Controlling flow turbulence with moving controllers

In this work, we consider how to improve the efficiency of controlling flow turbulence in two-dimensional Navier-Stokes equations. We suggest a control strategy which applies local feedback injections by moving controllers. In the moving frame, this strategy is equivalent to adding a gradient force term in the governing equation. It is shown that with the moving controllers, flow turbulence can be controlled more efficient than the usual pinning strategy with static controllers, provided that the number of controllers and the injection energy are the same. The physical mechanism underlying this higher control efficiency is heuristically analyzed. The advantages and difficulties of the proposed control strategy in practical applications are discussed.