Synchronization of Low Reynolds Number Plane Couette Turbulence

TL;DR

This paper shows that in low Reynolds number plane Couette turbulence, small scales synchronize based on large scale flow structures, revealing properties akin to an inertial manifold and providing insights into turbulence dynamics.

Contribution

It introduces a Fourier-based scale separation method that identifies stable subspaces and demonstrates scale synchronization in turbulent flow simulations.

Findings

Small scales synchronize when sharing the same large scale flow.

Synchronization occurs for streamwise wavelengths smaller than 130 wall units.

Small scale states decay to a state determined by large scale flow.

Abstract

We demonstrate that a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition identifies subspaces with stable Lyapunov exponents and allows the dynamics to exhibit properties of an inertial manifold, such as the synchronization of the small scales in simulations sharing the same large scales or equivalently the decay of all small scale flow states to the state uniquely determined from the large scale flow. This behaviour occurs for deviations with streamwise wavelength smaller than 130 wall units which was shown in earlier studies to correspond to the streamwise spectral peak of the cross-flow velocity components of the top Lyapunov vector of the turbulent flow.