Synchronization of Low Reynolds Number Plane Couette Turbulence

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.

References in corpus (6)

• State estimation in turbulent channel flow from limited observations
• Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel
• Transfer learning for nonlinear dynamics and its application to fluid turbulence
• The role of Coherent Structures and Inhomogeneity in Near-Field Inter-Scale Turbulent Energy Transfers
• A statistical state dynamics approach to wall-turbulence
• Self-critical machine-learning wall-modeled LES for external aerodynamics

Cited by in corpus (4)

• Synchronization of turbulence in channel flow
• Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents
• The conditional Lyapunov exponents and synchronisation of rotating turbulent flows
• Intrinsic relationship between synchronisation thresholds and Lyapunov vectors: evidence from large eddy simulations and shell models