Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 321

Figure 5.22. Temporal growth rate of the most unstable
mode of streaks as a function of the wavelength for
(

)

ˆ

+ + +

=Δ = ωβ u 2 . 5 , according to [SCH 00]

y max s

We have no additional elements of information to draw
conclusions about the universality of these results, which
depend on the initial conditions and on the basic flow. It
should be noted, however, that the analysis reported in
[SCH 00] is in quantitative agreement with the study
conducted by Jimenez and Moin [JIM 91], which relates to
the length scales necessary to maintain developed
turbulence in a channel flow. These authors [JIM 91]
determined the minimum streamwise length L and
spanwise breadth L of a channel in which a turbulent flow
with a small Reynolds number can be maintained with
statistical properties which are close to those in a fully
developed turbulent flow. The stu dy was conducted by means
of DNSs in the range 2, 000 . 22 Figure 5.23

recaps the results obtained by Jimenez and Moin [JIM 91].
The flow becomes turbulent in channels whose spanwise
breadth is slightly larger than the spacing between the

≤= Re U h ν ≤ 5, 000

c

22 It should be specified that the channel flow is absolutely stable (in the
nonlinear sense) for , according to [ORS 83].

Re ≤ 1, 000