Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T11:55:08.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetic flux ropes and convection

Published online by Cambridge University Press:  12 April 2006

D. J. Galloway ,
M. R. E. Proctor  and
N. O. Weiss
D. J. Galloway
Affiliation:
Astronomy Centre, University of Sussex, Brighton, England
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
N. O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
Get access Rights & Permissions [Opens in a new window]

Abstract

Three-dimensional cellular convection concentrates magnetic flux into ropes when the magnetic Reynolds number is large. Amplification of the magnetic field is limited by the Lorentz force and the maximum field in a flux rope can be estimated. Boundary-layer analysis yields a completely self-consistent solution for a model of convection driven by imposed horizontal temperature gradients, and the transition from a kinematic to a dynamic regime can be followed in detail. The maximum value of the amplified field is proportional to the square root of the ratio of the viscous to the magnetic diffusivity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 2 , 26 July 1978 , pp. 243 - 261
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Busse, F. H. 1975 Nonlinear interaction of magnetic field and convection. J. Fluid Mech. 71, 193–206.Google Scholar
Clark, A. 1965 Some exact solutions in magnetohydrodynamics with astrophysical applications. Phys. Fluids 8, 644–649.Google Scholar
Clark, A. 1966 Some kinematical models for small-scale solar magnetic fields. Phys. Fluids 9, 485–492.Google Scholar
Clark, A. & Johnson, A. C. 1967 Magnetic field accumulation in supergranules. Solar Phys. 2, 433–440.Google Scholar
Galloway, D. J. 1977 Axisymmetric convection with a magnetic field. In Problems of Stellar Convection (ed. E. A. Spiegel & J.-P. Zahn), pp. 188–194. Springer.
Galloway, D. J. & Moore, D. R. 1978 Axisymmetric convection in the presence of a magnetic field. Submitted to Geophys. Astrophys. Fluid Dyn.Google Scholar
Galloway, D. J., Proctor, M. R. E. & Weiss, N. O. 1977 Formation of intense magnetic fields near the surface of the sun. Nature 266, 686–689.Google Scholar
Jones, C. A., Moore, D. R. & Weiss, N. O. 1976 Axisymmetric convection in a cylinder. J. Fluid Mech. 73, 353–388.Google Scholar
Parker, E. N. 1963 Kinematical hydromagnetic theory and its application to the low solar photosphere. Astrophys. J. 138, 552–575.Google Scholar
Peckover, R. S. & Weiss, N. O, 1978 On the dynamic interaction between magnetic fields and convection. Mon. Not. Roy. Astr. Soc. 182, 189–208.Google Scholar
Proctor, M. R. E. 1975 Non-linear mean field dynamo models and related topics. Ph.D. dissertation, University of Cambridge.
Proctor, M. R. E. & Galloway, D. J. 1978 The dynamic effect of flux ropes on Rayleigh–Bénard convection. Submitted to J. Fluid Mech.Google Scholar
Spiegel, E. A. 1971 Convection in stars I. Basic Boussinesq convection. Ann. Rev. Astron. Astrophys. 9, 323–352.Google Scholar
Spitzer, L. 1957 Influence of fluid motions on the decay of an external magnetic field. Astrophys. J. 125, 525–534.Google Scholar
Weiss, N. O. 1966 The expulsion of magnetic flux by eddies. Proc. Roy. Soc. A 293, 310–328.Google Scholar
Weiss, N. O. 1975 Magnetic fields and convection. Adv. Chem. Phys. 32, 101–107.Google Scholar
Weiss, N. O. 1977 Magnetic fields and convection. In Problems of Stellar Convection (ed. E. A. Spiegel & J.-P. Zahn), pp. 176–187. Springer.