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Unsteady draining flows from a rectangular tank
Journal article   Open access   Peer reviewed

Unsteady draining flows from a rectangular tank

L.K. Forbes and G.C. Hocking
Physics of Fluids, Vol.19(8)
2007
DOI: https://doi.org/10.1063/1.2759891
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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 As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole.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.

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Collaboration types
Domestic collaboration
Citation topics
8 Earth Sciences
8.205 Ocean Dynamics
8.205.2114 Hydraulic Flows
Web Of Science research areas
Mechanics
Physics, Fluids & Plasmas
ESI research areas
Physics
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