  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.
