General Points - Transport and Coherent Structures in Wall Turbulence - page 50

∂
∂

P
x

that the wall flux of mean vorticity Ω is linked to along

z

( )

in a turbulent channel flow,
homogenous in x and z . In a boundary layer on a flat plate,
on the other hand,

∂∂ P x =− μ∂ ∂ Ω y

z

0

( )

since the average pressure
gradient is then null because of the boundary layer
approximation. Equation [1.69], which relates to the
fluctuating fields, of course remains valid in this latter case.

∂∂ Ω y = 0

z

0

The momentum balance equations at the wall give no
indication about the wall flux of wall-normal vorticity
( )

0

, which may not necessarily be zero although
strictly speaking,

∂ω ∂ y

y

. Indeed, we actually have:

ω = 0

y 0

GG

G

G

(

G

)

∇• ω =∇• ∇∧ u = 0

which implies

⎛ ⎞ ⎛ ∂ω

∂ω ∂ω

⎞

y

=−

x

+

z

⎜ ⎟ ⎜

⎟

∂ y ∂ x ∂ z

⎝ ⎠

⎝ ⎠

0

0

( )

and there is no reason for the flow to become null ∂ω ∂ y

y

0

locally and instantaneously.

The wall is a source of vorticity. The vorticity is created at
the wall and subsequently diffuses. It is then advected
and regenerated in a highly 3D environment. The transfer
of vorticity from one component to another is
perpetually occurring during this process. The dominant
component of vorticity near to the wall is in the spanwise