore, is simply u
τ

[PAN 07] indicates in his article that 1 and α =

β =

U c , according to equation [4.27].

The active structures give rise to the Reynolds shear
stress. This leads [PAN 07] to hypothesize that the