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Annual Review of Fluid Mechanics

Volume 48, 2016

Dynamics and Instabilities of Vortex Pairs

Abstract

This article reviews the characteristics and behavior of counter-rotating and corotating vortex pairs, which are seemingly simple flow configurations yet immensely rich in phenomena. Since the reviews in this journal by Widnall (1975) and Spalart (1998), who studied the fundamental structure and dynamics of vortices and airplane trailing vortices, respectively, there have been many analytical, computational, and experimental studies of vortex pair flows. We discuss two-dimensional dynamics, including the merging of same-sign vortices and the interaction with the mutually induced strain, as well as three-dimensional displacement and core instabilities resulting from this interaction. Flows subject to combined instabilities are also considered, in particular the impingement of opposite-sign vortices on a ground plane. We emphasize the physical mechanisms responsible for the flow phenomena and clearly present the key results that are useful to the reader for predicting the dynamics and instabilities of parallel vortices.

Keyword(s): Crow instability, elliptic instability, ground effect, merging, vortex interactions

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An erratum has been published for this article:
Erratum: Dynamics and Instabilities of Vortex Pairs
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2016-01-03
2024-04-19
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Literature Cited

  1. Asselin DJ, Williamson CHK. 2013. Vortex pair impinging on a horizontal ground plane. Phys. Fluids 25:091104 [Google Scholar]
  2. Asselin DJ, Williamson CHK. 2015. Influence of a ground plane on the long-wave three-dimensional instability of a vortex. J. Fluid Mech. Submitted manuscript
  3. Batchelor GK. 1964. Axial flow in trailing line vortices. J. Fluid Mech. 20:645–58 [Google Scholar]
  4. Bayly BJ. 1986. Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57:2160–63 [Google Scholar]
  5. Benton SI, Bons JP. 2014. Three-dimensional instabilities in vortex/wall interactions: linear stability and flow control Presented at Aerosp. Sci. Meet., 52nd, National Harbor, MD, AIAA Pap. 2014-1267
  6. Billant P. 2010. Zigzag instability of vortex pairs in stratified and rotating fluids. Part 1. General stability equations. J. Fluid Mech. 660:354–95 [Google Scholar]
  7. Billant P, Brancher P, Chomaz JM. 1999. Three-dimensional stability of a vortex pair. Phys. Fluids 11:2069–77 [Google Scholar]
  8. Billant P, Chomaz JM. 2000. Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418:167–88 [Google Scholar]
  9. Brandt LK, Nomura KK. 2007. The physics of vortex merger and the effects of ambient stable stratification. J. Fluid Mech. 592:413–46 [Google Scholar]
  10. Brandt LK, Nomura KK. 2010. Characterization of interactions of two unequal co-rotating vortices. J. Fluid Mech. 646:233–53 [Google Scholar]
  11. Breitsamter C. 2011. Wake vortex characteristics of transport aircraft. Progr. Aerosp. Sci. 47:89–134 [Google Scholar]
  12. Brion V, Sipp D, Jacquin L. 2014. Linear dynamics of the Lamb-Chaplygin dipole in the two-dimensional limit. Phys. Fluids 26:064103 [Google Scholar]
  13. Bristol RL, Ortega JM, Marcus PS, Savaş O. 2004. On cooperative instabilities of parallel vortex pairs. J. Fluid Mech. 517:331–58 [Google Scholar]
  14. Cantwell B, Rott N. 1988. The decay of a viscous vortex pair. Phys. Fluids 31:3213–24 [Google Scholar]
