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This paper discusses the control of coherent structures in turbulent flows,which has broad applications among complex systems in science and technology.Mean field games have been proved a powerful tool and are proposed here tocontrol the stochastic Lagrangian tracers as players tracking the flow field.We derive optimal control solutions for general nonlinear fluid systems usingmean field game models, and develop computational algorithms to efficientlysolve the resulting coupled forward and backward mean field system. A preciselink is established for the control of Lagrangian tracers and the scalarvorticity field based on the functional Hamilton-Jacobi equations derived fromthe mean field models. New iterative numerical strategy is then constructed tocompute the optimal solution with fast convergence. We verify the skill of themean field control models and illustrate their practical efficiency on aprototype model modified from the viscous Burger's equation under various costfunctions in both deterministic and stochastic formulations. The good modelperformance implies potential effectiveness of the strategy for more generalhigh-dimensional turbulent systems.

Mean Field Games for Controlling Coherent Structures in Nonlinear Fluid Systems