Nonlinear magnetoconvection in the presence of strong oblique fields

Journal of Fluid Mechanics

Volumn 410, Issue , 2000, Pages 285-322

  Julien, K ^a   Knobloch, E ^b   Tobias, S M ^a,c  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONVECTION; HEAT TRANSFER; MAGNETIC FIELD;

EID: 0033942606     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099007958     Document Type: Article

References (33)

1. ARTER, W. 1983 Nonlinear convection in an imposed horizontal magnetic field. Geophys. Astrophys. Fluid Dyn. 25, 259-292.
2. BABIN, A., MAHALOV, A. & NICOLAENKO, B. 1994 Long-time averaged Euler and Navier-Stokes equations for rotating fluids. In Structure and Dynamics of Nonlinear Wares in Fluids (ed. K. Kirchgässner & A. Mielke), pp. 145-157. World Scientific.
3. BASSOM, A. P. & ZHANG, K. 1994 Strongly nonlinear convection cells in a rapidly rotating fluid layer. Geophys. Astrophys. Fluid Dyn. 76, 223-238.
4. BLENNERHASSETT, P. J. & BASSOM, A. P. 1994 Nonlinear high-wavenumber Bénard convection. IMA J. Appl. Maths 52, 51-77.
5. BROWNJOHN, D. P., HURLBURT, N. E., PROCTOR, M. R. E. & WEISS, N. O. 1995 Nonlinear compressible magnetoconvection. Part 3. Travelling waves in a horizontal field. J. Fluid Mech. 300, 287-309.
6. CASH, J. R. & SINGHAL, A. 1982 High order method for the numerical solution of two-point boundary value problems. B.I.T. 22, 184-199.
7. CATTANEO, F. & HUGHES, D. W. 1988 The nonlinear breakup of a magnetic layer: instability to interchange modes. J. Fluid Mech. 196, 323-344.
8. CHANURASEKHAR, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
9. CLUNE, T. & KNOBLOCH, E. 1993 Pattern selection in three-dimensional magnetoconvection. Physica D 74, 151-176.
10. DANIELSON, R. E. 1961 The structure of sunspot penumbras. II. Theoretical. Astrophys. J. 134, 289-311.
11. HENRICI, P. 1962 Discrete Variable Methods in Ordinary Differential Equations. Wiley and Sons.
12. HUGHES, D. W. 1987 Finite amplitude solutions for interchange instabilities driven by magnetic buoyancy. Geophys. Astrophys. Fluid Dyn. 37, 297-343.
13. JULIEN, K. & KNOBLOCH, E. 1997 Fully nonlinear oscillatory convection in a rotating layer. Phys. Fluids 9, 1906-1913.
14. JULIEN, K. & KNOBLOCH, E. 1998 Strongly nonlinear convection cells in a rapidly rotating fluid layer: the tilted f-plane. J. Fluid Mech. 360, 141-178.
15. JULIEN, K., KNOBLOCH, E. & TOBIAS, S. M. 1999a Strongly nonlinear magnetoconvection in three dimensions. Physica D 128, 105-129.
16. JULIEN, K., KNOBLOCH, E. & TOBIAS, S. M. 1999b Highly supercritical convection in strong magnetic fields. In The Fluid Dynamics of Geophysics and Astrophysics (ed. Ferriz-Mas & M. Núñez). Gordon & Breach, to appear.
17. KNOBLOCH, E. 1994 Bifurcations in rotating systems. In Lectures on Solar and Planetary Dynamics (ed. M. R. E. Proctor & A. D. Gilbert), pp. 331-372. Cambridge University Press.
18. KNOBLOCH, E. & MERRYFIELD, W. J. 1992 Enhancement of diffusive transport in oscillatory flows. Astrophys. J. 401, 196-205.
19. MATTHEWS, P. C. 1999 Asymptotic solutions for nonlinear magnetoconvection. J. Fluid Mech. 387, 397-409.
20. MATTHEWS, P. C., HURLBURT, N. E., PROCTOR, M. R. E. & BROWNJOHN, D. P. 1992 Compressible magnetoconvection in oblique fields: linearized theory and simple nonlinear models. J. Fluid Mech. 240, 559-569.
21. MATTHEWS, P. C., PROCTOR, M. R. E., RUCKLIDGE, A. M. & WEISS, N. O. 1993 Pulsating waves in nonlinear magnetoconvection. Phys. Lett. A 183, 69-75.
22. MURPHY, J. O. & LOPEZ, J. M. 1987 Evolution of a horizontal scale for magnetoconvection. Proc. ASA 7, 112-116.
23. PROCTOR, M. R. E. 1986 Columnar convection in double-diffusive systems. Contemp. Maths 56, 267-276.
24. RUCKLIDGE, A. M., SCHMIDT, H. U. & WEISS, N. O. 1995 The abrupt development of penumbrae in sunspots. Mon. Not. R. Astron. Soc. 273, 491-498.
25. SILBER, M., RIECKE, H. & KRAMER, L. 1992 Symmetry-breaking Hopf bifurcation in anisotropic systems. Physica D 61, 260-278.
26. THOMAS, J. H. & WEISS, N. O. 1992 The theory of sunspots. In Sunspots: Theory and Observations (ed. J. H. Thomas & N. O. Weiss), pp. 3-59, Kluwer.
27. TITLE, A. M., FRANK, Z. A., SHINE, R. A., TARBELL, T. D., TOPKA, K. P., SCHARMER, G. & SCHMIDT, W. 1992 High resolution observations of the magnetic and velocity field of simple sunspots. In Sunspots: Theory and Observations (ed. J. H. Thomas & N. O. Weiss), pp. 195-219. Kluwer.
28. VAN DER BORGHT, R. & MURPHY, J. O. 1973 The combined effect of rotation and magnetic field on finite-amplitude thermal convection. Austral J. Phys. 26, 617-643.
29. VERONIS, G. 1959 Cellular convection with finite amplitude in a rotating fluid. J. Fluid Mech. 5, 401-435.
30. WEISS, N. O. 1981a Convection in an imposed magnetic field. Part 1. The development of nonlinear convection. J. Fluid Mech. 108, 247-272.
31. WEISS, N. O. 1981b Convection in an imposed magnetic field. Part 2. The dynamical regime. J. Fluid Mech. 108, 273-289.
32. WEISS, N. O., BROWNJOHN, D. P., HURLBURT, N. E. & PROCTOR, M. R. E. 1990 Oscillatory convection in sunspot umbrae. Mon. Not. R. Astron. Soc. 245, 434-452.
33. WEISS, N. O., BROWNJOHN, D. P., MATTHEWS, P. C. & PROCTOR, M. R. E. 1996 Photospheric convection in strong magnetic fields. Mon. Not. R. Astron. Soc. 283, 1153-1164.