  15. Cerretelli C, Williamson CHK. 2003a. A new family of uniform vortices related to vortex configurations before merging. J. Fluid Mech. 493:219–29 [Google Scholar]
  16. Cerretelli C, Williamson CHK. 2003b. The physical mechanism for vortex merging. J. Fluid Mech. 475:41–77 [Google Scholar]
  17. Chatelain P, Curioni A, Bergdorf M, Rossinelli D, Andreoni W, Koumoutsakos P. 2008. Billion vortex particle direct numerical simulations of aircraft wakes. Comput. Methods Appl. Mech. Eng. 197:1296–304 [Google Scholar]
  18. Chen AL, Jacob JD, Savaş O. 1999. Dynamics of corotating vortex pairs in the wakes of flapped airfoils. J. Fluid Mech. 382:155–93 [Google Scholar]
  19. Crouch J, Jacquin L. 2005. Aircraft trailing vortices/Tourbillons de sillages d'avions. C. R. Phys. 64–5, Spec. Issue Amsterdam: Elsevier [Google Scholar]
  20. Crouch JD, Miller GD, Spalart PR. 2001. Active-control system for breakup of airplane trailing vortices. AIAA J. 39:2374–81Studies four-vortex configurations for rapid aircraft wake breakup. [Google Scholar]
  21. Crow SC. 1970. Stability theory for a pair of trailing vortices. AIAA J. 8:2172–79Provides a theoretical description of the long-wave displacement instability of counter-rotating vortices. [Google Scholar]
  22. Dee FW, Nicholas OP. 1968. Flight measurements of wing-tip vortex motion near the ground Tech. Rep. CP 1065, Br. Aeronaut. Res. Council
  23. Delisi DP, Robins RE. 2000. Short-scale instabilities in trailing wake vortices in a stratified fluid. AIAA J. 38:1916–23 [Google Scholar]
  24. Deniau H, Nybelen L. 2009. Strategy for spatial simulation of co-rotating vortices. Int. J. Numer. Methods Fluids 61:23–56 [Google Scholar]
  25. Devenport WJ, Vogel CM, Zsoldos JS. 1999. Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices. J. Fluid Mech. 394:357–77 [Google Scholar]
  26. Dhanak MR, De Bernardinis B. 1981. The evolution of an elliptic vortex ring. J. Fluid Mech. 109:189–216 [Google Scholar]
  27. Donnadieu C, Ortiz S, Chomaz JM, Billant P. 2009. Three-dimensional instabilities and transient growth of a counter-rotating vortex pair. Phys. Fluids 21:094102 [Google Scholar]
  28. Dritschel DG. 1985. The stability and energetics of corotating uniform vortices. J. Fluid Mech. 157:95–134Presents the first linear stability analysis of uniform corotating, equal-area vortex pairs. [Google Scholar]
  29. Dritschel DG. 1986. The nonlinear evolution of rotating configurations of uniform vorticity. J. Fluid Mech. 172:157–82 [Google Scholar]
  30. Dritschel DG. 1995. A general theory for two-dimensional vortex interactions. J. Fluid Mech. 293:269–303 [Google Scholar]
  31. Dritschel DG, Waugh DW. 1992. Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics. Phys. Fluids A 4:1737–44 [Google Scholar]
  32. Duponcheel M. 2009. Direct and large-eddy simulation of turbulent wall-bounded flows PhD Thesis Univ. Cathol. Louvain
  33. Ehrenstein U, Rossi M. 1999. Equilibria of corotating nonuniform vortices. Phys. Fluids 25:3416–25 [Google Scholar]
  34. Eloy C, Le Dizès S. 1999. Three-dimensional instability of Burgers and Lamb-Oseen vortices in a strain field. J. Fluid Mech. 378:145–66 [Google Scholar]
  35. Eloy C, Le Dizès S. 2001. Stability of the Rankine vortex in a multipolar strain field. Phys. Fluids 13:660–76 [Google Scholar]
  36. Eloy C, Le Gal P, Le Dizès S. 2003. Elliptic and triangular instabilities in rotating cylinders. J. Fluid Mech. 476:357–88 [Google Scholar]
