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Unsteady draining flows from a rectangular tank

Phys. Fluids 19, 082104 (2007); doi:10.1063/1.2759891

Published 17 August 2007

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Lawrence K. Forbes
School of Mathematics and Physics, University of Tasmania, Hobart 7001, Tasmania, Australia

Graeme C. Hocking
School of Mathematics and Statistics, Division of Science, Murdoch University, Murdoch 6150, Western Australia
Two-dimensional, unsteady flow of a two-layer fluid in a tank is considered. Each fluid is inviscid and flows irrotationally. The lower, denser fluid flows with constant speed out through a drain hole of finite width in the bottom of the tank. The upper, lighter fluid is recharged at the top of the tank, with an input volume flux that matches the outward flux through the drain. As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole. However, waves are present at the interface, and they have a strong effect on the time at which the interface is first drawn into the drain. A linearized theory valid for small extraction rates is presented. Fully nonlinear, unsteady solutions are computed by means of a novel numerical technique based on Fourier series. For impulsive start of the drain, the nonlinear results are found to agree with the linearized theory initially, but the two theories differ markedly as the interface approaches the drain and nonlinear effects dominate. For wide drains, curvature singularities appear to form at the interface within finite time. ©2007 American Institute of Physics
History: Received 15 November 2006; accepted 30 May 2007; published 17 August 2007
Permalink: http://link.aip.org/link/?PHFLE6/19/082104/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.60.+i
    Flows in ducts, channels, nozzles, and conduits
  • 47.20.-k
    Hydrodynamic stability
  • YEAR: 2007

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (26)
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