- Knio, O. M. and Ting, L., Vortical flow outside a sphere and sound generation,
SIAM JOURNAL ON APPLIED MATHEMATICS, vol. 57 no. 4
pp. 972--981 .
(last updated on 2011/07/05)
Formulas are presented for an incompressible inviscid velocity field V with a vorticity field hi 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 R-3, which is induced by the same vorticity field Omega outside the sphere and the extension Omega = 0 inside. We derive formulas for the image velocity v* and the corresponding image potential Phi*, 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.