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On the instabilities of a potential vortex with a free surface

Mougel, Jérôme and Fabre, David and Lacaze, Laurent and Bohr, Tomas On the instabilities of a potential vortex with a free surface. (2017) Journal of Fluid Mechanics, 824. 230-264. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/jfm.2017.341

Abstract

In this paper, we address the linear stability analysis of a confined potential vortex with a free surface. This particular flow has been recently used by Tophøj et al. (Phys. Rev. Lett., vol. 110(19), 2013, article 194502) as a model for the swirling flow of fluid in an open cylindrical container, driven by rotating the bottom plate (the rotating bottom experiment) to explain the so-called rotating polygons instability (Vatistas J. Fluid Mech., vol. 217, 1990, pp. 241–248; Jansson et al., Phys. Rev. Lett., vol. 96, 2006, article 174502) in terms of surface wave interactions leading to resonance. Global linear stability results are complemented by a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) analysis in the shallow-water limit as well as new experimental observations. It is found that global stability results predict additional resonances that cannot be captured by the simple wave coupling model presented in Tophøj et al. (2013). Both the main resonances (thought to be at the root of the rotating polygons) and these secondary resonances are interpreted in terms of over-reflection phenomena by the WKBJ analysis. Finally, we provide experimental evidence for a secondary resonance supporting the numerical and theoretical analysis presented. These different methods and observations allow to support the unstable wave coupling mechanism as the physical process at the origin of the polygonal patterns observed in free-surface rotating flows.

Item Type:Article
Additional Information:Thanks to Cambridge University Press editor. The definitive version is available at https://www.cambridge.org/ The original PDF of the article can be found at https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-instabilities-of-a-potential-vortex-with-a-free-surface/5269DB6AB1C7742006F3458330BE8E96
HAL Id:hal-01629421
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 - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Technical University of Denmark (DENMARK)
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Deposited On:06 Nov 2017 13:13

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