Shear flow compositions on the Galerkin piano: A unified theory for instabilities, strange attractors, statistical mechanics and attractor control

A well-tuned Galerkin melody about fluid flows requires a piano with the right keys (called modes, e.g. POD), musical notes (physics resolution), an audience (observer), and a composer (control law) in case the music shall be changed. Here, we briefly review new key enablers for these tasks. Then, a finite-time thermodynamics is proposed bridging fluid mechanics disciplines and theoretical physics treasures. This formalism opens the path to fully nonlinear attractor control, as required for turbulence manipulation in experimental demonstrators. Presented studies include shear flows with simple to complex dynamics.