The decay of axisymmetric magnetic fields: A review of Cowling's theorem

SIAM Review

Volumn 38, Issue 4, 1996, Pages 553-564

  Núñez, Manuel ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Axisymmetric fields; Magnetohydrodynamics; Parabolic equations

Indexed keywords

ELECTRIC CONDUCTIVITY OF LIQUIDS; EQUATIONS OF MOTION; MAGNETOHYDRODYNAMICS; MATHEMATICAL MODELS; THEOREM PROVING;

AXISYMMETRIC MAGNETIC FIELDS; AXISYMMETRIC MOTIONS; COWLING'S THEOREM;

MAGNETIC FIELDS;

EID: 0030394499     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144594261578     Document Type: Article

References (32)

1. H. K. MOFFAT, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge University Press, Cambridge, UK, 1978.
2. E. N. PARICER, Cosmical Magnetic Fields: Their Origin and Their Activity, Clarendon Press, Oxford, UK, 1979.
3. F. KRAUSE AND K. H. RÄDLER, Mean-field Magnetohydrodynamics and Dynamo Theory, Pergamon Press, Oxford, UK, 1980.
4. J. LARMOR, How could a rotating body such as the sun become a magnet?, British Assoc. Advances Sci. Report (a) (1919), pp. 159-160.
5. T. G. COWLING, The magnetic field of sunspots, Monthly Notices Roy. Astronom. Soc., 94 (1934), pp. 39-48.
6. G. E. BACKUS AND S. CHANDRASEKHAR, On Cowling's theorem on the impossibility of self-maintained axisymmetric homogeneous dynamos, Proc. Nat. Acad. Sci. U.S.A., 42 (1956), pp. 105-109.
7. D. LORTZ, Impossibility of steady dynamos with certain symmetries, Phys. Fluids, 11 (1968), pp. 913-915.
8. E. C. BULLARD AND H. GELLMAN, Homogeneous dynamos and terrestrial magnetism, Philos. Trans. Roy. Soc. London Ser. A, 247 (1954), pp. 213-278.
9. R. D. GIBSON AND P. H. ROBERTS, The Bullard-Gellman dynamo, in Applications of Modern Physics to the Earth and Planetary Interiors, Wiley-Interscience, New York, 1969, p. 577.
10. T. G. COWLING, The dynamo maintenance of steady magnetic fields, Quart. J. Mech. Appl. Math., 10 (1957), pp. 129-136.
11. Y. B. ZELDOVICH AND A. A. RUZMAIKIN, The magnetic fields in a conducting fluid in two-dimensional motion, Soviet Phys. JETP, 51 (1980), pp. 493-497.
12. G. E. BACKUS, A class of self-sustaining dissipative spherical dynamos, Ann. Physics, 4 (1958), pp. 372-447.
13. D. LORTZ, A simple stationary dynamo model, Z. Naturforsch, 27 a (1972), pp. 1350-1354.
14. S.I. BRAGINSKII, Self-excitation of a magnetic field during the motion of a highly conducting fluid, Soviet Phys. JETP, 20 (1964), pp. 726-735.
15. M. GHIL AND S. CHILDRESS, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics, Springer-Verlag, New York, 1987.
16. R. W. JAMES, P. H. ROBERTS, AND D. E. WINCH, The Cowling anti-dynamo theorem, Geophys. Astrophys. Fluid Dynamics, 15 (1980), pp. 149-160.
17. D. J. IVERS AND R. W. JAMES, Axisymmetric antidynamo theorems in compressible non-uniform conducting fluids, Philos. Trans. Roy. Soc. London Ser. A, 312 (1984), pp. 179-218.
18. J. P. TODOESCHUCK AND M. G. ROCHESTER, The effect of compressible flow on anti-dynamo theorems, Nature, 284 (1980), pp. 250-251.
19. R. HIDE, Self-exciting dynamos and geomagnetic polarity changes, Nature, 293 (1981), pp. 728-729.
20. R. HIDE AND T. N. PALMER, Generalization of Cowling's theorem, Geophys. Astrophys. Fluid Dynamics, 19 (1982), pp. 301-309.
21. R. HIDE, The magnetic flux linkage of a moving medium: A theorem and geophysical applications, J. Geophys. Res., 86 (1981), pp. 11681-11687.
22. _, On the magnetic flux linkage of an electrically conducting fluid, Geophys. Astrophys. Fluid Dynamics, 12 (1979), pp. 171-176.
23. D. LORTZ AND R. MEYER-SPASCHE, On the decay of symmetric dynamo fields. Math. Methods Appl. Sci., 4 (1982), pp. 91-97.
24. _, On the decay of symmetric toroidal dynamo fields, Z. Naturforsch, 37 a (1982), pp. 736-740.
25. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
26. M. H. PROTTER AND H. F. WEINBERGER, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967.
27. E. W. STREDULINSKY, R. MEYER-SPASCHE, AND D. LORTZ, Asymptotic behaviour of solutions of certain parabolic problems with space and time dependent coefficients, Comm. Pure Appl. Math., 39 (1986), pp. 233-266.
28. D. GILBARD AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1977.
29. O. A. LADYZHENSKAYA AND N. N. URALT'SEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
30. D. LORTZ, R. MEYER-SPASCHE, AND E. W. STREDULINSKY, Asymptotic behaviour of the solutions of certain parabolic equations, Comm. Pure Appl. Math., 37 (1984), pp. 677-703.
31. Y. Du AND E. OTT, Growth rates for fast kinematic dynamo instabilities of chaotic fluid flows, J. Fluid Mech., 277 (1993), pp. 265-288.
32. I. KLAPPER AND L. S. YOUNG, Rigorous bounds on the fast dynamo growth rate involving topological entropy, Comm. Math. Phys., 173 (1995), pp. 623-646.