Equilibria of corotating nonuniform vortices

Physics of Fluids

Volumn 11, Issue 11, 1999, Pages 3416-3425

  Ehrenstein, U ^a,c   Rossi, M ^b  

^a UNIV LILLE   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002201760     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870200     Document Type: Article

References (24)

1. J. C. Mc Williams, "The vortices of two-dimensional turbulence," J. Fluid Mech. 219, 361 (1990).
2. J. Jimenez, H. K. Moffat, and C. Vasco, "The structure of the vortices in freely decaying two-dimensional turbulence," J. Fluid Mech. 313, 209 (1996).
3. A. D. Gilbert, "Spiral structures and spectra in two-dimensional turbulence," J. Fluid Mech. 193, 475 (1988).
4. E. Hopfinger, F. Browand, and Y. Gagne, "The structure of turbulence in homogeneous and stratified rotating fluids," J. Mécan. Théorique et Appliqué, Numéro spécial 21 (1983).
5. Y. Couder, "Observation expérimentale de la turbulence bidimensionnelle dans un film liquide mince," C.R. Acad. Sci. Paris, Ser. II 297, 641 (1983).
6. Y. Couder, J. M. Chomaz, and M. Rabaud, "On the hydrodynamics of soap films," Physica D 37, 384 (1989).
7. P. Tabeling, S. Burkhart, O. Cardoso, and H. Willaime, "Experimental study of freely decaying two-dimensional turbulence," Phys. Rev. Lett. 67, 3372 (1991).
8. N. K. R. Kevlahan and M. Farge, "Vorticity in two-dimensional turbulence: Creation, stability, and effect," J. Fluid Mech. 346, 49 (1997).
9. B. Legras and D. G. Dritschel, "The elliptical model of two-dimensional vortex dynamics. Part I. The basic state," Phys. Fluids A 3, 845 (1991).
10. D. G. Dritschel and B. Legras, "The elliptical model of two-dimensional vortex dynamics. Part II. Disturbance equations," Phys. Fluids A 3, 855 (1991).
11. M. V. Melander, N. J. Zabusky, and A. S. Styczek, "A moment model for vortex interactions of the two-dimensional Euler equations. Part I. Computational validation of a Hamiltonian elliptical representation," J. Fluid Mech. 167, 95 (1988).
12. M. V. Melander, N. J. Zabusky, and J. C. Mc Williams, "Symmetric vortex merger in two dimensions: causes and conditions," J. Fluid Mech. 195, 303 (1988).
13. D. G. Dritschel, "The stability and energetics of corotating uniform vortices," J. Fluid Mech. 157, 95 (1985).
14. P. G. Saffman, Vortex Dynamics, Cambridge Monographs on Mechanics and Applied Mathematics (Cambridge University Press, Cambridge, 1992).
15. O. Agullo and A. D. Verga, "Exact two vortices solutions of Navier-Stokes equations," Phys. Rev. Lett. 78, 2361 (1997).
16. R. T. Pierrehumbert, "A family of steady, translating vortex pairs with distributed vorticity," J. Fluid Mech. 99, 129 (1980).
17. P. G. Saffman and R. Szeto, "Equilibrium shapes of a pair of equal uniform vortices," Phys. Fluids 23, 2339 (1980).
18. D. G. Dritschel, "A general theory for two-dimensional vortex interactions," J. Fluid Mech. 293, 269 (1995).
19. H. B. Keller, "Numerical solution of bifurcation and nonlinear eigenvalue problems," in Application of Bifurcation Theory, edited by P. H. Rabinowitz (Academic, New York, 1977), pp. 359-384.
20. J. Norbury, "A family of steady vortex rings," J. Fluid Mech. 57, 417 (1973).
21. D. G. Dritschel, "On the persistence of nonaxisymmetric vortices in inviscid two-dimensional flows," J. Fluid Mech. 371, 141 (1998).
22. C. Canuto, A. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics (Springer, New York, 1987).
23. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Texts in Applied Mathematics (Springer, Berlin, 1992), Vol. 12.
24. E. A. Overman, "Steady-state solutions of the Euler equations in two dimensions. II. Local analysis of limiting V-states," SIAM (Soc., Ind. Appl. Math.) J. Appl. Math. 46, 765 (1986).