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Structure of a Bathtub Vortex : Importance of the Bottom Boundary Layer

Yukimoto, Shinji and Niino, Hiroshi and Noguchi, Takashi and Kimura, Ryuji and Moulin, Frédéric Structure of a Bathtub Vortex : Importance of the Bottom Boundary Layer. (2010) Theoretical and Computational Fluid Dynamics, 24 (1-4). 323-327. ISSN 0935-4964

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Official URL: http://dx.doi.org/10.1007/s00162-009-0128-3

Abstract

A bathtub vortex in a cylindrical tank rotating at a constant angular velocity [omega] is studied by meansof a laboratory experiment, a numerical experiment and a boundary layer theory. The laboratory and numerical experiments show that two regimes of vortices in the steady-state can occur depending on [omega] and the volume flux Q through the drain hole: when Q is large and [omega] is small, a potential vortex is formed in which angular momentum outside the vortex core is constant in the non-rotating frame. However, when Q is small or [omega] is large, a vortex is generated in which the angular momentum decreases with decreasing radius. Boundary layertheory shows that the vortex regimes strongly depend on the theoretical radial volume flux through the bottomboundary layer under a potential vortex : when the ratio of Q to the theoretical boundary-layer radial volume flux Qb (scaled by 2π R2([omega] ν)12 ) at the outer rim of the vortex core is larger than a critical value (of order 1), the radial flow in the interior exists at all radiiand Regime I is realized, where R is the inner radius of the tank and ν the kinematicviscosity.When the ratio is less than the critical value, the radial flow in the interior nearlyvanishes inside a critical radius and almost all of the radial volume flux occurs only in the boundary layer,resulting in Regime II in which the angular momentum is not constant with radius. This criterion is found to explain the results of the laboratory and numerical experiments very well.

Item Type:Article
Additional Information: Thanks to Springer Verlag editor. The definitive version is available at http://www.springer.com The original PDF of the article can be found at http://link.springer.com/article/10.1007%2Fs00162-009-0128-3
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Kyoto University (JAPAN)
Other partners > The Open University of Japan - OUJ (JAPAN)
Other partners > University of Tokyo (JAPAN)
Laboratory name:
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Deposited By: Frederic MOULIN
Deposited On:20 Nov 2013 16:14

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