Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 121

2.11. Rapid distortion

Consider an initially homogeneous turbulence (isotropic or
axisymmetrical), suddenly subjected to a strong, uniform
shear, whose strain rate is far greater than that induced by
large-scale energetic structures. We suppose that the mean
unsteady flow is

G

( )

()

[2.86]

Ut = β y ,0,0

The initial turbulence is distorted, with a distortion time

∝ Δ

U
Δ

()

[2.87]

T d = β t

y

Suppose that the initial turbulence is characterized by the
velocity scale u 0

1/2 of the large-scale structures and
their associated integral scale L 0 . Their persistence time is
then T L 0

()

= u i u i

L 0 u 0 . If =

T d [2.88] T L 0 >>

the energetic structures remain fixed and do not have the
time to transform and transfer their energy. The above
condition is written as

u 0
β

1 [2.89]

L 0 <<

in which case the nonlinear mechanisms can be neglected
and the equations can be linearized. In addition, we can also
consider the condition

L 2
ν

T

ν =

>> T d

L 2
ν

β >> 1

[2.90]