Eddy diffusivities in scalar transport

Details Eddy diffusivities in scalar transport Eddy diffusivities in scalar transport

1994-12-28

arxiv.org/abs/cond-mat/9412115v1

Physics

Condensed Matter

21 Pages + 6 Figures Postscript (appended as .tar file), Latex submitted Phys of Fluids

Scientific paper

10.1063/1.868651

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 P\'eclet number resummed by Pad\'e approximants and by 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 can be revealed from the singular behaviour of the eddy-diffusivity at very small molecular diffusivities.

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