Comptes Rendus
Instabilities, patterns
Shape dynamics of rotating polygons on the surface of liquid nitrogen in a Leidenfrost state
Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 457-473.

When liquid nitrogen is set into rotation in a warm pot, the surface, initially forming an axis-symmetrical, toroidal shape, spontaneously re-structures into a series of rotating polygons with a diminishing number of corners, while slowing down. This spontaneous “ordering” occurs despite the violently turbulent and boiling state of the fluid. We show experimentally that these shapes are well-described as a sum of a few Fourier modes, and we present experimental results for the development of the frequencies and amplitudes of these wave-modes during the transient process. We compare our results with the theoretical results for the instabilities of a potential vortex flow and argue that the first polygon formed in the transient process should be described by this theory. The paper is dedicated to the memory of Yves Couder, colleague, friend and a life-long source of inspiration.

Dans cet article nous nous intéressons au cas d’un volume d’azote liquide en état de caléfaction mis en rotation dans un récipient cylindrique chauffé. La surface libre du liquide, initialement sous forme d’un tore axisymétrique, va se déstabiliser et se restructurer en une série de polygones tournants dont le nombre de côtés diminue à mesure que le liquide ralentit. Ce facettage apparaît spontanément alors même que le liquide connait une violente ébullition et un écoulement extrêmement turbulent. Nous démontrons expérimentalement que les formes observées peuvent être décrites par la combinaison d’un petit nombre de modes de Fourier et nous étudions l’évolution de ces modes en termes d’amplitude et de fréquence depuis le premier polygone visible jusqu’à la fin de la rotation du liquide. Nous comparons nos résultats expérimentaux avec un modèle théorique décrivant la perte de stabilité des écoulements de type vortex potentiel et nous soutenons que le premier polygone observable suite à la déstabilisation de la forme axisymétrique peut être décrit par ce modèle. Cet article est dédié à la mémoire d’Yves Couder qui fut pour nous un collègue, un ami et une intarissable source d’inspiration.

Published online:
DOI: 10.5802/crmeca.24
Keywords: Rotating polygons, Fluid instabilities, Free surface flows, Spontaneous symmetry breaking, Shape dynamics

Jacob S. Bach 1; Alexis Duchesne 1, 2; Tomas Bohr 1

1 Department of Physics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
2 Université de Lille, CNRS, UMR 8520-IEMN, Avenue Poincaré, 59652 Villeneuve d’Ascq, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Shape dynamics of rotating polygons on~the~surface of liquid nitrogen in a {Leidenfrost~state}},
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Jacob S. Bach; Alexis Duchesne; Tomas Bohr. Shape dynamics of rotating polygons on the surface of liquid nitrogen in a Leidenfrost state. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 457-473. doi : 10.5802/crmeca.24. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.24/

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