Toroidal bubbles with circulation in ideal hydrodynamics: A variational approach

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 5 2, 2003, Pages 563011-5630111

  Ruban, V P ^a,b   Juul Rasmussen, J ^b  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BUBBLE FORMATION; COMPRESSIBILITY OF GASES; CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; HAMILTONIANS; INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; OSCILLATIONS; PROBLEM SOLVING; SURFACE TENSION; UNSTEADY FLOW; VECTORS; VELOCITY MEASUREMENT; VORTEX FLOW;

IRROTATIONAL FLOWS; VISCOUS DIFFUSIONS;

HYDRODYNAMICS;

EID: 0942267620     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. J.K. Walters and J.F. Davidson, J. Fluid Mech. 17, 321 (1963).
2. T.S. Lundgren and N.N. Mansour, J. Fluid Mech. 224, 177 (1991).
3. M. Sussman and P. Smereka, J. Fluid Mech. 341, 269 (1997).
4. http://www.bubblerings.com/bubblerings/
5. J. Ponstein, Appl. Sci. Res., Sect. A 8, 425 (1959).
6. T.J. Pedley, J. Fluid Mech. 30, 127 (1967); 32, 97 (1968).
7. T.J. Pedley, J. Fluid Mech. 30, 127 (1967); 32, 97 (1968).
8. V.I. Arnol'd, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer-Verlag, New York, 1989).
9. R. Salmon, Annu. Rev. Fluid Mech. 20, 225 (1988).
10. V.E. Zakharov and E.A. Kuznetsov, Usp. Fiz. Nauk 167, 1037 (1997) [Phys. Usp. 40, 1087 (1997)].
11. V.E. Zakharov and E.A. Kuznetsov, Usp. Fiz. Nauk 167, 1037 (1997) [Phys. Usp. 40, 1087 (1997)].
12. P.J. Morrison, Rev. Mod. Phys. 70, 467 (1998).
13. V.I. Il'gisonis and V.P. Lakhin, Fiz. Plasmy 25, 64 (1999) [Plasma Phys. Rep. 25, 58 (1999)].
14. V.I. Il'gisonis and V.P. Lakhin, Fiz. Plasmy 25, 64 (1999) [Plasma Phys. Rep. 25, 58 (1999)].
15. D.D. Holm, J.E. Marsden, and T.S. Ratiu, Adv. Math. 137, 1 (1998); in Large-scale Atmosphere-Ocean Dynamics 2: Geometric Methods and Models, edited by J. Norbury and I. Roulstone (Cambridge University Press, Cambridge, 2002), pp. 251-299.
16. D.D. Holm, J.E. Marsden, and T.S. Ratiu, Adv. Math. 137, 1 (1998); in Large-scale Atmosphere-Ocean Dynamics 2: Geometric Methods and Models, edited by J. Norbury and I. Roulstone (Cambridge University Press, Cambridge, 2002), pp. 251-299.
17. V.E. Zakharov, Prikl. Mekh. Tekh. Fiz. 2, 86 (1968).
18. D. Lewis, J. Marsden, R. Montgomery, and T. Ratiu, Physica D 18, 391 (1986).
19. A.I. Dyachenko, E.A. Kuznetsov, M.D. Spector, and V.E. Zakharov, Phys. Lett. A 221, 73 (1996).
20. A.I. Dyachenko, Y.V. L'vov, and V.E. Zakharov, Physica D 87, 233 (1995).
21. V.E. Zakharov and A.I. Dyachenko, Physica D 98, 652 (1996).
22. A.I. Dyachenko, V.E. Zakharov, and E.A. Kuznetsov, Fiz. Plazmy 22, 916 (1996) [Plasma Phys. Rep. 22, 829 (1996)].
23. A.I. Dyachenko, V.E. Zakharov, and E.A. Kuznetsov, Fiz. Plazmy 22, 916 (1996) [Plasma Phys. Rep. 22, 829 (1996)].
24. A.I. Dyachenko, Dok. Akad. Nauk 376, 27 (2001) [Dokl. Math. 63, 115 (2001)].
25. A.I. Dyachenko, Dok. Akad. Nauk 376, 27 (2001) [Dokl. Math. 63, 115 (2001)].
26. V.E. Zakharov, A.I. Dyachenko, and O.A. Vasilyev, Eur. J. Mech. B/Fluids 21, 283 (2002).
27. L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1987).
28. S. Hilgenfeldt, M.P. Brenner, S. Grossmann, and D. Lohse, J. Fluid Mech. 365, 171 (1998).
29. V.P. Ruban, Phys. Rev. E 64, 036305 (2001).
30. V.P. Ruban, Phys. Rev. D 62, 127504 (2000).
31. H. Hasimoto, J. Fluid Mech. 51, 477 (1972).
32. D. McSweeny (private communication).