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Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow

Fabre, David and Mougel, Jérôme Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow. (2014) Fluid Dynamics Research, 46 (6). 1-20. ISSN 0169-5983

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Official URL: http://dx.doi.org/10.1088/0169-5983/46/6/061415

Abstract

The free surface flow in a cylindrical tank over a rotating bottom is known to support spectacular three-dimensional patterns, including deformation of the inner free surface into the shape of rotating polygons, and sloshing behavior of the upper free surface (e.g. Iga et al., FDR 2014, same issue). Through a stability analysis of a simplified model of this flow, we show that such patterns can be explained as a resonance mechanism involving different families of waves. The approach extends a previous work (Tophoj et al., PRL 2013) which explained the rotating polygons as an interaction between gravity waves and centrifugal waves, under the assumption that the base flow can be modeled as a potential vortex. We show that this previous model is justified for strong rotation rates (Dry-Potential case), and that for weaker rotations it can be improved by introducing an inner vortex core in solid-body rotation, which either extends to the center of the plate (Wet case) or surrounds a dry central region (Dry-Composite case). The study of this improved model predicts two new kind of instabilities. The first occurs at low rotations (Wet case) and results from an interaction between gravity waves and the Kelvin-Kirchhoff wave (namely, oscillation of the boundary of the vortex core). This instability is proposed to be at the origin of the sloshing phenomenon. The second new instability occurs, for moderate rotations, (Dry-Composite case) as an interaction between gravity waves and a "Kelvin-Centrifugal" wave characterized by deformation of the inner surface and the vortex core boundary in opposite directions. This instability exists for all azimuthal wave numbers starting from m = 1, this case corresponding to a "monogon" pattern.

Item Type:Article
Additional Information:Thanks to IOP Publishing editor. The definitive version is available at http://iopscience.iop.org. The original PDF of the article can be found at Fluid Dynamics Research website : http://iopscience.iop.org/article/10.1088/0169-5983/46/6/061415/pdf ($33,00 US)
Audience (journal):International peer-reviewed journal
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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)
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Deposited By: Jerome MOUGEL
Deposited On:26 Oct 2015 08:18

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