Subharmonic dynamo action in the roberts flow

Geophysical and Astrophysical Fluid Dynamics

Volumn 96, Issue 2, 2002, Pages 115-133

  Plunian, F ^a   Radler K H ^b  

^a LEGI   (France)

^b ASTROPHYSIKALISCHES INSTITUT POTSDAM   (Germany)

Author keywords

Dynamo effect; Dynamo experiment; Mean field theory; Roberts flow; Subharmonic solutions

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FLOW OF FLUIDS; MAGNETIC FIELD EFFECTS; MAGNETIC FIELDS;

DYNAMO EFFECT; DYNAMO EXPERIMENT; MEAN-FIELD THEORY; ROBERTS FLOW; SUBHARMONIC SOLUTIONS;

DC GENERATORS;

DC GENERATORS; EIGENVALUES AND EIGENFUNCTIONS; FLOW OF FLUIDS; MAGNETIC FIELD EFFECTS; MAGNETIC FIELDS;

FLUID FLOW; HARMONIC ANALYSIS; MAGNETIC FIELD;

EID: 0038669780     PISSN: 03091929     EISSN: 10290419     Source Type: Journal    
DOI: 10.1080/03091920290004506     Document Type: Article

References (27)

1. Arnold, V.I. and Korkina, E.I., "The growth of a magnetic field in a three-dimensional steady incompressible flow", Vest. Mask. Un. Ta. Ser. 1. Matem. Mekh. 3, 43-46 (1983).
2. Busse, F.H., Müller, U., Stieglitz, R. and Tilgner, A., "A two-scale homogeneous dynamo: an extended analytical model and an experimental demonstration under development", Magnetohydrodynamics 32, 235-248 (1996).
3. Childress, S., "Alpha-effect in flux ropes and sheets", Phys. Earth Planet. Int. 20, 172-180 (1979).
4. Childress, S. and Gilbert, A.D., Stretch, Twist, Fold: The Fast Dynamo, Springer (1995).
5. Dombre, T., Frisch, U., Greene, J.M., Hénon, M., Mehr, A. and Soward, A.M., "Chaotic streamlines in the ABC flows", J. Fluid Mech. 167, 353-391 (1986).
6. Feudel, F., Seehafer, N. and Schmidtmann, O., "Fluid helicity and dynamo bifurcations", Phys. Lett. A 202, 73-78 (1995).
7. Galanti, B., Sulem, P.-L. and Pouquet, A., "Linear and nonlinear dynamos associated with ABC flows", Geophys. Astrophys. Fluid Dynam. 66, 183-208 (1992).
8. Galanti, B., Pouquet, A. and Sulem, P.-L., "Influence of the period of an ABC flow on its dynamo action", In: Solar and Planetary Dynamos (Eds. M.R.E. Proctor, P.C. Matthews and A.M. Rucklidge) pp. 99-104, Cambridge University Press (1993).
9. Galloway, D.J. and Frisch, U., "A numerical investigation of magnetic field generation in a flow with chaotic streamlines", Geophys. Astrophys. Fluid Dynam. 29, 13-18 (1984).
10. Galloway, D.J. and Frisch, U., "Dynamo action in a family of flows with chastic streamlines", Geophys. Astrophys. Fluid Dynam. 36, 53-83 (1986).
11. Gilbert, A.D. and Childress, S., "Evidence for fast dynamo action in a chaotic web", Phys. Rev. Lett. 65, 2133-2136 (1990).
12. Krause, F. and Rädler, K.-H., Mean-Field Magnetohydrodynamics and Dynamo Theory, Pergamon Press (1980).
13. Müller, U. and Stieglitz, R., "Can the Earth's magnetic field be simulated in the laboratory?", Naturwissenschaften 87, 381-390 (2000).
14. Plunian, F., Marty, Ph. and Alemany, A., "Kinematic dynamo action in a network of screw motions. Application to the core of a fast breeder reactor", J. Fluid Mech. 382, 137-154 (1999).
15. Rädler, K.-H., Apel, A., Apstein, E. and Rheinhardt, M., "Contributions to the Theory of the Planned Karlsruhe Dynamo Experiment", Report Astrophysical Institute Potsdam (1996).
16. Rädler, K.-H., Apstein, E., Rheinhardt, M. and Schüler, M., "Contributions to the Theory of the Planned Karlsruhe Dynamo Experiment - Supplements and Corrections", Report Astrophysical Institute Potsdam (1997a).
17. Rädler, K.-H., Apstein, E. and Schüler, M., "The Alpha-Effect in the Karlsruhe Dynamo Experiment", Proc. 3rd Int. Conf. on Transfer Phenomena in Magnetohydrodynamics and Electro-conducting Flows, Vol. I, Aussois, France, pp. 9-14 (1997b).
18. Rädler, K.-H., Apstein, E., Rheinhardt, M. and Schüler, M., "The Karlsruhe Dynamo Experiment - A Mean-Field Approach", Studia Geophysica et Geodaetica 42, 302-308 (1998).
19. Rädler, K.-H., Rheinhardt, M., Apstein, E. and Fuchs, H., "On the mean-field theory of the Karlsruhe Dynamo Experiment" accepted in Nonlinear Processes in Geophysics (2001).
20. Roberts, G.O., "Dynamo action of fluid motions with two-dimensional periodicity", Phil. Trans. R. Soc. Land. A 271, 411-454 (1972).
21. Soward, A.M., "Fast dynamo action in a steady flow", J. Fluid Mech. 180, 267-295 (1987).
22. Soward, A.M., "On dynamo action in a steady flow at large magnetic Reynolds number", Geophys. Astrophys. Fluid Dynam. 49, 3-22 (1989).
23. Soward, A.M., "A unified approach to a class of slow dynamos", Geophys. Astrophys. Fluid Dynam. 53, 81-107 (1990).
24. Soward, A.M., "Fast Dynamos", In: Lectures on Solar and Planetary Dynamos (Eds. M.R.E. Proctor and A.D. Gilbert) pp. 181-217, Cambridge University Press (1994).
25. Stieglitz, R. and Müller, U., "Experimental demonstration of a homogeneous two-scale dynamo", Phys. Fluids 13(3), 561-564 (2001).
26. Tilgner, A., "A kinematic dynamo with a small scale velocity field", Phys. Lett. A 226, 75 (1997).
27. Tilgner, A. and Busse, F.H., "Subharmonic dynamo action of fluid motions with two-dimensional periodicity", Proc. R. Soc. Land. A 448, 237-244 (1995).