Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 128

The distortion time is also linked to the integral scale by
way of T D ∝Λ T D , relation [2.94]

becomes equivalent to equation [2.92]. Conversely, for
t

K 1/2 . For short times t

<<

T D , the equilibrium behavior is quasi-steady, and >>

T D ∂

U
∂ y

[2.95] α eff =

Figure 2.32 shows the distribution of T D + in the inner
region of a fully developed turbulent channel flow. We can
see an almost-linear increase in

T + , from

near to the

T +

= 5

wall to T D +

80 . This latter value is near to the
period of regeneration of the coherent structures in the inner
layer, which is typically

70 at y + = =

. Note, in closing, that
relation [2.94] has interesting repercussions in one-point
modeling of unsteady turbulent flows subjected to forced
oscillations of velocity [TAR 05].

t +

= 100

Figure 2.32. Distortion time in inner variables in a fully developed
turbulent channel flow. This figure is adapted from [TAR 05]