Reduced-order models for closed-loop wake control

Abstract

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.