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Transient analysis of phreatic aquifers lying between two open channels
Author(s) -
Singh Sita Ram,
Jacob C. M.
Publication year - 1977
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/wr013i002p00411
Subject(s) - phreatic , aquifer , groundwater flow equation , mathematics , groundwater , mathematical analysis , groundwater flow , geology , geotechnical engineering
The unsteady state flow of water through an unconfined aquifer can be represented by the Boussinesq equation. The nonlinear term involving the highest derivative in this equation was approximated by a linear term, and the resulting approximate Bossinesq equation was linearized to a Fokker‐Planck equation by the method of functional transformation. Solutions to the problem of groundwater flow through phreatic aquifers lying between (1) constant water level boundaries and (2) variable water level boundaries were obtained from the general solution of the Fokker‐Planck equation for constant and variable rates of recharge and withdrawal. Variable rates of recharge and withdrawal were approximated by periodic step functions which represented two different rates, one each for both rainy and dry seasons. Variable water levels in the open channels were approximated by step functions, and the initial condition was represented by straight line segments. An analytical solution of the approximate Boussinesq equation was compared with the finite difference solution of the original Boussinesq equation. The difference between the two solutions was almost negligible, and therefore the applicability of the analytical solutions to groundwater resource management was established. The effect of variable water level boundaries on groundwater dynamics was studied by performing a sample calculation.