The study of vortex flows around solid obstacles is of considerable interest from both a theoretical and practical perspective. One geometry that has attracted renewed attention recently is that of vortex flows past a circular cylinder placed above a plane wall, where a stationary recirculating eddy can form in front of the cylinder, in contradistinction to the usual case (without the plane boundary) for which a vortex pair appears behind the cylinder. Here we analyze the problem of vortex flows past a cylinder near a wall through the lenses of the point-vortex model. By conformally mapping the fluid domain onto an annular region in an auxiliary complex plane, we compute the vortex Hamiltonian analytically in terms of certain special functions related to elliptic theta functions. A detailed analysis of the equilibria of the model is then presented. The location of the equilibrium in front of the cylinder is shown to be in qualitative agreement with recent experimental findings. We also show that a topological transition occurs in phase space as the parameters of the systems are varied.
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August 2017
Research Article|
August 01 2017
Vortex motion around a circular cylinder above a plane
G. L. Vasconcelos;
G. L. Vasconcelos
a)
1
Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco
, 50670-901 Recife, Brazil
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M. Moura
M. Moura
2
PoreLab, Department of Physics, University of Oslo
, P.O. Box 1048, Blindern, N-0316 Oslo, Norway
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a)
Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 29, 083603 (2017)
Article history
Received:
February 09 2017
Accepted:
July 12 2017
Citation
G. L. Vasconcelos, M. Moura; Vortex motion around a circular cylinder above a plane. Physics of Fluids 1 August 2017; 29 (8): 083603. https://doi.org/10.1063/1.4996241
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