Vortical flow outside a sphere and sound generation

Omar Knio*, Lu Ting

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Formulas are presented for an incompressible inviscid velocity field V with a vorticity field Ω outside of a rigid sphere and for the far-field sound generation. The velocity V is expressed as the sum of an image velocity v* and a known velocity v in ℜ3, which is induced by the same vorticity field Ω outside the sphere and the extension Ω = 0 inside. We derive formulas for the image velocity v* and the corresponding image potential Φ*, which in turn yields the far-field sound. These formulas are applied to define the velocity of a slender vortex filament in the presence of a rigid sphere and the associated far-field sound.

Original languageEnglish (US)
Pages (from-to)972-981
Number of pages10
JournalSIAM Journal on Applied Mathematics
Volume57
Issue number4
DOIs
StatePublished - Jan 1 1997

Keywords

  • Acoustic field
  • Spherical images
  • Vortical flow

ASJC Scopus subject areas

  • Applied Mathematics

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