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Articles

On the mother bodies of steady polygonal uniform vortices. Part I: numerical experiments

Pages 433-457 | Received 11 Jun 2022, Accepted 14 Oct 2022, Published online: 04 Nov 2022

References

  • Ablowitz, M.J. and Fokas, A.S., Complex Variables: Introduction and Applications, 2003 (Cambridge University Press: Cambridge).
  • Barbosa Aguiar, A.C., Instabilities of a shear layer in a barotropic rotating fluid. Ph.D. thesis, University of Oxford, UK, 2008.
  • Burbea, J., Motions of vortex patches. Lett. Math. Phys. 1982, 6, 1–16.
  • Deem, G.S. and Zabusky, N.J., Vortex waves: stationary “V states,” interactions, recurrence and breaking. Phys. Rev. Lett. 1977, 40, 859–862.
  • Gakhov, F.D., Boundary Value Problems, 1990 (Dover Publications: New York).
  • Hassainia, Z., Masmoudi, N. and Wheeler, M.H., Global bifurcation of rotating vortex patches. Commun. Pure Appl. Math. 2019, 73, 1933–1980.
  • Muskhelishvili, N.I., Singular Integral Equations, 2008 (Dover Publications: New York).
  • Riccardi, G., A complex analysis approach to the motion of uniform vortices. Ocean Dyn. 2018, 68, 273–293.
  • Riccardi, G., An investigation about polygonal steady vortices. In Proceedings of XXIV AIMETA Conference 2019, Lecture Notes in Mechanical Engineering, pp. 27–44, 2020a (Springer: Milan).
  • Riccardi, G., Remarks on equilibria of two-dimensional uniform vortices with polygonal symmetry. Eur. J. Mech. B Fluids 2020b, 83, 1–14.
  • Riccardi, G. and Dritschel, D.G., Evolution of the singularities of the Schwarz function corresponding to the motion of a vortex patch in the two-dimensional Euler equations. Regul. Chaotic Dyn. 2021, 26, 562–575.
  • Riccardi, G. and Durante, D., Elementi di Fluidodinamica, in Italian, 2006 (Springer: Milan).
  • Riccardi, G. and Durante, D., Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles. J. Appl. Math. 2008, 2008, Article ID 586567.
  • Saffman, P.G., Vortex Dynamics, 1992 (Cambridge University Press: Cambridge).
  • Sánchez-Lavega, A., del Río-Gaztelurrutia, T., Hueso, R., Pérez-Hoyos, S., García-Melendo, E., Antuñano, A., Mendikoa, I., Rojas, J.F., Lillo, J., Barrado-Navascués, D., Gomez-Forrellad, J.M., Go, C., Peach, D., Barry, T., Milika, D.P., Nicholas, P. and Wesley, A., The long-term steady motion of Saturn's hexagon and the stability of its enclosed jet stream under seasonal changes. Geophys. Res. Lett. 2014, 41, 1425–1431.
  • Savina, T.V., Sternin, B.Y. and Shatalov, V.E., On a minimal element for a family of bodies producing the same external gravitational field. Appl. Anal. 2005, 84, 649–668.
  • Tran, N.T., Applications of potential theoretic mother bodies in electrostatics. Am. J. Comput. Math. 2017, 7, 481–494.

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