  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 to
control the stochastic Lagrangian tracers as players tracking the flow field.
We derive optimal control solutions for general nonlinear fluid systems using
mean field game models, and develop computational algorithms to efficiently
solve the resulting coupled forward and backward mean field system. A precise
link is established for the control of Lagrangian tracers and the scalar
vorticity field based on the functional Hamilton-Jacobi equations derived from
the mean field models. New iterative numerical strategy is then constructed to
compute the optimal solution with fast convergence. We verify the skill of the
mean field control models and illustrate their practical efficiency on a
prototype model modified from the viscous Burger's equation under various cost
functions in both deterministic and stochastic formulations. The good model
performance implies potential effectiveness of the strategy for more general
high-dimensional turbulent systems.
