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Macrodispersion in a radially diverging flow field with finite Peclet Numbers: 2. Homogenization theory approach
Author(s) -
Attinger S.,
Neuweiler I.,
Kinzelbach W.
Publication year - 2001
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2000wr900312
Subject(s) - péclet number , homogenization (climate) , advection , dispersion (optics) , mechanics , tracer , physics , thermodynamics , optics , biodiversity , ecology , nuclear physics , biology
We study the transport behavior of a tracer in a radially diverging heterogeneous velocity field. Making use of homogenization theory, we derive effective transport equations. These effective transport equations are very similar to those defined on the local scale. However, the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients. For smoothly varying heterogeneous media, explicit results for effective radial dispersion coefficients are derived. Starting with the purely advective transport behavior (infinite Peclet numbers), we extend our calculations to transport with finite Peclet numbers. We find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion: Including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations. In contrast, effective dispersivities including diffusion are not constant but depend on the radial distance. We compare the results found by homogenization theory with those derived by Neuweiler et al . (this issue) by standard method of moments.