On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 4. Generalized isovorticity principle for three-dimensional flows

Journal of Fluid Mechanics

Volumn 390, Issue , 1999, Pages 127-150

  Vladimirov, V A ^a   Moffatt, H K ^b   Ilin, K I ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

KINETIC ENERGY; MAGNETOHYDRODYNAMICS; MATHEMATICAL TRANSFORMATIONS; PERTURBATION TECHNIQUES; RELAXATION PROCESSES; VARIATIONAL TECHNIQUES;

ISOVORTICITY;

VORTEX FLOW;

EID: 0032662208     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099004991     Document Type: Article

References (28)

1. ARNOLD, V. I. 1965 Variational principle for three dimensional steady flows of an ideal fluid. Prikl. Matem. i Mekh. 29, No. 5, 846-851 (English transi. J. Appl. Math. Mech. 29, 5).
2. ARNOLD, V. I. 1965 Variational principle for three dimensional steady flows of an ideal fluid. Prikl. Matem. i Mekh. 29, No. 5, 846-851 (English transi. J. Appl. Math. Mech. 29, 5).
3. ARNOLD, V. I. 1966 Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16, 316-361.
4. ARNOLD, V. I. & KHESIN, B. A. 1998 Topological Methods in Hydrodynamics. Springer.
5. BERNSTEIN, I. B. 1983 The variational principle for problems of ideal magnetohydrodynamic stability. In Handbook of Plasma Physics, Vol. 1 : Basic Plasma Physics I, pp. 421-449. North-Holland.
6. BERNSTEIN, I. B., FRIEMAN, E. A., KRUSKAL, M. D. & KULSRUD, R. M. 1958 An energy principle for hydromagnetic stability theory. Proc. R. Soc. Lond. A 244, 17-40.
7. CHANDRASEKHAR, S. 1987 Ellipsoidal Figures of Equilibrium. Dover.
8. FREEDMAN, M.H. 1988 A note on topology and magnetic energy in incompressible perfectly conducting fluids. J. Fluid Mech. 194, 549-551.
9. FRIEDLANDER, S. & VISHIK, M. 1990 Nonlinear stability for stratified magnetohydrodynamics. Geophys. Astrophys. Fluid Dyn. 55, 19-45.
10. FRIEDLANDER, S. & VISHIK, M. 1995 On stability and instability criteria for magnetohydrodynamics. Chaos 5 (2), 416-423.
11. HÉNON, M. 1966 Sur la topologie des lignes de courant dans un cas particulier. C.R. Acad. Sci. Paris 262, 312-314.
12. HOLM D. D., MARSDEN J. E., RATIU T. & WEINSTEIN A. 1985 Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123, Nos. 1 & 2, 1-116.
13. KHESIN, B. A. & CHEKANOV, Yu. V. 1989 Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in D dimensions. Physica D 40, 119-131.
14. LIFSHJTZ, A. E. 1989 Magnetohydrodynamics and Spectral Theory. Kluwer.
15. MARSDEN, J., RATIU, T. & WEINSTEIN, A. 1984 Semidirect product and reduction in mechanics. Trans. Am. Math. Soc. 281, 147-177.
16. MOFFATT H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117-129.
17. MOFFATT H. K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals. J. Fluid Mech. 159, 359-378.
18. MOFFATT H. K. 1986 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations. J. Fluid Mech. 166, 359-378.
19. MOFFATT H. K. 1989 On the existence, structure and stability of MHD equilibrium states. In Turbulence and Nonlinear Dynamics in MHD Flows (ed. M. Meneguzzi et al.), pp. 185-195. Elsevier.
20. MOREAU J.-J. 1961 Constantes d'un ilot tourbillonnaire en fluide parfait barotrope. C. R. Acad. Sci. Paris 252, 2810-2812.
21. ONO, T. 1995 Riemannian geometry of the motion of an ideal incompressible magnetohydrodynamical fluid. Physica D 81, 207-220.
22. ROUCHON, P. 1991 On the Arnol'd stability criterion for steady-state flows of an ideal fluid. Eur. J. Mech. B/Fluids 10, 651-661.
23. VISHIK, S. M. & DOLZHANSKII F. V. 1978 Analogs of the Euler-Lagrange equations and magnetohydrodynamics equations related to Lie groups. Sov. Math. Dokl. 19, 149-153.
24. VLADIMIROV, V. A. & MOFFATT, H. K. 1995 On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 1. Fundamental principles. J. Fluid Mech. 283, 125-139.
25. VLADIMIROV, V. A., MOFFATT, H. K. & ILIN, K. I. 1996 On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 2. Stability criteria for two-dimensional flows. J. Fluid Mech. 329, 187-205.
26. VLADIMIROV, V. A., MOFFATT, H. K. & ILIN, K. I. 1997 On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 3. Stability criteria for axisymmetric flows. J. Plasma Phys. 57, 3, 89-120.
27. WOLTJER, L. 1958 A theorem on force-free magnetic fileds. Proc. Natl Acad. Sci. 257, 76-79.
28. ZEITLIN, V. & KAMBE, T. 1993 Two-dimensional ideal magnetohydrodynamics and differential geometry. J. Phys. A: Math. Gen. 26, 5025-5031.