Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 358

unstable steady-state solutions for the Couette flow, similar
to those discovered by Nagata [NAG 90]. We will not go into
detail about this aspect in this topic. Interested readers can
consult [WAL 97].

5.9. Triggering of the mechanism

In the previous chapter, we gave a detailed discussion of
the scales governing the frequency of the ejections, and
concluded that f is governed by inner wall scales rather
than outer scales. The reasonable interpretation of f as the
frequency of regeneration of the near-wall structures
implies, a priori , that any triggering mechanism cannot be
linked to the outer flow. The DNS performed by Jimenez and
Pinelli [JIM 99] lend significant support to this hypothesis.
These authors extend their simulations in the minimum
channel (see [JIM 91]) to apply to Reynolds numbers ranging
up to Re τ = 633 . The spanwise dimension of the channel is

kept at . However, the spanwise integral scale near

to the center is typically

L + =

100

, according to [KIM 87],

L = 0.5 h

int

+

which means that at , the external structures

in the minimum channel are “squashed” at

h e
τ

== 633

L + =

100 , whereas

they should actually extend until . The

external structure of the flow, therefore, is greatly modified,
the classic cascade mechanism is interrupted, and in spite of
this the profiles of the turbulent velocity- and vorticity
intensities remain essentially unchanged in the inner layer
50

+ +

L >

0.5

h =

317

y +

. Thus, a profound structural modification to the
outer layer causes only a slight modification to the internal
structure and the regeneration mechanism. The minimum
transition Reynolds number in a channel flow is
3

<

. Jimenez
and Pinelli [JIM 99] quite rightly stressed that the
mechanism of (bypass) transition does not need an outer

Re = hU / ν = 0 [ORS 83], which is close to h +

=

50

c