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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Harkin, Anthony A. Kaper, Tasso J. and Nadim, Ali 2013. Energy transfer between the shape and volume modes of a nonspherical gas bubble. Physics of Fluids, Vol. 25, Issue. 6, p. 062101.

    Birkin, Peter R. Offin, Douglas G. Vian, Christopher J. B. Leighton, Timothy G. and Maksimov, Alexey O. 2011. Investigation of noninertial cavitation produced by an ultrasonic horn. The Journal of the Acoustical Society of America, Vol. 130, Issue. 5, p. 3297.

    Akhatov, I.Sh. and Konovalova, S.I. 2005. Regular and chaotic dynamics of a spherical bubble. Journal of Applied Mathematics and Mechanics, Vol. 69, Issue. 4, p. 575.

    Femat, Ricardo Alvarez-Ramírez, José and Soria, Alberto 1998. Chaotic flow structure in a vertical bubble column. Physics Letters A, Vol. 248, Issue. 1, p. 67.

    Feng, Z. C. and Leal, L. G. 1997. NONLINEAR BUBBLE DYNAMICS. Annual Review of Fluid Mechanics, Vol. 29, Issue. 1, p. 201.

  • Journal of Fluid Mechanics, Volume 286
  • March 1995, pp. 257-276

Chaotic mode competition in the shape oscillations of pulsating bubbles

  • D. Zardi (a1) and G. Seminara (a1)
  • DOI:
  • Published online: 01 April 2006

A possible mechanism for the occurrence of the phenomenon of erratic drift of bubbles in liquids subjected to acoustic waves was proposed by Benjamin & Ellis (1990) who showed that nonlinear interactions between adjacent perturbation modes expressed in terms of spherical harmonics of any order may lead to the excitation of mode 1 which is equivalent to a displacement of the bubble centroid. We show that indeed such a mechanism can give rise to a chaotic process at least under the conditions experimentally investigated by Benjamin & Ellis (1990). In fact we examine the case in which the angular frequency ω of the incident wave is sufficiently close to both the natural frequency of mode n + 1 (ωn + 1) and twice the natural frequency of mode n (2ωn) thus exciting simultaneously a subharmonic mode n and a synchronous mode n + 1. The value of n is set equal to 3 in accordance with Benjamin & Ellis' (1990) observation. A classical multiple scale analysis allows us to follow the development of these perturbations in the weakly nonlinear regime to find an autonomous system of quadratically coupled nonlinear differential equations governing the evolution of the amplitudes of the perturbations on a slow time scale. As obtained by Gu & Sethna (1987) for the Faraday resonance problem, we find both regular and chaotic solutions of the above system. Chaos is found to develop for large enough values of the amplitude of the acoustic excitation within some region in the parameter space and is reached through a period-doubling sequence displaying the typical characteristics of Feigenbaum scenario.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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