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

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