In the late 90s, Pierre-Louis Lions proposed a systematic way of studying large time coherent structure of 2-D turbulence by nsing a variational problem.The vari ational problem was formulated using heuristic arguments.I will report a program (working in progress) on deriving the variational problem from a microscopically de fined dynamic model.The issue can essentially be viewed as computing entropy and studying its limit behavior for an infinite system of interacting stochastic vortices.The entropy computation is a large deviation problem.Hamilton-Jacobi techniques becomes handy both for proving large deviation and for studying limit behavior of the entropy in this context.