Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains

Autor:	Darren Crowdy, Jonathan Marshall
Rok vydání:	2005
Předmět:	Explicit formulae General Mathematics Mathematical analysis General Engineering General Physics and Astronomy Process function Conformal map Topology Vortex symbols.namesake symbols Transformation property Hamiltonian (quantum mechanics) Mathematics
Zdroj:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 461:2477-2501
ISSN:	1471-2946 1364-5021
DOI:	10.1098/rspa.2005.1492
Popis:	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.
Databáze:	OpenAIRE
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