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Weakly Nonlinear Approximation of Periodic Flow in Phreatic Aquifers
Author(s) -
Smith Anthony J.
Publication year - 2008
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2007.00418.x
Subject(s) - nonlinear system , phreatic , aquifer , flow (mathematics) , frequency domain , mathematics , constant (computer programming) , position (finance) , rule of thumb , mathematical analysis , geology , mechanics , geotechnical engineering , geometry , computer science , physics , groundwater , algorithm , finance , quantum mechanics , economics , programming language
Published frequency‐domain solutions of periodic flow in aquifers apply strictly to mathematically linear systems that arise when aquifer diffusivity is assumed constant in space and time. This assumption can be invalid in phreatic aquifers that experience spatiotemporal variation in the free surface position and consequent variation in saturated thickness. A weakly nonlinear approach to formulating and solving periodic flow problems in the frequency domain can be applied in situations where conventional linearized approximations break down. The weakly nonlinear equations provide robust approximations of the true nonlinear response and require much less computational effort and time to solve than the full nonlinear problem. Nondimensional rules of thumb are presented for choosing between linear, weakly nonlinear and nonlinear solution strategies.