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Physics of Fluids / Volume 19 / Issue 8 / ARTICLES / Interfacial Flows

Phys. Fluids 19, 082104 (2007); http://dx.doi.org/10.1063/1.2759891 (14 pages)

Unsteady draining flows from a rectangular tank

Lawrence K. Forbes1 and Graeme C. Hocking2

1School of Mathematics and Physics, University of Tasmania, Hobart 7001, Tasmania, Australia
2School of Mathematics and Statistics, Division of Science, Murdoch University, Murdoch 6150, Western Australia

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(Received 15 November 2006; accepted 30 May 2007; published online 17 August 2007)

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 As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole.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

Article Outline

  1. INTRODUCTION
  2. MATHEMATICAL MODEL AND FORMULATION
  3. THE LINEARIZED SOLUTION
  4. THE NUMERICAL SOLUTION TECHNIQUE
  5. PRESENTATION OF RESULTS
  6. DISCUSSION AND CONCLUSION

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KEYWORDS and PACS

Keywords

confined flow, flow instability, tanks (containers)

PACS

  • 47.60.-i

    Flow phenomena in quasi-one-dimensional systems

  • 47.20.-k

    Flow instabilities

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2759891

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    P. A. Tyvand, “Unsteady free-surface flow due to a line source,” Phys. Fluids A 4, 671 (1992)PFADEB000004000004000671000001.

    T. Miloh and P. A. Tyvand, “Nonlinear transient free-surface flow and dip formation due to a point sink,” Phys. Fluids A 5, 1368 (1993)PFADEB000005000006001368000001.

    I. Cohen and S. R. Nagel, “Scaling at the selective withdrawal transition through a tube suspended above the fluid surface,” Phys. Rev. Lett. 88, 074501 (2002).

    I. Cohen, “Scaling and transition structure dependence on the fluid viscosity ratio in the selective withdrawal transition,” Phys. Rev. E 70, 026302 (2004).

    S. Courrech du Pont and J. Eggers, “Sink flow deforms the interface between a viscous liquid and air into a tip singularity,” Phys. Rev. Lett. 96, 034501 (2006).


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