Analytical solutions for distributed multipolar vortex equilibria on a sphere | Zendy

Darren Crowdy | Zendy; Martin Cloke | Zendy

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Analytical solutions for distributed multipolar vortex equilibria on a sphere

Author(s) -

Darren Crowdy,

Martin Cloke

Publication year - 2002

Publication title -

physics of fluids

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.188

H-Index - 180

eISSN - 1089-7666

pISSN - 1070-6631

DOI - 10.1063/1.1521727

Subject(s) - stereographic projection , vortex , physics , vorticity , classical mechanics , euler equations , conformal map , euler's formula , surface (topology) , planar , mathematical analysis , geometry , mechanics , quantum mechanics , mathematics , computer graphics (images) , computer science

Analytical solutions of the steady Euler equations corresponding to stationary multipolar vortices on a sphere are derived. The solutions represent localized regions of distributed vorticity consisting of uniform vortex patches with a finite set of superposed point vortices. The mathematical method combines stereographic projection with conformal mapping theory to generalize a class of exact solutions for planar multipolar vortices developed by Crowdy [Phys. Fluids 11, 2556 (1999)] to the physically more important scenario of multipolar vortices on a spherical surface. The solutions are believed to be the first examples of analytical solutions of the Euler equations on a sphere involving patches of distributed vorticity with nontrivial shape.

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