Orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow
Phys. Rev. Fluids 11, 054603 – Published 14 May, 2026
DOI: https://doi.org/10.1103/mtw2-29r3
Abstract
We perform an unstable periodic orbit (UPO) analysis of moderately developed Couette turbulence with large-eddy simulations (LES) using a static eddy viscosity model. The UPOs extracted here are invariant solutions to the LES dynamical system, and their instability characterizes the dynamics of large-scale motions resolved by LES, providing insights into the mechanisms underlying Navier-Stokes turbulence. We find that spanwise vortices, stretched between streamwise rolls, approach the walls, over which new spanwise vortices are generated. The stretching of these vortices is driven by strong shear layers induced by the streamwise rolls. This vortex-generation mechanism, as revealed by the LES UPOs, is a significant dynamical process in LES turbulence at high Reynolds numbers. By computing local Lyapunov exponents, which quantify the least stable perturbation growth rates along the UPOs, we show that the stretching process amplifies their growth. The corresponding Lyapunov vectors highlight the instability of prominent shear layers through which the stretched spanwise vortices emerge between the rolls. Our results suggest that high-strain-rate structures in developed turbulence play a central role in shaping the geometrical structure of turbulent orbits in phase space.
