Abstract:
Point vortices have been extensively studied in vortex dynamics. The generalization to higher singularities, starting with vortex dipoles, is not so well understood.We obtain a family of equations of motion for inviscid vortex dipoles and discuss limitations of the concept.We then investigate viscous vortex dipoles, using two different formulations to obtain their propagation velocity. We also derive an integro-differential for the motion of a viscous vortex dipole parallel to a straight boundary.
\Bibitem{LleNag13}
\by Stefan G. Llewellyn Smith, Raymond J. Nagem
\paper Vortex Pairs and Dipoles
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 194--201
\mathnet{http://mi.mathnet.ru/rcd105}
\crossref{https://doi.org/10.1134/S1560354713010140}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3040992}
\zmath{https://zbmath.org/?q=an:1273.76070}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000317623400014}
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https://www.mathnet.ru/eng/rcd105
https://www.mathnet.ru/eng/rcd/v18/i1/p194
This publication is cited in the following 13 articles:
A. I. Bulycheva, K. M. Kulik, V. V. Yanovsky, “Motion of a point dipole in a strip”, Phys. Rev. Fluids, 10:1 (2025)
Björn Gustafsson, “Vortex Pairs and Dipoles on Closed Surfaces”, J Nonlinear Sci, 32:5 (2022)
Morteza Sharifi, Behruz Raesi, “Vortex Theory for Two Dimensional Boussinesq Equations”, Applied Mathematics and Nonlinear Sciences, 5:2 (2020), 67
Gustafsson B., “Vortex Motion and Geometric Function Theory: the Role of Connections”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 377:2158 (2019), 20180341
J. N. Reinaud, K. V. Koshel, E. A. Ryzhov, “Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation”, Phys. Fluids, 30:9 (2018), 096604
U. Habibah, H. Nakagawa, Ya. Fukumoto, “Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers”, Fluid Dyn. Res., 50:3 (2018), 031401
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
S. D. Peterson, M. Porfiri, “Energy exchange between coherent fluid structures and ionic polymer metal composites, toward flow sensing and energy harvesting”, Ionic Polymer Metal Composites (IPMCS): Smart Multi-Functional Materials and Artificial Muscles, v. 2, RSC Smart Materials, 18, ed. M. Shahinpoor, Royal Soc Chemistry, 2016, 1–18
E. Kanso, Tsang Alan Cheng Hou, “Pursuit and synchronization in hydrodynamic dipoles”, J. Nonlinear Sci., 25:5, SI (2015), 1141–1152
E. Kanso, Tsang Alan Cheng Hou, “Dipole models of self-propelled bodies”, Fluid Dyn. Res., 46:6 (2014), 061407
Yu. Matsumoto, K. Ueno, “A dynamical system of interacting dipoles in two-dimensional flows”, Fluid Dyn. Res., 46:3 (2014), 031413
Tsang Alan Cheng Hou, E. Kanso, “Dipole interactions in doubly periodic domains”, J. Nonlinear Sci., 23:6 (2013), 971–991
S. D. Peterson, M. Porfiri, “Impact of a vortex dipole with a semi-infinite rigid plate”, Phys. Fluids, 25:9 (2013), 093103
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