---
res:
bibo_abstract:
- 'In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille
flow. The Reynolds number ( ) for which turbulence first appears in a given experiment
– the ‘natural transition point’ – depends on imperfections of the set-up, or,
more precisely, on the magnitude of finite amplitude perturbations. At onset,
turbulence typically only occupies a certain fraction of the flow, and this fraction
equally is found to differ from experiment to experiment. Despite these findings,
Reynolds proposed that after sufficiently long times, flows may settle to steady
conditions: below a critical velocity, flows should (regardless of initial conditions)
always return to laminar, while above this velocity, eddying motion should persist.
As will be shown, even in pipes several thousand diameters long, the spatio-temporal
intermittent flow patterns observed at the end of the pipe strongly depend on
the initial conditions, and there is no indication that different flow patterns
would eventually settle to a (statistical) steady state. Exploiting the fact that
turbulent puffs do not age (i.e. they are memoryless), we continuously recreate
the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce
periodic boundary conditions for the puff pattern. This procedure allows us to
study the evolution of the flow patterns for arbitrary long times, and we find
that after times in excess of advective time units, indeed a statistical steady
state is reached. Although the resulting flows remain spatio-temporally intermittent,
puff splitting and decay rates eventually reach a balance, so that the turbulent
fraction fluctuates around a well-defined level which only depends on . In accordance
with Reynolds’ proposition, we find that at lower (here 2020), flows eventually
always resume to laminar, while for higher ( ), turbulence persists. The critical
point for pipe flow hence falls in the interval of $2020 , which is in very good
agreement with the recently proposed value of . The latter estimate was based
on single-puff statistics and entirely neglected puff interactions. Unlike in
typical contact processes where such interactions strongly affect the percolation
threshold, in pipe flow, the critical point is only marginally influenced. Interactions,
on the other hand, are responsible for the approach to the statistical steady
state. As shown, they strongly affect the resulting flow patterns, where they
cause ‘puff clustering’, and these regions of large puff densities are observed
to travel across the puff pattern in a wave-like fashion.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Mukund
foaf_name: Vasudevan, Mukund
foaf_surname: Vasudevan
foaf_workInfoHomepage: http://www.librecat.org/personId=3C5A959A-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Björn
foaf_name: Hof, Björn
foaf_surname: Hof
foaf_workInfoHomepage: http://www.librecat.org/personId=3A374330-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-2057-2754
bibo_doi: 10.1017/jfm.2017.923
bibo_volume: 839
dct_date: 2018^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0022-1120
- http://id.crossref.org/issn/1469-7645
dct_language: eng
dct_publisher: Cambridge University Press (CUP)@
dct_title: The critical point of the transition to turbulence in pipe flow@
...