Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 311

Figure 5.17. Conditional averages of the velocity fields in the plane y-z at
a)

x + = x + = 0

(detection plane) and b) , according to [BRO 93].

See text for further details

30

The local flow induced by the QSVs dissipates or
intensifies depending on the nature of the interaction with
the basic flow. In accordance with the arguments given in
the previous section, suppose that the local velocity-

( )

i uyzt

,;

are independent of x during the
first moments of the regeneration process. The initial
distribution of the vorticity is, in this case,

( )

and vorticity fields ω yzt ,;

i

∂ wv ∂ ∂ u ∂ u

ω =−

i i

; ω =

i

; ω −

i

[5.49]

xi yi zi

∂ y ∂ z ∂ z ∂ y

s uxyzt - this time
dependent on x -is then established intermittently around
the QSV. The mechanism which gives rise to

( )

Now suppose that a secondary field ,,;

is set
aside for the moment, with the aim being to determine the
evolution of the secondary field, and especially the evolution
of the wall-normal vorticity

∂∂ x

, which
plays a key role in the reproduction of the structures.
[TAR 95a] proceeds by linearization around

ω∂∂∂∂ = uz − wx

ys s s

( )

and

i uyzt

,;