  37. Fabre D. 2002. Instabilitités et instationnarités dans les tourbillons: application aux sillages d'avions PhD Thesis Univ. Paris VI
  38. Fabre D, Jacquin L, Loof A. 2002. Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration. J. Fluid Mech. 451:319–28 [Google Scholar]
  39. Fabre D, Sipp D, Jacquin L. 2006. The Kelvin waves and the singular modes of the Lamb-Oseen vortex. J. Fluid Mech. 551:235–74 [Google Scholar]
  40. Felli M, Camussi R, Felice FD. 2011. Mechanisms of evolution of the propeller wake in the transition and far fields. J. Fluid Mech. 682:5–53 [Google Scholar]
  41. Fukumoto Y. 2003. The three-dimensional instability of a strained vortex tube revisited. J. Fluid Mech. 493:287–318 [Google Scholar]
  42. Fukumoto Y, Hattori Y. 2005. Curvature instability of a vortex ring. J. Fluid Mech. 526:77–115 [Google Scholar]
  43. Garten JF, Werne J, Fritts DC, Arendt S. 2001. Direct numerical simulations of the Crow instability and subsequent vortex reconnection in a stratified fluid. J. Fluid Mech. 426:1–45 [Google Scholar]
  44. Gerz T, Holzäpfel F, Darracq D. 2002. Commercial aircraft wake vortices. Progr. Aerosp. Sci. 38:181–208 [Google Scholar]
  45. Harris DM, Williamson CHK. 2012. Instability of secondary vortices generated by a vortex pair in ground effect. J. Fluid Mech. 700:148–86 [Google Scholar]
  46. Harvey JK, Perry FJ. 1971. Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9:1659–60 [Google Scholar]
  47. Holzäpfel F, Gerz T, Baumann R. 2001. The turbulent decay of trailing vortex pairs in stably stratified environments. Aerosp. Sci. Technol. 5:95–108 [Google Scholar]
  48. Holzäpfel F, Hofbauer T, Darracq D, Moet H, Garnier F, Ferreira Gago C. 2003. Analysis of wake vortex decay mechanisms in the atmosphere. Aerosp. Sci. Technol. 7:263–75 [Google Scholar]
  49. Hopfinger EJ, van Heijst GJF. 1993. Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25:241–89 [Google Scholar]
  50. Jiménez J. 1975. Stability of a pair of co-rotating vortices. Phys. Fluids 18:1580–81 [Google Scholar]
  51. Jing F, Kanso E, Newton PK. 2012. Insights into symmetric and asymmetric vortex mergers using the core growth model. Phys. Fluids 24:073101 [Google Scholar]
  52. Josserand C, Rossi M. 2007. The merging of two co-rotating vortices: a numerical study. Eur. J. Mech. B Fluids 26:779–94 [Google Scholar]
  53. Kelvin L. 1880. On the vibrations of a columnar vortex. Philos. Mag. 10:155–68 [Google Scholar]
  54. Kerswell RR. 1999. Secondary instabilities in rapidly rotating fluids: inertial wave breakdown. J. Fluid Mech. 382:283–306 [Google Scholar]
  55. Kerswell RR. 2002. Elliptical instability. Annu. Rev. Fluid Mech. 34:83–113 [Google Scholar]
  56. Kida S, Takaoka M. 1994. Vortex reconnection. Annu. Rev. Fluid Mech. 26:169–77 [Google Scholar]
  57. Klein R, Majda AJ, Damodaran K. 1995. Simplified equations for the interaction of nearly parallel vortex filaments. J. Fluid Mech. 288:201–48 [Google Scholar]
  58. Kramer W, Clercx HJH, van Heijst GJF. 2007. Vorticity dynamics of a dipole colliding with a no-slip wall. Phys. Fluids 19:126603 [Google Scholar]
  59. Lacaze L, Birbaud AL, Le Dizès S. 2005. Elliptic instability in a Rankine vortex with axial flow. Phys. Fluids 17:017101 [Google Scholar]
  60. Lacaze L, Ryan K, Le Dizès S. 2007. Elliptic instability in a strained Batchelor vortex. J. Fluid Mech. 577:341–61Describes the effect of axial flow on elliptic instability in realistic vortices. [Google Scholar]
