Anisotropic diffusion in fluids with steady periodic velocity fields

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Abstract
The authors study the effective diffusivity tensor D for a contaminant carried by a steady periodic two-dimensional velocity field, in the limit of small molecular diffusivity chi . They discuss a generic model where the transport process is strongly anisotropic for the presence of channels (where, if one neglects Brownian motion, the motion is ballistic) among the convection cells. It is shown that for the longitudinal (along the channels direction) diffusivity one has: D/sub /// varies as 1/ chi , while for the transverse diffusivity: Dperpendicular to varies as chi . The behaviour D/sub /// approximately Dperpendicular to varies as chi 12/, which is typical of the Rayleigh-Benard system, is found to hold at intermediate values of chi . The scaling arguments are supported by extended numerical simulations.