logo CRAS
Comptes Rendus. Mécanique
Instability of a swirling bubble ring
Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 519-535.

Part of the special issue: Tribute to an exemplary man: Yves Couder

A toroidal bubble or a cylindrical gas jet are known to be subjected to the Rayleigh–Plateau instability. Air bubble rings produced by beluga whales and dolphins however are observed that remain stable for long times. In the present work, we analyse the generation of such toroidal bubbles via numerical simulations, in particular how the process depends on surface tension. Their stability properties are then briefly analysed. For the estimated Reynolds and Weber numbers relative to the bubbles produced by these animals, the presence of a vortex inside and around the bubble is found to strongly stabilize the Rayleigh–Plateau instability.

Published online:
DOI: 10.5802/crmeca.22
Keywords: Instability, Vortex ring, Two-phase flow, Rayleigh–Plateau, Direct numerical simulation
Yonghui Xu 1; Ivan Delbende 2, 3; Daniel Fuster 4; Maurice Rossi 4

1 Sorbonne Université, UMR 7190, Institut Jean Le Rond d’Alembert, 75005 Paris, France
2 LIMSI, CNRS, Université Paris-Saclay, rue du Belvédère, 91405 Orsay, France
3 Sorbonne Université, UFR d’Ingénierie, 4 place Jussieu, 75005 Paris, France
4 CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, 75005 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Yonghui Xu and Ivan Delbende and Daniel Fuster and Maurice Rossi},
     title = {Instability of a swirling bubble ring},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {519--535},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {6-7},
     year = {2020},
     doi = {10.5802/crmeca.22},
     language = {en},
TI  - Instability of a swirling bubble ring
JO  - Comptes Rendus. Mécanique
PY  - 2020
DA  - 2020///
SP  - 519
EP  - 535
VL  - 348
IS  - 6-7
PB  - Académie des sciences, Paris
UR  - https://doi.org/10.5802/crmeca.22
DO  - 10.5802/crmeca.22
LA  - en
ID  - CRMECA_2020__348_6-7_519_0
ER  - 
%0 Journal Article
%T Instability of a swirling bubble ring
%J Comptes Rendus. Mécanique
%D 2020
%P 519-535
%V 348
%N 6-7
%I Académie des sciences, Paris
%U https://doi.org/10.5802/crmeca.22
%R 10.5802/crmeca.22
%G en
%F CRMECA_2020__348_6-7_519_0
Yonghui Xu; Ivan Delbende; Daniel Fuster; Maurice Rossi. Instability of a swirling bubble ring. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 519-535. doi : 10.5802/crmeca.22. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.22/

[1] Y. Couder Observation expérimentale de la turbulence bidimensionnelle dans un film liquide mince, C. R. Acad. Sci. Paris II, Volume 297 (1983), pp. 641-645

[2] O. Cadot; S. Douady; Y. Couder Characterization of the low pressure filaments in three-dimensional turbulent shear flow, Phys. Fluids, Volume 7 (1995), pp. 630-646 | DOI

[3] Dramaqueen21409 Dolphin Blowing Rings https://www.youtube.com/watch?v=2m6ie3MVIAw (Youtube video, last seen 2020)

[4] Happy Mind Beluga whales blowing bubble rings https://www.youtube.com/watch?v=Iiuv2ELttaQ (Youtube video, last seen 2020)

[5] Lord Rayleigh Xvi. On the instability of a cylinder of viscous liquid under capillary force, Lond. Edinburgh Dublin Phil. Mag. J. Sci., Volume 34 (1892) no. 207, pp. 145-154 | Zbl

[6] Lord Rayleigh Xix. On the instability of cylindrical fluid surfaces, Lond. Edinburgh Dublin Phil. Mag. J. Sci., Volume 34 (1892) no. 207, pp. 177-180 | Zbl

[7] L. M. Hocking; D. H. Michael The stability of a column of rotating liquid, Mathematica, Volume 6 (1959) no. 1, pp. 25-32 | MR | Zbl

[8] J. P. Kubitschek; P. D. Weidman The effect of viscosity on the stability of a uniformly rotating liquid column in zero gravity, J. Fluid Mech., Volume 572 (2007), pp. 261-286 | DOI | MR | Zbl

[9] J. P. Kubitschek; P. D. Weidman Helical instability of a rotating viscous liquid jet, Phys. Fluids, Volume 19 (2007) no. 11 (114108) | Zbl

[10] J. Gillis; B. Kaufman The stability of a rotating viscous jet, Q. Appl. Math., Volume 19 (1962) no. 4, pp. 301-308 | DOI | MR | Zbl

[11] P. D. Weidman; M. Goto; A. Fridberg On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity, Z. Angew. Math. Phys., Volume 48 (1997) no. 6, pp. 921-950 | DOI | MR | Zbl

[12] TheScubaGuru Shooting Underwater Hydro-Rings https://www.youtube.com/watch?v=5KdsVsiZ6bU (Youtube, last seen 2020)

[13] Thomas Lee Underwater bubble ring https://www.youtube.com/watch?v=4mbu2ueMe2E (Youtube, last seen 2020)

[14] Christian Wedoy How To Make Underwater Bubble Rings - Bubble Ring Tutorial https://www.youtube.com/watch?v=vFbN31EuMvc (Youtube, last seen 2020)

[15] P. G. Saffman Vortex Dynamics, Cambridge University Press, Cambridge, 1992 | Zbl

[16] T. T. Lim; T. B. Nickels Vortex rings, Fluid Vortices (S. I. Green, ed.) (Fluid Mechanics and Its Applications), Volume 30, Springer, Dordrecht, 1995, pp. 95-153 | DOI

[17] S. Popinet Basilisk (http://basilisk.fr)

[18] S. Popinet A quadtree-adaptive multigrid solver for the Serre–Green–Naghdi equations, J. Comput. Phys., Volume 302 (2015), pp. 336-358 | DOI | MR | Zbl

[19] J. D. Gibbon; A. S. Fokas; C. R. Doering Dynamically stretched vortices as solution of the 3D Navier–Stokes equations, Physica D, Volume 132 (1999), pp. 497-510 | DOI | Zbl

[20] A. J. Bernoff; J. F. Lingevitch Rapid relaxation of an axisymmetric vortex, Phys. Fluids, Volume 6 (1994) no. 11, pp. 3717-3723 | DOI | Zbl

[21] J. C. McWilliams The emergence of isolated coherent vortices in turbulent flow, J. Fluid Mech., Volume 146 (1984), pp. 21-43 | DOI | Zbl

[22] R. Robert; J. Sommeria Statistical equilibrium states for two-dimensional flows, J. Fluid Mech., Volume 229 (1991), pp. 291-310 | DOI | MR | Zbl

[23] J. Eggers; E. Villermaux Physics of liquid jets, Rep. Prog. Phys., Volume 71 (2008), pp. 16-18 | DOI

Cited by Sources: