Eddy diffusivities in scalar transport

Standard and anomalous transport in incompressible flow is investigated using multiscale techniques. Eddy diffusivities emerge from the multiscale analysis through the solution of an auxiliary equation. From the latter it is derived an upper bound to eddy diffusivities, valid for both static and time‐dependent flow. The auxiliary problem is solved by a perturbative expansion in powers of the Peclet number resummed by Pade approximants and a conjugate gradient method. The results are compared to numerical simulations of tracers dispersion for three flows having different properties of Lagrangian chaos. It is shown on a concrete example how the presence of anomalous diffusion in deterministic flows can be revealed from the singular behavior of the eddy diffusivity at very small molecular diffusivities.