  61. Lamb H. 1932. Hydrodynamics. Cambridge, UK: Cambridge Univ. Press, 6th ed..
  62. Landman MJ, Saffman PG. 1987. The three-dimensional instability of strained vortices in a viscous fluid. Phys. Fluids 30:2339–42 [Google Scholar]
  63. Laporte F. 2002. Simulation numérique appliquée à la caractérisation et aux instabilités des tourbillons de sillage des avions de transport PhD Thesis, INPT, Toulouse
  64. Laporte F, Corjon A. 2000. Direct numerical simulations of the elliptic instability of a vortex pair. Phys. Fluids 12:1016–31 [Google Scholar]
  65. Laporte F, Leweke T. 2002. Elliptic instability of trailing vortices: experiment and direct numerical simulation. AIAA J. 40:2483–94 [Google Scholar]
  66. Le Dizès S. 2000a. Non-axisymmetric vortices in two-dimensional flows. J. Fluid Mech. 406:175–98 [Google Scholar]
  67. Le Dizès S. 2000b. Three-dimensional instability of a multipolar vortex in a rotating flow. Phys. Fluids 12:2762–74 [Google Scholar]
  68. Le Dizès S. 2004. Viscous critical-layer analysis of vortex normal modes. Stud. Appl. Math. 112:315–32 [Google Scholar]
  69. Le Dizès S, Lacaze L. 2005. An asymptotic description of vortex Kelvin modes. J. Fluid Mech. 542:69–96 [Google Scholar]
  70. Le Dizès S, Laporte F. 2002. Theoretical predictions for the elliptic instability in a two-vortex flow. J. Fluid Mech. 471:169–201Presents a general formula for the elliptic instability growth rate in a vortex pair. [Google Scholar]
  71. Le Dizès S, Verga A. 2002. Viscous interaction of two co-rotating vortices before merging. J. Fluid Mech. 467:389–410 [Google Scholar]
  72. Legras B, Dritschel DG. 1993. Vortex stripping and the generation of high vorticity gradients in two-dimensional flows. Appl. Sci. Res. 51:445–55 [Google Scholar]
  73. Leishman JG. 2006. Principles of Helicopter Aerodynamics. Cambridge, UK: Cambridge Univ. Press
  74. Levy H, Forsdyke AG. 1927. The stability of an infinite system of circular vortices. Proc. R. Soc. Lond. A 114:594–604 [Google Scholar]
  75. Leweke T, Meunier P, Laporte F, Darracq D. 2001. Controlled interaction of co-rotating vortices Presented at 3rd ONERA-DLR Aerosp. Symp. (ODAS 2001), Paris, Pap. S2-3
  76. Leweke T, Williamson CHK. 1998. Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360:85–119Provides the first experimental identification of the elliptic instability in an open flow. [Google Scholar]
  77. Leweke T, Williamson CHK. 2011. Experiments on long-wavelength instability and reconnection of a vortex pair. Phys. Fluids 23:024101 [Google Scholar]
  78. Lim TT. 1989. An experimental study of a vortex ring interacting with an inclined wall. Exp. Fluids 7:453–63 [Google Scholar]
  79. Luton JA, Ragab SA. 1997. The three-dimensional interaction of a vortex pair with a wall. Phys. Fluids 9:2967–80 [Google Scholar]
  80. Luzzatto-Fegiz P, Williamson CHK. 2010. Stability of elliptical vortices from “Imperfect-Velocity-Impulse” diagrams. Theor. Comput. Fluid Dyn. 24:181–88 [Google Scholar]
  81. Luzzatto-Fegiz P, Williamson CHK. 2012. Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams. J. Fluid Mech. 706:323–50 [Google Scholar]
  82. Mariotti A, Legras B, Dritschel DG. 1994. Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys. Fluids A 6:3954–62 [Google Scholar]
  83. Mayer EW, Powell KG. 1992. Viscous and inviscid instabilities of a trailing vortex. J. Fluid Mech. 245:91–114 [Google Scholar]
  84. Melander MV, McWilliams JC, Zabusky NJ. 1987. Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech. 178:137–59 [Google Scholar]
  85. Melander MV, Zabusky NJ, McWilliams JC. 1988. Symmetric vortex merger in two-dimensions: causes and conditions. J. Fluid Mech. 195:303–40 [Google Scholar]
  86. Meunier P, Ehrenstein U, Leweke T, Rossi M. 2002. A merging criterion for two-dimensional co-rotating vortices. Phys. Fluids 14:2757–66 [Google Scholar]
  87. Meunier P, Le Dizès S, Leweke T. 2005. Physics of vortex merging. C. R. Phys. 6:431–50 [Google Scholar]
