Skip to main content
×
Home
    • Aa
    • Aa

Nonlinear oscillations of non-spherical cavitation bubbles in acoustic fields

  • P. Hall (a1) and G. Seminara (a2)
Abstract

The nonlinear stability of gas bubbles in acoustic fields is studied using a multiple-scale type of expansion. In particular the development of a subharmonic or a synchronous perturbation to the flow is investigated. It is shown when an equilibrium non-spherical shape oscillation of a bubble is stable. If the amplitude of the sound field is ε then it is shown that subharmonic perturbations of order ε½ can exist and be stable. Furthermore synchronous perturbations of order ε can exist and be stable. It is shown that synchronous perturbations, unlike the subharmonic case where the bifurcation is symmetric, bifurcate transcritically when the driving frequency is varied and also undergo secondary bifurcations. It is further shown that, in certain cases, the latter properties of the synchronous modes cause the flow to exhibit a hysteresis phenomenon when the driving frequency is varied.

Copyright
References
Hide All
Benjamin, T. B. & Strasberg, M. 1958 J. Acoust. Soc. Am. 30, 697 (abstract).
Davidson, B. J. & Riley, N. 1971 J. Sound Vib. 15, 217.
Elder, S. A. 1959 J. Acoust. Soc. Am. 31, 54.
Eller, A. I. 1969 J. Acoust. Soc. Am. 46, 1246.
Eller, A. I. & Crum, L. A. 1970 J. Acoust. Soc. Am. 47, 762.
Gould, R. K. 1966 J. Acoust. Soc. Am. 40, 219.
Hsieh, D. Y. 1974 J. Acoust. Soc. Am. 56, 392.
Hsieh, D. Y. & Plesset, M. S. 1961 J. Acoust. Soc. Am. 33, 206.
Plesset, M. S. & Mitchell, T. P. 1950 Quart. Appl. Math. 13, 419.
Plesset, M. & Prosperetti, A. 1977 Ann. Rev. Fluid Mech. 9, 145.
Prosperetti, A. 1974 J. Acoust. Soc. Am. 56, 878.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 58 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.