Controlling Turbulence as a Chaotic System

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ABSTRACT Proposal Number: CTS 9729189 Principal Investigator: Moser This is a grant to explore a particularly promising technique for controlling turbulence by exploiting its chaotic nature. In particular, the details of the evolution of the turbulence are highly sensitive to small perturbations. Thus, judiciously chosen small control inputs can in principle produce large changes in the evolution of the flow. In most situations it is important that the control input require very little energy so that the benefits of modifying the flow are not out-weighed by the cost of the control. Several schemes have been developed to control low dimensional chaotic systems using very small control inputs. In the research proposed here, these schemes will be applied to a simple turbulent fluid flow (the minimal turbulent channel), in which drag reduction will be the objective. In these control techniques, one selects as the goal dynamics for the system, one of the presumably infinite number of unstable periodic trajectories that are expected to be embedded in the chaotic attractor of the system. Since this is a natural, although unstable, system trajectory, controlling to this goal dynamic just requires stabilizing it, which can be done with very small control inputs.