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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York, 12180, USA

    Peter R. Kramer

  2. Center for Atmosphere-Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Shane R. Keating

Authors
  1. Peter R. Kramer
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  2. Shane R. Keating
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Correspondence to Peter R. Kramer.

Additional information

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).

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Kramer, P.R., Keating, S.R. Homogenization theory for a replenishing passive scalar field. Chin. Ann. Math. Ser. B 30, 631–644 (2009). https://doi.org/10.1007/s11401-009-0196-0

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  • DOI: https://doi.org/10.1007/s11401-009-0196-0

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