, Volume 30, Issue 5, pp 631-644

Homogenization theory for a replenishing passive scalar field

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Abstract

Homogenization theory provides a rigorous framework for calculating the effective diffusivity of a decaying passive scalar field in a turbulent or complex flow. The authors extend this framework to the case where the passive scalar fluctuations are continuously replenished by a source (and/or sink). The basic structure of the homogenized equations carries over, but in some cases the homogenized source can involve a non-trivial coupling of the velocity field and the source. The authors derive expressions for the homogenized source term for various multiscale source structures and interpret them physically.

Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday with Gratitude and Admiration
Project supported by the National Science Foundation “Collaborations in Mathematical Geosciences” (No. OCE-0620956).