Unstable periodic orbits in plane Couette flow with the Smagorinsky model

2nd Multiflow Summer School on Turbulence

Sasaki, Eiichi^1 ; Kawahara, Genta^1 ; Sekimoto, Atsushi^2 ; Jiménez, Javier^2

Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, Japan^1

School of Aeronautics, U. Politécnica de Madrid, Madrid, Spain^2

关键词: Bifurcation structures;    Eddy viscosity model;    Plane Couette flow;    Root mean square velocity;    Saddle node bifurcation;    Smagorinsky constants;    Smagorinsky model;    Unstable periodic orbits;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/708/1/012003/pdf
DOI  :  10.1088/1742-6596/708/1/012003

来源: IOP

【 摘 要 】

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.