Fluid Mechanics = "Single"-Particle Control: From Control to Turbulence and Back
published: Oct. 16, 2012, recorded: September 2012, views: 4158
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
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.
Download slides: cyberstat2012_chertkov_fluid_mechanics_01.pdf (1.0 MB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !