Unstable periodic orbits in plane Couette flow with the Smagorinsky model

Eiichi Sasaki, Genta Kawahara, Atsushi Sekimoto, Javier Jiménez

Research output: Contribution to journalConference articlepeer-review

7 Citations (Scopus)


We aim at a description of the logarithmic velocity profile of wall turbulence in terms of unstable periodic orbits (UPOs) for plane Couette flow with a Smagorinsky-type eddy viscosity model. We study the bifurcation structure with respect to the Smagorinsky constant, arising from the gentle UPO reported by Kawahara and Kida [1] for the Navier-Stokes (NS) equation. We find that the obtained UPOs in the large eddy simulation (LES) system connect to those in the NS system, and that the gentle UPO in the LES system is an edge state branch whose stable manifold separates LES turbulence from an LES 'laminar' state. As the Reynolds number decreases this solution arises as the saddle solution of the saddle-node bifurcation. Meanwhile, the mean and root-mean-square velocity profiles of the node solution of the LES gentle UPO are in good agreement with those of LES turbulence.

Original languageEnglish
Article number012003
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - Apr 29 2016
Externally publishedYes
Event2nd Multiflow Summer School on Turbulence - Madrid, Spain
Duration: May 25 2015Jun 26 2015

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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