General Points - Transport and Coherent Structures in Wall Turbulence - page 51

G G . If we now consider the evolution of
the wall-normal vorticity component, we have

() ( )

direction, Ω+ x ω xt ,

z z

2

D ω ∂ ω

∂ v ∂ v ∂ v

( )

y y

[1.70]

= ω + ω + ω + Ω + ν

x y z z

Dt ∂ x ∂ y ∂ z ∂ x ∂ x

l l

which can be simplified as:

D ω

⎛ ⎞ ⎛ ⎞

∂∂ v w u w v ∂ ∂ ∂

y

= + −

⎜ ⎟ ⎜ ⎟

Dt ∂∂ x y ∂ z ∂ x ∂ y

⎝ ⎠ ⎝ ⎠

2

⎛ ∂∂ u v

yz xx

⎞ ∂

+Ω− + ν ω

⎜ ⎟

z y

∂∂ ∂∂

⎝ ⎠

l l

Figure 1.20. Transfer of the spanwise vorticity component into wall-
normal and streamwise vorticity in the inner sublayer of a turbulent wall
flow. The local zones of streamwise vorticity may roll up into coherent
quasi-streamwise vortices (QSVs)

A simple analysis of the order of magnitude is sufficient to
show that the predominant production term of is

ω

y

+

, which is
nothing but the stretching of the spanwise vorticity

Ω

z vz

∂∂ in the inner sublayer, where Ω≈ 1

Ω by

z

the shear vz . We can, therefore, suggest a simplified

physical image of the dynamics of vorticity in the buffer
sublayer. The normal vorticity is null at the wall, but is

∂∂