A note on withdrawal from a two-layer fluid through a line sink in a porous medium

Graeme Charles Hocking, Hong Zhang

Abstract


The steady response of the free surface of a fluid in a porous medium is considered during extraction of the fluid through a line sink. A conformal mapping approach is used to derive exact solutions to a family of problems in which the line sink is place at the apex of a wedge-shaped impermeable boundary, including the limiting cases of an ubounded aquifer and a flat-bottomed aquifer of finite depth. Both critical cusp solutions and sub-critical solutions are computed exactly as a Fourier sine series.

doi:10.1017/S144618110800028X

Keywords


porous medium; selective withdrawal; hodograph method; exact solution; line sink



DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1366



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.