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Group invariance and field‐scale solute transport
Author(s) -
Sposito Garrison,
Jury William A.
Publication year - 1986
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/wr022i013p01743
Subject(s) - scaling , scale invariance , vadose zone , convection–diffusion equation , field (mathematics) , mathematics , statistical physics , scale (ratio) , invariant (physics) , boundary value problem , dispersion (optics) , physics , mathematical analysis , geometry , geology , geotechnical engineering , statistics , mathematical physics , optics , quantum mechanics , pure mathematics , groundwater
The conventional measurement and statistical characterization of solute dispersion coefficients and convection velocities in a field‐scale vadose zone are based on the assumption that the convection‐dispersion equation governs solute transport locally. The implications of this hypothesis are investigated mathematically through a study of the space and time coordinate transformations which leave the one‐dimensional convection‐dispersion equation (CDE) invariant in form. It is shown that there are just six nontrivial space‐time transformations under which this CDE is invariant. The pioneering field‐scale leaching experiment reported by J. W. Biggar and D. R. Nielsen (1976) is used to make a typical application of these results. When the boundary condition in the Biggar‐Nielsen experiment is imposed, the number of possible space‐time transformations of the CDE reduces to two, one of which is a scaling transformation related closely to scale transformations of the solute transport coefficients. These results and the assumption that sets of transport coefficients corresponding to widely separated regions in a vadose zone are statistically independent are sufficient to prove that the field‐wide probability distribution of the transport coefficients (taken as random variables) will be lognormal. The methodology developed in this study can be applied to any field‐scale solute transport phenomenon for which the partial differential equation governing solute movement locally is assumed known.