Wiener filtering in wall turbulence

This work explores the application of control theory to turbulent channel flow. We use linear optimal control theory to design estimators and controllers that use real-time wall measurements to either reconstruct the internal flow field or compute control inputs to reduce drag. A peculiar feature of this study is the use of Wiener filtering, formulated in the frequency domain, which provides a computationally efficient alternative to conventional time-domain design approaches. The proposed framework integrates the best possible (linear) description of both system noise, representing the effect of nonlinear terms neglected by linearization, and linear model of the channel flow. Notwithstanding the highly preliminary nature of this work, we already demonstrate with DNS an interesting amount of drag reduction at Re τ = 200, and discuss several avenues to further improve control performance.