Control of Turbulent Boundary Layers: A Biased Overview

Brianno Coller, Control and Dynamical Systems, California Institute of Technology

I begin by reviewing pertinent boundary layer phenomena whose dynamics are responsible for the majority of turbulent kinetic energy production. Most recent efforts to control or suppress such phenomena have either focused on heuristic quasi-static ideas, or upon methods with stronger mathematical foundation, but which are too computationally intensive for practical implementation on the Navier-Stokes equations. After briefly discussing these approaches, I present an alternative which, from the standpoint of dynamical complexity, lies between these extremes.

The control strategies we develop are inspired by low dimensional models of the turbulent boundary for which symmetry plays a vital role in determining the global behavior. Heteroclinic cycles which mimic key aspects of the turbulence production process are robust features of the models. The control input enters the equations in a bilinear fashion. We stabilize the equilibria within a general class of heteroclinic attractors by exploiting symmetry and resorting to concepts from optimal control theory.

There are several more milestones to surpass before the strategies can be applied to the boundary layer. Finally, I propose a future direction for the research.