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Analytical Solution for One‐Dimensional Drainage: Burgers' and Simplified Forms
Author(s) -
Warrick A. W.,
Parkin Gary W.
Publication year - 1995
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 - 10.1029/95wr02284
Subject(s) - thermal diffusivity , dimensionless quantity , burgers' equation , water content , mathematics , nonlinear system , residual , square root , drainage , diffusion equation , function (biology) , mathematical analysis , diffusion , mechanics , thermodynamics , geotechnical engineering , geology , physics , geometry , partial differential equation , engineering , ecology , metric (unit) , operations management , algorithm , quantum mechanics , evolutionary biology , biology
Solutions are developed for Burgers' equation and for the surface water content subject to one‐dimensional drainage. These are found as limiting cases of Richards' equation using diffusivity and conductivity functions from Fujita as extended by Broadbridge and White. The solution from Burgers' equation can generally be expressed as a function of only a dimensionless time, depth, and initial reduced water content. For the more strongly nonlinear case, initially the surface water content decreases in proportion to the square root of time. For large times, the surface water content approaches the residual water content inversely with the square root of time.