# Linear control of coherent structures in wall-bounded turbulence at Re$_\tau = 2000$

## TL;DR

This paper explores linear feedback control of large-scale turbulent structures in a wall-bounded flow at Re$_\tau$=2000, demonstrating effective strategies for energy reduction with minimal sensor and actuator placement.

## Contribution

It introduces a linear control framework augmented with eddy viscosity to efficiently estimate and suppress large-scale turbulence in high-Reynolds-number flows.

## Key findings

- Control with sparse sensors and actuators performs comparably to full-field control.
- Large-scale turbulence can be effectively estimated and controlled with minimal instrumentation.
- The linear model provides low-cost insights into turbulence management.

## Abstract

We consider linear feedback flow control of the largest scales in an incompressible turbulent channel flow at a friction Reynolds number of Re$_{\tau}$ = 2000. A linear model is formed by linearizing the Navier-Stokes equations about the turbulent mean and augmenting it with an eddy viscosity. Velocity perturbations are then generated by stochastically forcing the linear operator. The objective is to reduce the kinetic energy of these velocity perturbations at the largest scales using body forces. It is shown that a control set-up with a well-placed array of sensors and actuators performs comparably to either measuring the flow everywhere (while limiting actuators to a single wall height) or actuating the flow everywhere (while limiting sensors to a single wall height). In this way, we gain insight (at low computational cost) into how the very large scales of turbulence are most effectively estimated and controlled.