Control of Bursting Events in a Turbulent Boundary Layer Model

Brian Coller, Theoretical and Applied Mechanics, Cornell University

The talk represents joint work with Philip Holmes and John Lumley in which we investigate the possibility of using feedback to control the burst/sweep dynamics of a turbulent boundary layer. We model the natural dynamics of the system by a set of ten coupled ODEs as derived by Aubry et al. [JFM 1988]. I begin by briefly describing the model and the crucial symmetries and structural features it possesses. After showing how the control affects the model, I describe a time-dependent coordinate transformation which renders a bilinear structure for the leading order dynamics near the set we wish to stabilize. A controller which is geometric in nature is then derived using our knowledge of the global dynamics, and some standard tools from optimal control theory. Because of the structure of the open-loop system, however, our desired state cannot be completely stabilized. In other words, we cannot completely eliminate bursting, but we can significantly delay it.