  88. Meunier P, Leweke T. 2000. Unstable vortex merger. Phys. Fluids 12:S6 [Google Scholar]
  89. Meunier P, Leweke T. 2001. Three-dimensional instability during vortex merging. Phys. Fluids 13:2747–50Presents experimental observations of elliptic instability in corotating vortices. [Google Scholar]
  90. Meunier P, Leweke T. 2005. Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533:125–59 [Google Scholar]
  91. Miyazaki T, Fukumoto Y. 1992. Three-dimensional instability of strained vortices in stably stratified fluid. Phys. Fluids A 4:2515–22 [Google Scholar]
  92. Moffatt HK, Kida S, Ohkitani K. 1994. Stretched vortices: the sinews of turbulence; large-Reynolds-number asymptotics. J. Fluid Mech. 259:241–64 [Google Scholar]
  93. Moore DW, Saffman PG. 1971. Structure of a line vortex in an imposed strain. Aircraft Wake Turbulence and Its Detection JH Olsen, A Goldburg, M Rogers 339–54 New York: Plenum [Google Scholar]
  94. Moore DW, Saffman PG. 1975. The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. A 346:413–25Explains how elliptic instability is associated with a mechanism of Kelvin-mode resonance. [Google Scholar]
  95. NATO (N. Atl. Treaty Organ.) 1996. The Characterization and Modification of Wakes from Lifting Vehicles in Fluids Vol. 584 NATO AGARD Conf. Proc Brussels: NATO
  96. Nomura KK, Tsutsui H, Mahoney D, Rottman JW. 2006. Short-wavelength instability and decay of a vortex pair in a stratified fluid. J. Fluid Mech. 553:283–322 [Google Scholar]
  97. Nybelen L, Paoli R. 2009. Direct and large-eddy simulations of merging in corotating vortex system. AIAA J. 47:157–67 [Google Scholar]
  98. Orlandi P. 1990. Vortex dipole rebound from a wall. Phys. Fluids A 2:1429–36 [Google Scholar]
  99. Ortega JM, Bristol RL, Savaş O. 2003. Experimental study of the instability of unequal-strength counter-rotating vortex pairs. J. Fluid Mech. 474:35–84 [Google Scholar]
  100. Otheguy P, Billant P, Chomaz JM. 2006. The effect of planetary rotation on the zigzg instability of co-rotating vortices in a stratified fluid. J. Fluid Mech. 553:273–81 [Google Scholar]
  101. Otheguy P, Chomaz JM, Augier P, Kimura Y, Billant P. 2015. Pairing of two vertical columnar vortices in a stratified fluid. Eur. J. Mech. B Fluids 49:413–25 [Google Scholar]
  102. Overman EA, Zabusky NJ. 1982. Evolution and merger of isolated vortex structures. Phys. Fluids 25:1297–305 [Google Scholar]
  103. Peace AJ, Riley N. 1983. A viscous vortex pair in ground effect. J. Fluid Mech. 129:409–26 [Google Scholar]
  104. Pierrehumbert RT. 1986. Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57:2157–60 [Google Scholar]
  105. Pullin DI. 1992. Contour dynamics methods. Annu. Rev. Fluid Mech. 24:89–115 [Google Scholar]
  106. Rabinovitch J, Brion V, Blanquart G. 2012. Effect of a splitter plate on the dynamics of a vortex pair. Phys. Fluids 24:074110 [Google Scholar]
  107. Roberts KV, Christiansen JP. 1972. Topics in computational fluid mechanics. Comput. Phys. Commun. Suppl. 3:14–32 [Google Scholar]
  108. Rossow VJ. 1999. Lift-generated vortex wakes of subsonic transport aircraft. Prog. Aerosp. Sci. 35:507–660 [Google Scholar]
  109. Roy C, Leweke T, Thompson MC, Hourigan K. 2011. Experiments on the elliptic instability in vortex pairs with axial core flow. J. Fluid Mech. 677:383–416 [Google Scholar]
  110. Roy C, Schaeffer N, Le Dizès S, Thompson M. 2008. Stability of a pair of co-rotating vortices with axial flow. Phys. Fluids 20:094101 [Google Scholar]
  111. Ryan K, Butler CJ, Sheard GJ. 2012. Stability characteristics of a counter-rotating unequal-strength Batchelor vortex pair. J. Fluid Mech. 696:374–401 [Google Scholar]
  112. Ryan K, Sheard GJ. 2007. Non-linear growth of short-wave instabilities in a Batchelor vortex pair. Proc. 16th Australas. Fluid Mech. Conf. P Jacobs, T McIntyre, M Cleary, D Buttsworth, D Mee 1463–69 Brisbane: Univ. Queensland [Google Scholar]
  113. Saffman PG. 1992. Vortex Dynamics Cambridge, UK: Cambridge Univ. Press
