Riemannian geometry of irrotational vortex acoustics

Details Riemannian geometry of irrotational vortex acoustics Riemannian geometry of irrotational vortex acoustics

2001-10-10

arxiv.org/abs/cond-mat/0110211v2

Phys.Rev.Lett. 88 (2002) 110201

Physics

Condensed Matter

4 pages, 2 figures, RevTex4. Discussion of focal length added; to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.88.110201

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the ``acoustic geometry'' that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity $\Gamma/(2\pi cb)$, where $\Gamma$ is the vortex circulation, $c$ the speed of sound, and $b$ the impact parameter.

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