Journal of Applied Mathematics
Volume 2008 (2008), Article ID 586567, 40 pages
doi:10.1155/2008/586567
Research Article

Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles

Department of Aerospace and Mechanical Engineering, Second University of Naples, Via Roma 29, Aversa, 81031 Caserta, Italy

Received 6 June 2008; Accepted 8 September 2008

Academic Editor: Bernard Geurts

Copyright © 2008 G. Riccardi and D. Durante. 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. P. G. Saffman, Vortex Dynamics, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, NY, USA, 1992. View at Zentralblatt MATH · View at MathSciNet
  2. P. J. Davis, The Schwarz Function and Its Applications, The Carus Mathematical Monographs, no. 17, The Mathematical Association of America, Washington, DC, USA, 1974. View at Zentralblatt MATH · View at MathSciNet
  3. J. R. Kamm, Shape and stability of two-dimensional uniform vorticity regions, Ph.D. thesis, California Institute of Technology, Pasadena, Calif, USA, 1987.
  4. G. Riccardi, “Intrinsic dynamics of the boundary of a two-dimensional uniform vortex,” Journal of Engineering Mathematics, vol. 50, no. 1, pp. 51–74, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Crowdy, “A class of exact multipolar vortices,” Physics of Fluids, vol. 11, no. 9, pp. 2556–2564, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. Crowdy, “Multipolar vortices and algebraic curves,” Proceedings of the Royal Society of London. Series A, vol. 457, no. 2014, pp. 2337–2359, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. Crowdy and M. Cloke, “Stability analysis of a class of two-dimensional multipolar vortex equilibria,” Physics of Fluids, vol. 14, no. 6, pp. 1862–1876, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. D. Crowdy, “The construction of exact multipolar equilibria of the two-dimensional Euler equations,” Physics of Fluids, vol. 14, no. 1, pp. 257–267, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. D. Crowdy, “Exact solutions for rotating vortex arrays with finite-area cores,” Journal of Fluid Mechanics, vol. 469, pp. 209–235, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. D. Crowdy and J. Marshall, “Growing vortex patches,” Physics of Fluids, vol. 16, no. 8, pp. 3122–3130, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. Aref and D. L. Vainchtein, “Point vortices exhibit asymmetric equilibria,” Nature, vol. 392, no. 6678, pp. 769–770, 1998. View at Publisher · View at Google Scholar
  12. D. Crowdy and J. Marshall, “Analytical solutions for rotating vortex arrays involving multiple vortex patches,” Journal of Fluid Mechanics, vol. 523, pp. 307–337, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. Gned, D. Durante, G. Riccardi, and L. Zannetti, “The self-induced dynamics of vortex patches,” in Proceedings of IUTAM Symposium on 150 Years of Vortex Dynamics, Lyngby, Denmark, October 2008.
  14. N. J. Zabusky, M. H. Hughes, and K. V. Roberts, “Contour dynamics for the Euler equations in two dimensions,” Journal of Computational Physics, vol. 30, no. 1, pp. 96–106, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. G. Dritschel, “Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows,” Computer Physics Reports, vol. 10, no. 3, pp. 77–146, 1989. View at Publisher · View at Google Scholar
  16. D. I. Pullin, “Contour dynamics methods,” Annual Review of Fluid Mechanics, vol. 24, pp. 89–115, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. V. Melander, J. C. McWilliams, and N. J. Zabusky, “Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation,” Journal of Fluid Mechanics, vol. 178, pp. 137–159, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH