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International Journal of Differential Equations
Volume 2012 (2012), Article ID 929626, 10 pages
http://dx.doi.org/10.1155/2012/929626
Research Article

Some Nonlinear Vortex Solutions

1Department of Mathematics and Statistics, York University, Toronto, ON, Canada M3J 1P3
2Department of Applied Mathematics, University of Western Ontario, London, ON, Canada N6A 5B7
3Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

Received 3 June 2011; Revised 10 November 2011; Accepted 24 November 2011

Academic Editor: Bashir Ahmad

Copyright © 2012 Michael C. Haslam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J.-M. Chomaz, “Global instabilities in spatially developing flows: non-normality and nonlinearity,” Annual Review of Fluid Mechanics, vol. 37, pp. 357–392, 2005. View at Publisher · View at Google Scholar
  2. P. G. Saffman, Vortex Dynamics, Cambridge University Press, New York, NY, USA, 1992.
  3. J. M. Faddy and D. I. Pullin, “Flow structure in a model of aircraft trailing vortices,” Physics of Fluids, vol. 17, no. 8, Article ID 085106, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. T. Siegmann-Hegerfeld, S. Albensoeder, and H. C. Kuhlmann, “Two- and three-dimensional flows in nearly rectangular cavities driven by collinear motion of two facing walls,” Experiments in Fluids, vol. 45, no. 5, pp. 781–796, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. K. W. Chow, S. C. Tsang, and C. C. Mak, “Another exact solution for two-dimensional, inviscid sinh Poisson vortex arrays,” Physics of Fluids, vol. 15, no. 8, pp. 2437–2440, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. Tur, V. Yanovsky, and K. Kulik, “Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions,” Physica D, vol. 240, no. 13, pp. 1069–1079, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. T. Stuart, “On finite amplitude oscillations in laminar mixing layers,” Journal of Fluid Mechanics, vol. 29, pp. 417–440, 1967.
  8. R. Mallier and S. A. Maslowe, “A row of counter-rotating vortices,” Physics of Fluids A, vol. 5, no. 4, pp. 1074–1075, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J. Liouville, “Sur l'équation aux différences partielles 2logλ/uv±λ2/2a2=0,” Journal de Mathématiques Pures et Appliquées, vol. 18, pp. 71–72, 1853.
  10. D. G. Crowdy, “General solutions to the 2D Liouville equation,” International Journal of Engineering Science, vol. 35, no. 2, pp. 141–149, 1997. View at Publisher · View at Google Scholar
  11. J. Schmid-Burgk, Zweidimensionale selbstkonsistente Lösungen stationären Wlassovgleichung für Zweikomponentenplasmen, Diplomarbeit, Ludwig-Maximilians-Universität München, 1965.
  12. G. W. Walker, “Some problems illustrating the forms of nebuloe,” Proceedings of the Royal Society A, vol. 91, no. 631, pp. 410–420, 1915.
  13. A. Barcilon and P. G. Drazin, “Nonlinear waves of vorticity,” Studies in Applied Mathematics, vol. 106, no. 4, pp. 437–479, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. C. Ting, H. H. Chen, and Y. C. Lee, “Exact solutions of a nonlinear boundary value problem: the vortices of the two-dimensional sinh-Poisson equation,” Physica D, vol. 26, no. 1–3, pp. 37–66, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications Inc., New York, NY, USA, 1992.