Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model

TL;DR

This study investigates the bifurcation structure of unstable periodic orbits in plane Couette flow using LES with the Smagorinsky model, revealing new vortex phenomena and their role in turbulence dynamics.

Contribution

It introduces a bifurcation analysis of UPOs in LES with the Smagorinsky model, connecting to known Navier-Stokes solutions and identifying novel spanwise vortices.

Findings

Detected bifurcation points linking known UPOs.

Identified spanwise vortices in LES UPOs.

Vortices enhance turbulent momentum transfer.

Abstract

In order to obtain insights into dynamics of developed plane Couette turbulence, this paper considers bifurcation structure of unstable periodic orbits (UPOs) in the large-eddy-simulation (LES) system with the Smagorinsky-type eddy viscosity model. Treating the Smagorinsky constant as a bifurcation parameter, we detect the bifurcation points connecting two known UPOs which were separately discovered in the Navier--Stokes system [G. Kawahara and S. Kida, J. Fluid Mech., 449, 291--300 (2001)]. At the moderately high Reynolds number, the LES UPO of the present study possesses the spanwise vortices which seem to be caused by the streak instability and appear in the central region of the channel. We note that to our knowledge a spanwise vortex has not been reported through the UPO analysis of wall flows. The stretched spanwise vortices of the LES UPO enhance transfer of the streamwise turbulent momentum as in developed near-wall turbulence.