Model reduction and closed-loop control of small amplitude perturbations in transitional open-flows

Open-flows undergoing instabilities and turbulent fluctuations are commonly encountered in engineering applications. For example, bluff-body flows, jet flows, boundary-layer flows or open-cavity flows represent just a few examples of such configurations. These configurations exhibit shear and separations that generate strong spatio-temporal coherent fluctuations, which may be detrimental to the performance of a system (increased drag, induced vibrations, etc). These fluctuations may be described as instabilities or as large-scale turbulent structures. In the following, we aim at reconstructing time-averaged and fluctuating properties of the flow fields from scarce measurements, at developing linear and non-linear reduced-order models of the fluctuation dynamics, and design open-loop and closed-loop strategies to mitigate them or to modify their spectral content.

For these purposes, we will intensively make use of linearized methods, which is the focus of these talks. For example, the coherent structures in the flow fields will be described by global modes or resolvent modes associated to the Navier-Stokes equations linearized around the base- or mean-flows. The use of adjoint methods and weakly nonlinear expansions will then help identify the sensitivity of the flow fields and build reduced-order models.