期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 461, 期 2060, 页码 2477-2501出版社
ROYAL SOC
DOI: 10.1098/rspa.2005.1492
关键词
point vortex; Kirchhoff-Routh; Hamiltonian
Explicit formulae for the Kirchhoff-Routh path functions (or Hamiltonians) governing the motion of N-point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero. The method uses the Schottky-Klein prime function to find representations of the hydrodynamic Green's function in multiply connected circular domains. The Green's function is then used to construct the associated Kirchhoff-Routh path function. The path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains. Illustrative examples are presented for the case of single vortex motion in multiply connected domains.
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