The interaction of perturbed vortex rings and its sound generation. Part II

N. W.M. Ko, Chi Kin Randolph Leung, C. C.K. Tang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


The present work extends the study of interactions of two coaxial vortex rings of thin cores with azimuthal instability to wavenumber range 6 ≤ m ≤ 11. Unstable modes are found at 6 ≤ m ≤ 10. Stable mode is found only at m = 11. The present range of unstable wavenumbers m = 1, 2, 5 to 10 of the two interacting vortices is wider than m* = 8 of a single vortex ring of the same property of core structure. Besides the category of stable mode, two other categories of the unstable mode, namely the odd-m and even-m modes, are classified. The odd-m unstable mode of m = 5, 7 and 9 concerns the evolution of star-like structure of one vortex ring with tail sheaths trailing behind. This unstable mode has slower evolution and becomes unstable after the third slip through. The even-m unstable mode of m = 6, 8 and 10 more rapid evolution and becomes unstable after the second slip through. Either one (m = 8 and 10) or two (m = 6) interacting vortex rings evolve into star-like structure with roll-shape sheaths. At m = 8, the unstable mode m* = 8 of a single vortex ring, besides the evolution of the roll-shape structure, sheaths wrapping the rolls are also found. Although quadrupole sound radiation is still observed, the far field sound pressure fluctuations depend on the interaction modes, with the roll-shape one (even-m mode) generally the highest, followed by the tail shape one (odd-m mode). The criterion for the onset of unstable mode established in the previous study is also confirmed for the higher wavenumbers.
Original languageEnglish
Pages (from-to)511-541
Number of pages31
JournalJournal of Sound and Vibration
Issue number3
Publication statusPublished - 2 Dec 1999

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


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