Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 71

Figure 2.2. Balance of turbulent kinetic energy
in a fully developed turbulent channel flow where
Re

=180
[MAN 88]

τ

y
in the turbulent kinetic energy balance equati on [2.29]. In
the constant shear stress sublayer, we have:

Consider the term representing production P K =− uv ∂ U ∂

2 . This
zone is fully turbulent: it is sufficiently far from the wall so
that the viscosity plays no major role, but sufficiently close
to it so that the total stress does not vary significantly. No
quantity should depend on

− uv ≈ u

τ

in this zone. Given that we can
express the dissipation in the form

ν

3

(by simple
dimensional analysis), it is thus sufficient to properly
determine the velocity and length scales, u

*

ε ∝ u ε l ε

K

and l . With

ε ε

regard to the former, u is imposed naturally. Also, the

length scale of the dissipation must be based on a local scale
s o that l

ε =

u

τ

y . The equality P K

= ε * then leads us to

ε ∝

y = κ

∂ U

∂

u

, i.e. a logarithmic distribution of U .

τ

=

y κ y