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Convection in an imposed magnetic field. Part 1. The development of nonlinear convection

Published online by Cambridge University Press:  20 April 2006

N. O. Weiss
N. O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Nonlinear two-dimensional magnetoconvection in a Boussinesq fluid has been studied in a series of numerical experiments with values of the Chandrasekhar number Q ≤ 4000 and the ratio ζ of the magnetic to the thermal diffusivity in the range 1 ≥ ζ ≥ 0·025. If the imposed field is strong enough, convection sets in as overstable oscillations which give way to steady convection as the Rayleigh number R is increased. In the dynamical regime that follows, magnetic flux is concentrated into sheets at the sides of the cells, from which the motion is excluded.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 247 - 272
Copyright
© 1981 Cambridge University Press

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References

Biermann, L. 1941 Der gegenwärtige Stand der Theorie konvektiver Sonnenmodelle. Vierteljahrschr. Astr. Ges. 76, 194–200.Google Scholar
Busse, F. H. 1975 Nonlinear interaction of magnetic field and convection. J. Fluid Mech. 71, 193–206.Google Scholar
Chandrasekhar, S. 1952 On the inhibition of convection by a magnetic field. Phil. Mag. 43 (7), 501–532.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
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
Cowling, T. G. 1953 Solar electrodynamics. In The Sun (ed. G. P. Kuiper), pp. 532–591. University of Chicago Press.
Cowling, T. G. 1957 Magnetohydrodynamics. Interscience.
Da costa, L. N., Knobloch, E. & Weiss, N. O. 1981 Oscillations in double-diffusive convection. J. Fluid Mech. (to appear).Google Scholar
Danielson, R. E. 1961 The structure of sunspot penumbras. II. Theoretical. Astrophys. J. 134, 289–311.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. 1978 The origin of running penumbral waves. Mon. Not. Roy. Astron. Soc. 184, 49P–52P.Google Scholar
Galloway, D. J. & Moore, D. R. 1979 Axisymmetric convection in the presence of a magnetic field. Geophys. Astrophys. Fluid Dyn. 12, 73–106.Google Scholar
Galloway, D. J., Proctor, M. R. E. & Weiss, N. O. 1978 Magnetic flux ropes and convection. J. Fluid Mech. 87, 243–261.Google Scholar
Galloway, D. J. & Weiss, N. O. 1981 Convection and magnetic fields in stars. Astrophys. J. 243, 945–953.Google Scholar
Gibson, R. D. 1966 Overstability in the magnetohydrodynamic Bénard problem at large Hartmann numbers. Proc. Camb. Phil. Soc. 62, 287–299.Google Scholar
Huppert, H. & Moore, D. R. 1976 Nonlinear double-diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Knobloch, E. & Proctor, M. R. E. 1981 Nonlinear periodic convection in double-diffusive systems. J. Fluid Mech. 108, 291–316.Google Scholar
Knobloch, E., Weiss, N. O. & Da costa, L. N. 1981 Oscillatory and steady convection in a magnetic field. J. Fluid Mech. (to appear).Google Scholar
Malkus, W. V. R. & Veronis, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.Google Scholar
Moore, D. R., Peckover, R. S. & Weiss, N. O. 1973 Difference methods for time-dependent two-dimensional convection. Comp. Phys. Comm. 6, 198–220.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh-Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Parker, E. N. 1963 Kinematical hydromagnetic theory and its application to the low solar photosphere. Astrophys. J. 138, 552–575.Google Scholar
Parker, E. N. 1979 Cosmical Magnetic Fields. Clarendon.
Peckover, R. S. & Weiss, N. O. 1978 On the dynamic interaction between magnetic fields and convection. Mon. Not. Roy. Astron. Soc. 182, 189–208.Google Scholar
Proctor, M. R. E. & Galloway, D. J. 1978 The dynamic effect of flux ropes on Rayleigh-Bénard convection. J. Fluid Mech. 90, 273–287.Google Scholar
Proctor, M. R. E. & Weiss, N. O. 1978 Magnetic flux ropes. In Rotating Fluids in Geophysics (ed. P. H. Roberts & A. M. Soward), pp. 389–408. Academic.
Roberts, P. H. 1967 Introduction to Magnetohydrodynamics. Longmans.
Spiegel, E. A. 1972 Convection in stars II. Special effects. Ann. Rev. Astron. Astrophys. 10, 261–304.Google Scholar
Thompson, W. B. 1951 Thermal convection in a magnetic field. Phil. Mag. 42 (7), 1417–1432.Google Scholar
Veronis, G. 1959 Cellular convection with finite amplitude in a rotating fluid. J. Fluid Mech. 5, 401–435.Google Scholar
Walén, C. 1949 On the Vibratory Rotation of the Sun. Stockholm: Lindstahl.
Weiss, N. O. 1964 Convection in the presence of restraints. Phil. Trans. Roy. Soc. A 256, 99–147.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. Problems of Stellar Convection (ed. E. A. Spiegel & J.-P. Zahn), pp. 176–187. Springer.