CRITICAL SURFACE CONING DUE TO A LINE SINK IN A VERTICAL DRAIN CONTAINING A POROUS MEDIUM

Author:

AL-ALI S.ORCID,HOCKING G. C.ORCID,FARROW D. E.ORCID

Abstract

The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.

Publisher

Cambridge University Press (CUP)

Subject

Mathematics (miscellaneous)

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Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A spectral modelling approach for fluid flow into a line sink in a confined aquifer;European Journal of Applied Mathematics;2021-11-01

2. MODELLING OF WITHDRAWAL OF A STRATIFIED FLUID FROM A POROUS MEDIUM;Bulletin of the Australian Mathematical Society;2021-04-12

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