  114. Saffman PG, Szeto R. 1980. Equilibrium of a pair of equal uniform vortices. Phys. Fluids 23:2339–42 [Google Scholar]
  115. Schaeffer N, Le Dizès S. 2007. Influence of an elliptic instability on the merging of a co-rotating vortex pair. 18ème Congrès Français de Mécanique Pap. CFM2007-1038 Courbevoie: AFM [Google Scholar]
  116. Schaeffer N, Le Dizès S. 2010. Nonlinear dynamics of the elliptic instability. J. Fluid Mech. 646:471–80 [Google Scholar]
  117. Shariff K, Leonard A. 1992. Vortex rings. Annu. Rev. Fluid Mech. 24:235–79 [Google Scholar]
  118. Sipp D, Jacquin L. 2003. Widnall instabilities in vortex pairs. Phys. Fluids 15:1861–74 [Google Scholar]
  119. Sipp D, Jacquin L, Cossu C. 2000. Self-adaptation and viscous selection in concentrated two-dimensional dipoles. Phys. Fluids 12:245–48 [Google Scholar]
  120. So J, Ryan K, Sheard GS. 2011. Short-wave instabilities on a vortex pair of unequal strength circulation ratio. Appl. Math. Model. 35:1571–90 [Google Scholar]
  121. Spalart PR. 1998. Airplane trailing vortices. Annu. Rev. Fluid Mech. 30:107–38 [Google Scholar]
  122. Ting L, Tung C. 1965. Motion and decay of a vortex in a nonuniform stream. Phys. Fluids 8:1039–51 [Google Scholar]
  123. Trieling RR, Beckers M, van Heijst GJF. 1997. Dynamics of monopolar vortices in a strain flow. J. Fluid Mech. 345:165–201 [Google Scholar]
  124. Trieling RR, Velasco Fuentes OU, van Heijst GJF. 2005. Interaction of two unequal corotating vortices. Phys. Fluids 17:087103 [Google Scholar]
  125. Tsai CY, Widnall SE. 1976. The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73:721–33 [Google Scholar]
  126. van Heijst GJF, Clercx HJH. 2009. Laboratory modeling of geophysical vortices. Annu. Rev. Fluid Mech. 41:143–64 [Google Scholar]
  127. Velasco Fuentes OU. 2005. Vortex filamentation: its onset and its role on axisymmetrization and merger. Dyn. Atmos. Oceans 40:23–42 [Google Scholar]
  128. Vermeer LJ, Sørensen JN, Crespo A. 2003. Wind turbine wake aerodynamics. Progr. Aerosp. Sci. 39:467–510 [Google Scholar]
  129. Waite ML, Smolarkiewicz. 2008. Instability and breakdown of a vertical vortex pair in a strongly stratified fluid. J. Fluid Mech. 606:239–73 [Google Scholar]
  130. Waleffe F. 1989. The 3D instability of a strained vortex and its relation to turbulence PhD Thesis Mass. Inst. Technol. Cambridge:
  131. Waleffe F. 1990. On the three-dimensional instability of strained vortices. Phys. Fluids A 2:76–80Provides the link between local and global descriptions of the elliptic instability. [Google Scholar]
  132. Widnall SE. 1972. The stability of a helical vortex filament. J. Fluid Mech. 54:641–63 [Google Scholar]
  133. Widnall SE. 1975. The structure and dynamics of vortex filaments. Annu. Rev. Fluid Mech. 7:141–65 [Google Scholar]
  134. Widnall SE, Bliss D, Tsai CY. 1974. The instability of short waves on a vortex ring. J. Fluid Mech. 66:35–47Presents the first theoretical description of the elliptic instability. [Google Scholar]
  135. Widnall SE, Bliss DB, Zalay A. 1971. Theoretical and experimental study of the instability of a vortex pair. Aircraft Wake Turbulence and Its Detection JH Olsen, A Goldburg, M Rogers 305–38 New York: Plenum [Google Scholar]
  136. Williamson CHK, Chomaz JM. 1997. The exploding vortex pair. Phys. Fluids 9S4
  137. Williamson CHK, Leweke T, Asselin DJ, Harris DM. 2014. Phenomena, dynamics and instabilities of vortex pairs. Fluid Dyn. Res. 46:061425 [Google Scholar]
  138. Winckelmans G, Cocle R, Dufresne L, Capart R. 2005. Vortex methods and their application to trailing wake vortex simulations. C. R. Phys. 6:467–86 [Google Scholar]
  139. Yasuda I, Flierl GR. 1995. Two-dimensional asymmetric vortex merger: contour dynamics experiment. J. Oceanogr. 51:145–70 [Google Scholar]
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Dynamics and Instabilities of Vortex Pairs
Annual Review of Fluid Mechanics 48, 507 (2016); https://doi.org/10.1146/annurev-fluid-122414-034558
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