Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 371

In the opposite case, however, the thickness of the vorticity
layer will increase until it reaches

δ + under the influence of
diffusion. The asymptotic thickness is reached after a time
t +

a

1/ 2

⎡

± 1

⎤

⎛

+ 2

⎞

2 δ 1 +

⎢

+

⎥

t ≈

iA

γ − 1

⎜ ⎟

B

π γ

+

⎢ ⎥

⎝ ⎠

⎣ ⎦

B

For sufficiently long times, the local vorticity disappears
exponentially over time in the direction of the term
( )

. On the other hand, the negative

ω

+

∝− exp γ

B t

+ +

yA +

vorticity layer is far away from the stagnation flow

created by B , and it is therefore affected only by the viscosity
(Figure 5.44). The maximum vorticity in this layer decreases
as

ω −

yA

. From this, we can conclude that for ω

− ∝

1 t

+

yA

+ +

t >> 2 γ , the positive vorticity layer disappears more ω +

B yA

rapidly than . A zone of concentrated asymmetry ω −

yA

results, thus causing the
regeneration of a new shear layer

Δ ( , , ,) x yzt = ∂ω ∂ x ' − ∂ω ∂ x '

y + y −

. ω∂ ∝− wx ∂

y

Tardu and colleagues [TAR 07a, TAR 08a] opted for a
bypass transition study, which makes analysis easier to
perform, and conducted numerical experiments using DNS
which clearly demonstrated the validity of the analysis
detailed above. Two structures, A and B , were inserted into
a Poiseuille flow. These structures are individually stable,
but the assigned spanwise asymmetry and their specific
interaction causes a rapid rise in energy and the formation of
a thin wall of shear, which is rapidly ejected away from the
wall toward the outer layer. The process eventually causes a
turbulent spot and then triggers a rapid transition to a fully
developed turbulent flow. This mechanism, which is
somewhat deterministic, has also been successfully applied