The structure of a two-dimensional viscous dipole is accurately analyzed using both numerical simulations and theoretical analyses. First, a model is proposed, which computes the dipole velocity and the vortex ellipticity based on a heuristic relation between a vortex patch and a vortex with distributed vorticity profile. Second, during the stage where vortices are close to each other, a generalized self-similar solution is postulated to describe the vorticity profiles observed during the viscous spreading of the dipole. Numerical as well as theoretical considerations are given, which demonstrate the adequacy of such a hypothesis. Finally the structure of the tail that is generated behind the dipole is given in an analytical form, which favorably compares to numerical results.
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July 2009
Research Article|
July 31 2009
The dynamics of a viscous vortex dipole
Ivan Delbende;
Ivan Delbende
a)
1Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI-CNRS, UPR 3251),
Université Pierre et Marie Curie-Paris 6
, BP 133, 91403 Orsay Cedex, France
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Maurice Rossi
Maurice Rossi
2Institut Jean le Rond d’Alembert (IJLRDA-UPMC, UMR 7190), CNRS,
Université Pierre et Marie Curie-Paris 6
, 4 Place Jussieu, 75252 Paris Cedex 05, France
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a)
Electronic mail: ivan.delbende@limsi.fr.
Physics of Fluids 21, 073605 (2009)
Article history
Received:
December 19 2008
Accepted:
June 23 2009
Citation
Ivan Delbende, Maurice Rossi; The dynamics of a viscous vortex dipole. Physics of Fluids 1 July 2009; 21 (7): 073605. https://doi.org/10.1063/1.3183966
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