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Fluid Mechanics = "Single"-Particle Control: From Control to Turbulence and Back

Fluid Mechanics = "Single"-Particle Control: From Control to Turbulence and Back

This video was recorded at Workshop on Statistical Physics of Inference and Control Theory, Granada 2012. We show that different flows studied in fluid mechanics can be understood as following from generalized gauge-invariant stochastic control formulations of a single particle under different conditions. We describe in this language of control theory compressible and incompressible fluid mechanics, and how governing equations for the control field becomes Navier-Stocks equations of different flavors. In a particular case of stochastic control without any strong (dynamically enforced) constraints and costs of space and dynamics varying/fluctuating in 1+1 dimensional time-space, we arrive at the Burgulence (Burgers turbulence), decaying or forced depending on details of the setting. Different stages of development and interaction of shocks are interpreted in terms of control. This is a work in progress in collaboration with V. Chernyak and following from related work on ``Stochastic Control as a Non-Equilibrium Statistical Physics" with V. Chernyak, J. Bierkens and H.J. Kappen.

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