January 20 ,2016
Speaker: Dr. Eiichi Sasaki, Osaka University
Title: Unstable periodic orbits in plane Couette flow with the Smagorinsky model
Abstract: First, I will discuss high Reynolds number turbulence in channels, modelling by Large Eddy Simulation and the role of Unstable Periodic Orbits (UPOs).
We then aim at a description of the logarithmic velocity profile of wall turbulence in terms of 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 (2001) for the Navier-Stokes (NS) equation. We find that the obtained UPOs in the 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.
The mean and root-mean-square velocity profiles of the upper branch of the LES gentle UPO are in good agreement with those of LES turbulence.