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Transport in three‐dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations
Author(s) -
Kapoor Vivek,
Gelhar Lynn W.
Publication year - 1994
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 - 10.1029/94wr00076
Subject(s) - microscale chemistry , advection , dissipation , dispersion (optics) , hydraulic conductivity , flux (metallurgy) , mechanics , materials science , thermodynamics , physics , soil science , mathematics , environmental science , optics , mathematics education , soil water , metallurgy
The concentration variance, i.e., mean squared concentration fluctuations, undergoes mean advection, a local dispersive flux, and a macrodispersive flux due to a correlation between squared concentration perturbations and velocity perturbations. The products of the macrodispersion coefficient and the squared gradient of the mean concentration field determine the rate of production of concentration variance. The rate of dissipation of concentration variance is determined by the product of the local dispersion coefficient and the mean squared gradient of the concentration perturbation field. Variance dissipation is represented as a first‐order decay with the decay coefficient equal to twice the sum of the local dispersion coefficient divided by the squared concentration microscale. The concentration microscale, estimated for an advection‐dominated log hydraulic conductivity microscale, is an increasing function of the log conductivity microscale. Thus the larger the log conductivity microscale is, the slower is the rate of dissipation of concentration fluctuations by local dispersion and vice versa. The wave number squared dependence of fluctuation dissipation requires intensive sampling to realistically model the log conductivity spectrum and its microscale, which determines the rate of dissipation of concentration fluctuations by the action of local dispersion. There is no mechanism of destroying concentration fluctuations without the action of local dispersion.