Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
