A low-dimensional model of separation bubbles

In this work, motivated by the problem of model-based predictive control of separated flows, we identify the key variables and the requirements on a model-based observer and construct a prototype low-dimensional model to be embedded in control applications. , using a phenomenological physics-based approach and dynamical systems and singularity theories, we uncover the low-dimensional nature of the complex dynamics of actuated separated flows and capture 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.