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Macroscopic Balance Equations in Soils and Aquifers: The Case of Space‐ and Time‐Dependent Instrumental Response
Author(s) -
Baveye Philippe,
Sposito Garrison
Publication year - 1985
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/wr021i008p01116
Subject(s) - weighting , function (biology) , momentum (technical analysis) , mathematics , aquifer , mathematical analysis , space time , statistical physics , physics , geology , geotechnical engineering , groundwater , chemistry , finance , evolutionary biology , acoustics , economics , biology
Macroscopic balance equations for mass and linear momentum in soils and aquifers are derived in the relativist concept under the condition that all physical variables are associated with a single instrumental weighting function that depends on both position and time. The resulting balance equations differ in concept from expressions obtained recently in the representative elementary volume (REV) approach by exhibiting additional terms that depend on the time and space derivatives of the instrumental weighting function. These terms indicate that mass and linear momentum balance at the macroscopic scale are not preserved unless the weighting function has space‐time invariance properties over the period and spatial domain of measurement.