Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 171

twice the total wall enstrophy. By combining this with
equation [3.37] and averaging, we find

( )

[3.47]

ν ωω ε

2

+=

2 *

x 0 z 0 K 0

where is the dissipation of kinetic energy at the wall. The
readers can verify that relation [3.47] is nothing but the local
kinetic energy transport equation at

*

ε K 0

. This relation was = 0 y

already obtained in the previous chapter.

Figure 3.23 shows the results found by Blackburn et al.
[BLA 96], obtained using DNS in a turbulent channel flow at
. We can see that in the viscous
sublayer. This equilibrium is broken in the buffer sublayer
and progressively disappears toward the outer layer.

Re τ = 395 A ij A ji ≈ S ij S ji

Figure 3.23. Behavior of the invariants A and S in a) viscous sublayer,
b) buffer sublayer and c) logarithmic sublayer according to [BLA 96]. The
values are rendered dimensionless in relation to the outer scales