Turbulence suppression in plane Couette flow using reduced-order models

Abstract

We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of controllability modes, truncated to a few streamwise and spanwise wavenumbers. Such ROMs were found to reproduce key aspects of nonlinear turbulence dynamics in Couette flow with only a few hundreds degrees of freedom. Here we use the ROM to devise a control strategy. For that, we consider a ROM with an extra forcing term, consisting in a steady body force. The spatial structure of the forcing is given by a linear combination of Stokes modes, optimised using a gradient-descent algorithm in order to minimise the total fluctuation energy. The optimisation is performed at different Reynolds numbers, with the optimal forcing leading to laminarisation of the flow in all cases. The forcing mechanism acts by strongly reducing the shear in a large central portion of the channel. This disrupts the dynamics of large-scale streaks and rolls and hinders the main energy input to the system. When the forcing is active, the flow reaches a new laminar state which is linearly stable and whose linear transient growth is substantially reduced with respect to that of laminar Couette flow. These features prompt the flow to return to the laminar Couette state when the forcing is switched off. Body forces optimised in the ROM are subsequently applied to the full NS system in direct numerical simulations (DNS) for the same flow configurations. The same control mechanisms are observed in the DNS, where laminarisation is also achieved. The present work opens up interesting possibilities for turbulence control. We show that the ROMs provide an effective framework to design turbulence control strategies, despite the high degree of truncation with respect to the full system.

References in corpus (21)

• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction
• On a self-sustained process at large scale in the turbulent channel flow
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow
• Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
• On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
• Self-sustaining process of minimal attached eddies in turbulent channel flow
• Destabilizing turbulence in pipe flow
• Extreme-scale motions in turbulent plane Couette flows
• Cause-and-effect of linear mechanisms sustaining wall turbulence
• On the role of nonlinear correlations in reduced-order modeling
• On the self-sustained nature of large-scale motions in turbulent Couette flow
• Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions
• Stabilisation and drag reduction of pipe flows by flattening the base profile
• Designing a minimal baffle to destabilise turbulence in pipe flows
• Structure interactions in a reduced-order model for wall-bounded turbulence
• Upper edge of chaos and the energetics of transition in pipe flow
• Multi-scale invariant solutions in plane Couette flow: a reduced-order model approach
• Linear stability of Poiseuille flow over a steady spanwise Stokes layer