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Two‐Dimensional Similarity Solution: Theory and Application to the Determination of Soil‐Water Diffusivity
Author(s) -
Turner Neil C.,
Parlange JeanYves
Publication year - 1975
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1975.03615995003900030013x
Subject(s) - thermal diffusivity , water content , similarity (geometry) , constant (computer programming) , soil science , similarity solution , mathematics , moisture , variable (mathematics) , diffusion equation , environmental science , mathematical analysis , chemistry , thermodynamics , geotechnical engineering , physics , geology , computer science , boundary layer , artificial intelligence , image (mathematics) , programming language , organic chemistry , service (business) , economy , economics
The Bruce and Klute methods (1956) to measure the soil‐water diffusivity ( D ) relies on the existence of a similarity solution for the one‐dimensional movement of water when the soil‐water potential is maintained constant at one end of a horizontal column of soil. If the flux is kept constant along a line‐source, a similarity solution exists also in two‐dimensions and an exact equation for this case is derived: D =ψ − 12d ψ d θ∫ θ o θψ 2 ( a ) d awhere θ o is the initial moisture content, θ is the moisture content after time, t , and ψ is the similarity variable. The application of this equation in measuring the soil‐water diffusivity of a sandy soil is shown.