Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 306

Figure 5.15 shows the scenario described by Brooke and
Hanratty [BRO 93] and the sequence of events linked to a
“mother” quasi-streamwise vortex with . The vorticity

linked to the structure and its size gradually increases over
time. The mother vortex ( M ) is surrounded by two zones of
positive streamwise vorticity in Figure 5.15, with the layer on
the right-hand side extending right up to the wall. It is not
certain that this characteristic will be a universal element of
the regeneration, and in particular a specific detail of the
sample under observation. The stagnation flow induced by the
“sweep” (

ω > 0

x

) on the immediate right-hand side of M
creates a local area of high pressure. A layer of negative
streamwise vorticity develops on the left-hand “ejection” side
(

,

0 0

u > v <

) of M . The interaction of the high-pressure zone
caused by the stagnation flow with the high-velocity streak
0

, u < 0 v > 0

is the final stage in the regeneration process. The key
element is the creation of a local zone in which the spanwise
velocity w increases progressively in the streamwise
direction. A dependence on x is established by the formation
of the shear layer

u >

around the structures, which are
significantly elongated in the mean direction of the flow. The
apparition of

∂∂ wx

around the structures of at least 300 inner
variables in length is an entirely separate issue, which we will
return to at various junctures later in this chapter. The shear
layer

∂∂ x

appears to be a freshly created compact zone of
wall-normal vorticity

∂∂ wx

. During this time,
the high-pressure zone drives the mother structure and

ω∂∂ ∂∂ = uz wx −

y

to
the left, as we can see in the last tile in Figure 5.15. The shear
layer

ω

y

is tilted by the mean shear and increases the
secondary streamwise vorticity

∂∂> wx 0

induced by the mother
structure at the start of the process. When the necessary
conditions are fulfilled, this secondary layer is concentrated in
a compact region, rolls up and gives rise to a “baby” QSV
whose sign of vorticity is opposite to the mother vortex.

ω < 0

x