Chinese Annals of Mathematics, Series B

, Volume 30, Issue 5, pp 631–644

Homogenization theory for a replenishing passive scalar field


DOI: 10.1007/s11401-009-0196-0

Cite this article as:
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.


Homogenization Turbulent transport Source Pumping 

2000 MR Subject Classification


Copyright information

© Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA
  2. 2.Center for Atmosphere-Ocean ScienceCourant Institute of Mathematical Sciences, New York UniversityNew YorkUSA