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

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.