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Abstract

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between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain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.

Item Type:	Article
Authors/Creators:	Forbes, LK and Hocking, GC
Journal or Publication Title:	Physics of Fluids
Publisher:	American Institute of Physics, Circulation and Fulfillment Division
ISSN:	1070-6631
DOI / ID Number:	10.1063/1.2759891
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