Homogenization theory for a replenishing passive scalar field
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- Kramer, P.R. & Keating, S.R. Chin. Ann. Math. Ser. B (2009) 30: 631. doi:10.1007/s11401-009-0196-0
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.