Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 218

The coherent vortices merge to form larger-scale
structures, and the spacing of the streaks (which is simply
their spanwise signature) and their thickness (characterized
by

) increase with increasing y + . Figure 4.17 illustrates a
number of re su lts drawn from the existing body of literature.
A tendency

σ λ

y + is clearly perceptible, regardless of the
Reynolds number

λ + ∝

. We can see that the data
found by Rajaee et al. [RAJ 95] are higher than an earlier set
of measurements which are grouped closely together. These
authors determined the spacing of the streaks by way of the
minimum of the spanwise correlations of u

Re θ ≤ 6,000

( ) ( )

ux y t ux yzt ,,0, ,,,

( )

0 i 0 i

[4.5]

Rx = 0, yzt , , = 0 =

uu

()

uy

2

at a fixed distance y from the wall. The method is based on
the fact that the spanwise correlation of u changes sign with
a (negative) minimum which marks the half-periodicity

2
in a flow induced by two counter-rotating vortices. The
coherent vortices are random in time and space in a
turbulent flow. According to [RAJ 95], though, this random
nature should not affect the validity of the method because of
the hypothetical velocity field induced by the counter-
rotating structures

λ

() ()

uUy = sin ⎡ zrt − ⎤

⎣ ⎦

() ()

[4.6]

vVy = cos ⎡ zrt − ⎤

⎣ ⎦

dV

()

w =− sin ⎡ z − r t ⎤

⎣ ⎦

dy

where rt is a random function. This flow represents an

infinite periodic sequence of counter-rotating rolls moving
randomly in relation to one another. The simple
transformation z

()

() → z implies that R uu z ()

is not affected

− rt