Statistical non-locality of dynamically coherent structures

We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to given flow state. In doing so, we obtain expressions for turbulent diffusivity as function statistics spectrum. When are continuous-time Markov process finite state space, calculations amenable analytic treatment. more complex, show how approximate fluxes hierarchies space processes. The ensemble average flux is expressed linear operator that acts on tracer. recover classical estimate tensor, components which integrated autocorrelation velocity field in limit becomes local and time.