Civil Engineering Reference
In-Depth Information
5.7.4.
Bypass transition
It is necessary to introduce a few basic notions concerning
bypass transition to aid in the understanding of certain
models of regeneration of the near-wall structures, which
will be discussed later on in this chapter. These notions have
already been presented in Chapter 2 of [TAR 11a, TAR 11b],
and we briefly recap certain characteristics of bypass
transition in this section. Interested readers can consult
more specifically targeted publications, such as [SCH 01],
[BRE 90a, BRE 90b, LUN 91, LUN 92, HEN 93, BEC 98]
and [TAR 08a] for further information.
The classic transition mechanism involving Tollmienn-
Schlicting waves can be replaced with a much faster
process in certain conditions [MOR 69]. Thus, the local
disturbances - caused by rough surfaces, for example - can
rapidly become amplified in a subcritical basic flow. We can
look again at the illustration of this phenomenon by the
effect of a contra rotating vortex pair (CRVP) analyzed in
[TAR 11a] and [TAR 11b].
26
The basic flow is the Poiseuille
flow and the Reynolds number (based on the velocity in the
center of the channel and over the half-height) is subcritical
at
.
27
The stream function of the initial
disturbance, i.e. the CRVP, is
Re
=
3, 000
⎡
2
2
⎤
⎛ ⎞
⎛ ⎞ ⎛ ⎞
()
x
x
z
′
[5.85]
ψε
=
fy
z
exp
−
−
⎜ ⎟
⎢
⎜ ⎟
⎜ ⎟
⎥
l
l
l
⎝ ⎠
⎝ ⎠
⎝ ⎠
⎣
⎦
x
x
z
where
is the intensity of the disturbance,
l
and
z
l
are,
respectively, the characteristic length scales in the
26 These results, which are similar to those obtained by Henningson
et al.
[HEN 93], were found by our own direct numerical simulations. The
domain of computation is
60
ε
in the streamwise, wall-normal
and spanwise directions. The grid contains 512*128*128 points.
27 Remember that the critical Reynolds number for linear stability of the
Poiseuille flow is 5,675. The lower bound of the sub-critical transition is
Re
= 1,000 [ORS 93].
π
hh
* 2
*16
π
h
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