  This work uncovers the low-dimensional nature the complex dynamics of
actuated separated flows. Namely, motivated by the problem of model-based
predictive control of separated flows, we identify the requirements on a
model-based observer and the key variables and propose a prototype model in the
case of thick airfoils as motivated by practical applications.
  The approach in this paper differs fundamentally from the logic behind known
models, which are either linear or based on POD-truncations and are unable to
reflect even the crucial bifurcation and hysteresis inherent in separation
phenomena. This new look at the problem naturally leads to several important
implications, such as, firstly, uncovering the physical mechanisms for
hysteresis, secondly, predicting a finite amplitude instability of the bubble,
and thirdly to new issues to be studied theoretically and tested
experimentally. More importantly, by employing systematic reasoning, the
low-dimensional nature of these complex phenomena at the coarse level is
revealed.
