Optimal feedback control of turbulent channel flow

Feedback control equations were developed and tested for computing wall normal control velocities to control turbulent flow in a channel with the objective of reducing drag. The technique used is the minimization of a 'cost functional' which is constructed to represent some balance of the drag integrated over the wall and the net control effort. A distribution of wall velocities is found which minimizes this cost functional some time shortly in the future based on current observations of the flow near the wall. Preliminary direct numerical simulations of the scheme applied to turbulent channel flow indicates it provides approximately 17 percent drag reduction. The mechanism apparent when the scheme is applied to a simplified flow situation is also discussed.