Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control

TL;DR

This paper presents a linear feedback control strategy that effectively relaminarizes turbulent channel flow at Re_tau=100 by targeting large-scale motions, ensuring energy decay of perturbations and convergence of flow state estimates.

Contribution

It introduces a one-time offline synthesis control method that guarantees monotonic energy decay and convergence, applicable to turbulent flow with full-domain sensing and actuation.

Findings

Control successfully relaminarizes flow at Re_tau=100

Large-scale motions above streak spacing are effectively controlled

Minimal effort needed once laminar flow is achieved

Abstract

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller's estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow ($Re_\tau=100$) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl's theory of sheared turbulence.