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Vortex dynamics on a domain with holes

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Abstract

We explore the relationship between the hydrodynamic Green’s function and the Dirichlet Green’s function in a bounded domain with holes. This relationship is expressed using the harmonic measures on the domain, following the work of Flucher and Gustafsson (Vortex motion in two-dimensional hydrodynamics, energy renormalization and stability of vortex pairs, TRITA preprint series, 1997). The explicit form of this relation expresses velocity in terms of vorticity in a way which turns out to be very convenient, especially for analysis. We explain the advantages and describe some applications.

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Authors and Affiliations

  1. IMECC, Universidade Estadual de Campinas-UNICAMP, Caixa Postal 6065, Campinas, SP, 13083-970, Brazil

    Milton da Costa Lopes Filho & Helena J. Nussenzveig Lopes

Authors
  1. Milton da Costa Lopes Filho
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  2. Helena J. Nussenzveig Lopes
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Correspondence to Milton da Costa Lopes Filho.

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Communicated by H. Aref

M. da Costa Lopes Filho’s research supported in part by CNPq grant #303.301/2007-4 and H. J. Nussenzveig Lopes’s research supported in part by CNPq grant #302.214/2004-6.

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Lopes Filho, M.d.C., Nussenzveig Lopes, H.J. Vortex dynamics on a domain with holes. Theor. Comput. Fluid Dyn. 24, 51–57 (2010). https://doi.org/10.1007/s00162-009-0141-6

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  • DOI: https://doi.org/10.1007/s00162-009-0141-6

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