General Points - Transport and Coherent Structures in Wall Turbulence - page 14

The turbulent boundary layer equations are finally
reduced to:

2

U U Uuv
UV U
x

∂ ∂ dU ∂ ∂

[1.22]

+ =

∞

+ ν −

∞ 2

∂ ∂ y dx ∂ y ∂ y

Figure 1.3. Scale characteristics of a turbulent boundary layer
and a local turbulent structure

1.7. Scales in a wall-bounded turbulent flow

We will begin by introducing the velocity and length
scales needed to describe the physics of wall turbulence and
turbulent transfer at the rigid boundary. The meaning of
these scales will become clearer when we introduce the
mixing-length-type closures later in this chapter. Generally
speaking, we can distinguish two zones in a wall flow: a
near-wall zone, where the flow is controlled by the internal
scales , and a zone relatively far from the wall, governed by
the external scales .

The near-wall zone is characterized by the wall shear
stress

( )

and the kinematic viscosity . We

τμ∂∂ = uy

ν

0

0

introduce a fictitious velocity based on the shear

at the wall, called the friction velocity. This velocity scale
accurately describes the turbulent state near to the wall,
because without shear (vorticity), no turbulence can be

u τ = τ ρ

0