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From generation to chaotic motion of a ring configuration of vortex structures on a sphere

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Abstract

This is a review article of recent research developments on the motion of a polygonal ring configuration of vortex structures with singular vorticity distributions in incompressible and inviscid flows on a non-rotating sphere. Numerical computation of a single vortex sheet reveals that the Kelvin-Helmholtz instability gives rise to the formation of a polygonal ring arrangement of rolling-up spirals. An application of methods of Hamiltonian dynamics to the N-vortex problem on the sphere shows that the motion of the ring configuration of homogeneous point vortices, which is a simple model for the rolling-up spirals, becomes chaotic after a long time evolution. Some remarks on an extension of the present research and a generic non-self-similar collapse are also provided.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, Sapporo, Japan

    Takashi Sakajo

  2. PRESTO, Japan Science and Technology Agency, Tokyo, Japan

    Takashi Sakajo

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  1. Takashi Sakajo
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Correspondence to Takashi Sakajo.

Additional information

Communicated by H. Aref

I would like to show my gratitude to School of Mathematics at the University of Sheffield for giving me nice research environments from September 2008 through March 2009. Partially supported by JSPS grant 19654014.

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Sakajo, T. From generation to chaotic motion of a ring configuration of vortex structures on a sphere. Theor. Comput. Fluid Dyn. 24, 151–156 (2010). https://doi.org/10.1007/s00162-009-0116-7

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  • DOI: https://doi.org/10.1007/s00162-009-0116-7

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