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Rotating Polygon Instability of a Swirling Free Surface Flow

Tophoj, Laust and Mougel, Jérôme and Bohr, Tomas and Fabre, David Rotating Polygon Instability of a Swirling Free Surface Flow. (2013) Physical Review Letters (PRL), 110. 1-5. ISSN 0031-9007

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Official URL: http://dx.doi.org/10.1103/PhysRevLett.110.194502

Abstract

We explain the rotating polygon instability on a swirling fluid surface [G. H. Vatistas, J. Fluid Mech. 217, 241 (1990) and Jansson et al., Phys. Rev. Lett. 96, 174502 (2006)] in terms of resonant interactions between gravity waves on the outer part of the surface and centrifugal waves on the inner part. Our model is based on potential flow theory, linearized around a potential vortex flow with a free surface for which we show that unstable resonant states appear. Limiting our attention to the lowest order mode of each type of wave and their interaction, we obtain an analytically soluble model, which, together with estimates of the circulation based on angular momentum balance, reproduces the main features of the experimental phase diagram. The generality of our arguments implies that the instability should not be limited to flows with a rotating bottom (implying singular behavior near the corners), and indeed we show that we can obtain the polygons transiently by violently stirring liquid nitrogen in a hot container.

Item Type:Article
Additional Information:Thanks to APS editor. The original publication is available at http://prl.aps.org
HAL Id:hal-00914775
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)
Other partners > Danmarks Tekniske Universitet - DTU (DENMARK)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:03 Dec 2013 17:26

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