Dynamo effect in parity-invariant flow with large and moderate separation of scales

Geophysical and Astrophysical Fluid Dynamics

Volumn 95, Issue 3-4, 2001, Pages 227-268

  Zheligovsky, V A ^a,b,c   Podvigina, O M ^a,b,c   Frisch, U ^a  

^a CNRS   (France)

^b INSTITUTE OF EARTHQUAKE PREDICTION THEORY AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Eddy diffusivity; Instability; Kinematic magnetic dynamo; Multiscale expansion

Indexed keywords

EID: 0037585829     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Archontis, V. (2000). Linear, Non-Linear and Turbulent Dynamos, Ph.D. thesis, Copenhagen, available at http://www.astro.ku.dk/∼bill/phd/phd.ps.gz
2. Axelsson, O. (1996). Iterative solution methods. Cambridge University Press, Cambridge.
3. Bensoussan, A., Lions, J.-L. and Papanicolaou, G. (1978). Asymptotic Analysis for Periodic Structures. North Holland.
4. Busse, F.H. (2000). Homogeneous dynamos in planetary cores and in the laboratory. Ann. Rev. Fluid Mech., 32, 383-408.
5. Dorch, S.B.F. (2000). On the structure of the magnetic field in a kinematic ABC flow dynamo. Physics Scripta, 61, 717-722.
6. Dubrulle, B. and Frisch, U. (1991). Eddy viscosity of parity-invariant flow. Phys. Rev. A, 43, 5355-5364.
7. Fauve, S. (1999). Recherche expérimentale sur l'effet dynamo (in French), Laboratoire de Physique Statistique (CNRS, UMR 8550). 5 pp. Ecole Normale Supérieure, Paris, France.
8. Frisch, U. (1995). Turbulence. The legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge.
9. Frisch, U., Zhen, Su She and Thual, O. (1986). Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model. J. Fluid Mech., 168, 221-240.
10. Gailitis, A., Lielausis, O.A., Dement'ev, S., Platacis, E., Cifersons, A., Gerbeth, G., Gundrum, T., Stefani, F., Christen, M., Han̈el, H. and Will, G. (2000). Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility. Phys. Rev. Lett., 84, 4365-4368.
11. Galanti, B., Sulem, P.L. and Pouquet, A. (1992). Linear and non-linear dynamos associated with ABC flows. Geophys. Astrophys. Fluid Dynam., 66, 183-208.
12. Galloway, D.J. and Zheligovsky, V.A. (1994). On a class of non-axisymmetric flux rope solutions to the electromagnetic induction equation. Geophys. Astrophys. Fluid Dynam., 76, 253-264.
13. Gama, S., Vergassola, M. and Frisch, U. (1994). Negative eddy viscosity in isotropically forced two-dimensional flow: linear and nonlinear dynamics. J. Fluid Mech., 260, 95-126.
14. Kato, T. (1980). Perturbation theory for linear operators. Springer-Verlag, Berlin, Heidelberg, New York.
15. Kozlov, S.M. (1978). Averaging of differential operators with almost periodic fast oscillating coefficients (in Russian). Matematicheskiy sbornik., 107(2), 199-217.
16. Kraichnan, R.H. (1976). Diffusion of weak magnetic fields by isotropic turbulence. J. Fluid Mech., 75, 657-676.
17. Krause, F. and Rädler, K.-H. (1980). Mean-field Magnetohydrodynamics and Dynamo Theory. Academic-Verlag, Berlin.
18. Lanotte, A., Noullez, A., Vergassola, M. and Wirth, A. (1999). Large-scale dynamo by negative magnetic eddy diffusivities. Geophys. Astrophys. Fluid Dynam., 91, 131-146.
19. Nore, C., Brachet, M.E., Politano, H., Pouquet, A. (1997). Dynamo action in the Taylor-Green vortex near threshold. Phys. Plasmas, 4, 1-3.
20. Plunian, F. and Rädler, K.-H. (2000). The Roberts dynamo model. Application to the Karlsruhe experiment. Geophys. Astrophys. Fluid Dynam., submitted.
21. Plunian, F. and Rädler, K.-H. (2001). Subharmonic dynamo action in the Roberts flow. Magnitnaya Gidrodinamika, special issue on dynamo-experiments, to appear.
22. Podvigina, O.M. (1999a). Spatially-periodic steady solutions to the three-dimensional Navier-Stokes equation with the ABC force. Physica D., 128, 250-272.
23. Podvigina, O.M. (1999b). Evolutionary and steady solutions to the Navier-Stokes equation with the ABC forcing (in Russian). Institute of Mechanics, Lomonosov Moscow State University.
24. Podvigina, O.M. and Zheligovsky, V.A. (1997). An optimized iterative method for numerical solution of large systems of equations based on the extremal property of zeroes of Chebyshev polynomials. J. Sci. Computing, 12, 443-464.
25. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992). Numerical Recipes. Cambridge University Press, Cambridge.
26. Roberts, G.O. (1972). Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. R. Soc. Lond., A271, 411-454.
27. Steenbeck, M., Krause, F. and Rädler, K.-H. (1966). A calculation of the mean electro-motive force in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces. Z. Naturforsch, 21a, 369-376.
28. Stieglitz, R. and Müller, U. (2001). An experimental demonstration of a homogeneous two scale dynamo. Proceedings of NATO ARW Dynamo and dynamics, a mathematical challenge. August 21-26, 2000. Institut d'Études Scientifiques de Cargèse, to appear.
29. Tilgner, A. (1997). A kinematic dynamo with a small scale velocity field. Phys. Lett. A., 226, 75-79.
30. Vishik, M.M. (1986). Periodic dynamo. I (in Russian). In: Mathematical Methods of Seismology and Geodynamics (Comput. Seism., 19). pp. 186-215. Nauka, Moscow.
31. Vishik, M.M. (1987). Periodic dynamo. II (in Russian). In: Numerical Modeling and Analysis of Geophysical Processes (Comput. Seism., 20). pp. 12-22. Nauka, Moscow.
32. Wirth, A., Gama, S. and Frisch, U. (1995). Eddy viscosity of three-dimensional flow. J. Fluid Mech., 288, 249-264.
33. Zheligovsky, V. (1993). Numerical solution of the kinematic dynamo problem for Beltrami flows in a sphere. J. Sci. Computing, 8, 41-68.
34. Zheligovsky, V.A. (2001). A Chebyshev iterative method with operator splitting for evaluation of roots of large systems of equations (in Russian), accepted Proceeding of International Workshop on Nonlinear Problems of hydrodynamics stability, Moscow, 2000. Institute of Mechanics, Lomonosov Moscow State University, Moscow University Press. Also available at http://www.obs-nice.fr./etc7/vlad.ps.gz
35. Zhikov, V.V., Kozlov, S.M., Oleynik, O.A. and Ha Tien Ngoan (1979). Averaging and G-convergence of differential operators (in Russian). Uspekhi Matematicheskih Nauk, 34(5), 63-133.