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A balloon bursting underwater

  • A. R. Vasel-Be-Hagh (a1), R. Carriveau (a1) and D. S.-K. Ting (a1)


A buoyant vortex ring produced by an underwater bursting balloon was studied experimentally. The effect of dimensionless surface tension on characteristics including rise velocity, rate of expansion, circulation, trajectory, and lifetime of the vortex ring bubble was investigated. Results showed reasonable agreement with the literature on vortex rings produced by conventional approaches. It was observed that as the dimensionless surface tension increased, the rise velocity, the circulation and consequently the stability of the vortex ring bubble increased; however, the rate of expansion tends toward constant values. A semi-analytical model is proposed by modifying the drag-based model presented by Sullivan et al. (J. Fluid Mech., vol. 609, 2008, pp. 319–347) to make it applicable to buoyant vortex rings. The modified model suggests that the vortex ring expansion is essentially due to the buoyancy force. An expression is also derived for the circulation in terms of the initial volume of the balloon and the depth at which the balloon bursts.


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Cheng, M., Lou, J. & Lim, T. T. 2013 Motion of a bubble ring in a viscous fluid. Phys. Fluids 25, 119.
Gan, L., Dawson, J. R. & Nickels, T. B. 2012 On the drag of turbulent vortex rings. J. Fluid Mech. 709, 85105.
Hershberger, R. E., Bolster, D. & Donnelly, R. J. 2010 Slowing of vortex rings by development of Kelvin waves. Phys. Rev. E 82, 036309.
Joseph, D., Funada, T. & Wang, J. 2007 Potential Flows of Viscous and Viscoelastic Liquids. Cambridge University Press.
Krutzsch, C. H. 1939 Ber eine experimentell Beobachtete Erscheinung an Wirbelringen bei ihrer translatorischen Bewegung in Wirklichen Flussigkeiten. Ann. Phys. Berlin 427 (6), 497523.
Lundgren, T. S. & Mansour, N. N. 1991 Vortex ring bubbles. J. Fluid Mech. 224, 177196.
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 1532.
Pedley, T. J. 1968 The toroidal bubble. J. Fluid Mech. 32, 97112.
Reynolds, O. 1876 On the resistance encountered by vortex rings and the relation between the vortex rings and the streamlines of a disk. Nature 14, 477479.
Sirakov, B. T., Greitzer, E. M. & Tan, C. S. 2005 A note on irrotational viscous flow. Phys. Fluids 17 (10), 13.
Sullivan, I. S., Niemela, J. J., Hershberger, R. E., Bolster, D. & Donnelly, R. J. 2008 Dynamics of thin vortex rings. J. Fluid Mech. 609, 319347.
Turner, J. S. 1957 Buoyant vortex rings. Proc. R. Soc. Lond. A 239, 6175.
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99140.
Walters, J. K. & Davidson, J. F. 1963 The initial motion of a gas bubble formed in an inviscid liquid. J. Fluid Mech. 17, 321336.
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