Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T06:30:08.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetic structures in a dynamo simulation

Published online by Cambridge University Press:  26 April 2006

A. Brandenburg ,
R. L. Jennings ,
Å. Nordlund ,
M. Rieutord ,
R. F. Stein  and
I. Tuominen
A. Brandenburg
Affiliation:
Nordita, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
R. L. Jennings
Affiliation:
DAMTP, University of Cambridge, Silver St, Cambridge CB3 9EW, UK Present address: Shell Research BV, Postbus 60, 2280 AB Rijswijk, The Netherlands.
Å. Nordlund
Affiliation:
Theoretical Astrophysics Center, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark Copenhagen University Observatory, Øster Voldgade 3, DK-1350 Copenhagen, Denmark
M. Rieutord
Affiliation:
Observatoire Midi-Pyrénées, 14 av. E. Belin, F-31400 Toulouse, France CERFACS, 42, Avenue Coriolis, F-31057 Toulouse, France
R. F. Stein
Affiliation:
Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
I. Tuominen
Affiliation:
Observatory, PO Box 14, SF-00014 University of Helsinki, Finland Dept. of Geosciences and Astronomy, University of Oulu, PO Box 333, 90571 Oulu, Finland
Get access Rights & Permissions [Opens in a new window]

Abstract

We use three-dimensional simulations to study compressible convection in a rotating frame with magnetic fields and overshoot into surrounding stable layers. The, initially weak, magnetic field is amplified and maintained by dynamo action and becomes organized into flux tubes that are wrapped around vortex tubes. We also observe vortex buoyancy which causes upward flows in the cores of extended downdraughts. An analysis of the angles between various vector fields shows that there is a tendency for the magnetic field to be parallel or antiparallel to the vorticity vector, especially when the magnetic field is strong. The magnetic energy spectrum has a short inertial range with a slope compatible with k+1/3 during the early growth phase of the dynamo. During the saturated state the slope is compatible with k−1. A simple analysis based on various characteristic timescales and energy transfer rates highlights important qualitative ideas regarding the energy budget of hydromagnetic dynamos.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 306 , 10 January 1996 , pp. 325 - 352
Copyright
© 1996 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

André, J.-C. & Lesieur, M. 1977 Influence of helicity on high Reynolds number isotropic turbulence. J. Fluid Mech. 81, 187–207.Google Scholar
Batchelor, G. K. 1950 On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. R. Soc. Lond. A 201, 405–416.Google Scholar
Brandenburg, A., Nordlund, A., Stein, R. F. & Torkelsson, U. 1995a Dynamo generated turbulence and large scale magnetic fields in a Keplerian shear flow. Astrophys. J. 446, 741–754.Google Scholar
Brandenburg, A., Procaccia, I. & Segel, D. 1995b The size and dynamics of magnetic flux structures in MHD turbulence. Phys. Plasmas 2, 1148–1156.Google Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1–30.Google Scholar
Cattaneo, F., Hughes, D. W. & Weiss, N. O. 1991 What is a stellar dynamo? Mon. Not. R. Astron. Soc. 253, 479–484.
Dittrich, P. K., Molchanov, S. A., Ruzmaikin, A. A. & Sokoloff, D. D. 1988 Stationary distribution of the value of the magnetic field in a random flow. Magnetohydrodynamics 24, 274–276.Google Scholar
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vortex filaments in turbulence. Phys. Rev. Lett. 67, 983–986.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
Gilman, P. A. 1983 Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II. Dynamos with cycles and strong feedbacks. Astrophys. J. Suppl. 53, 243–268.Google Scholar
Glatzmaier, G. A. 1985 Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone. Astrophys. J. 291, 300–307.Google Scholar
Hurlburt, N. E., Toomre, J. & Massaguer, J. M. 1984 Two-dimensional compressible convection extending over multiple scale heights. Astrophys. J. 282, 557–573.Google Scholar
Hurlburt, N. E., Toomre, J. & Massaguer, J. M. 1986 Nonlinear compressible convection penetrating into stable layers and producing internal gravity waves. Astrophys. J. 311, 563–577.Google Scholar
Hyman, J. M. 1979 A method of lines approach to the numerical solution of conservation laws. In Advances in Computation Methods for Partial Differential Equations, Vol. III (ed.R. Vichnevetsky & R. S. Stepleman), pp. 313–343. Publ. IMACS.
Jennings, R. L., Brandenburg, A., Nordlund, Å. & Stein, R. F. 1992 Evolution of a magnetic flux tube in two dimensional penetrative convection. Mon. Not. R. Astron. Soc. 259, 465–473.Google Scholar
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.Google Scholar
Kerr, R. M. 1987 Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59, 783–786.Google Scholar
Kida, S., Yanase, S. & Mizushima, J. 1991 Statistical properties of MHD turbulence and turbulent dynamo. Phys. Fluids A 3, 457–465.Google Scholar
Kraichnan, R. H. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387.Google Scholar
Kraichnan, R. H. 1990 Models of intermittency in hydrodynamic turbulence. Phys. Rev. Lett. 65, 575–578.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd Edn. Martinius Nijhoff.
Meneguzzi, M. & Pouquet, A. 1989 Turbulent dynamos driven by convection. J. Fluid Mech. 205, 297–312.Google Scholar
Moffatt, H. K. 1961 The amplification of a weak magnetic applied magnetic field by turbulence in fluids of moderate conductivity. J. Fluid Mech. 11, 625–635.Google Scholar
Nordlund, A., Brandenburg, A., Jennings, R. L., Rieutord, M., Ruokolainen, J., Stein, R. F. & Tuominen, I. 1992 Dynamo action in stratified convection with overshoot. Astrophys. J. 392 647–652 (referred to herein as Paper I).Google Scholar
Nordlund, Å. & Stein, R. F. 1990 3-D Simulations of solar and stellar convection and magnetoconvection. Comput. Phys. Commun. 59, 119–125.Google Scholar
Parker, E. N. 1979 The instability of a horizontal magnetic field in an atmosphere stable against convection. Astrophys. Space Sci. 62, 135–142.Google Scholar
Parker, E. N. 1984 Magnetic buoyancy and the escape of magnetic fields from stars. Astrophys. J. 281, 839–845.Google Scholar
Pelz, R. B., Yakhot, V., Orszag, S. A., Shtilman, L. & Levich, E. 1985 Velocity-vorticity patterns in turbulent flow. Phys. Rev. Lett. 54, 2505–2508.
Petrovay, K. 1991 Topological pumping in the lower overshoot layer The Sun and Cool Stars: Activity, Magnetism, Dynamos (ed. I. Tuominen, D. Moss & G. Rüdiger). Lecture Notes in Physics, vol. 380, pp. 67–70. Springer.
Pouquet A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354.Google Scholar
Pouquet A. & Patterson, G. S. 1978 Numerical simulation of helical magnetohydrodynamic turbulence. J. Fluid Mech. 85, 305–323.Google Scholar
Pumir, A., Shraiman, B. & Siggia, E. D. 1991 Exponential tails and random advection. Phys. Rev. Lett. 66, 2984–2987.Google Scholar
Rieutord, M. & Zahn, J.-P. 1995 Turbulent plumes in stellar convective envelopes. Astron. Astrophys. 296, 127–138.Google Scholar
Ruzmaikin, A. A. & Shukurov, A. M. 1982 Spectrum of the galactic magnetic field. Astrophys. Space Sci. 82, 397–407.Google Scholar
Schüssler, M. 1977 On buoyant magnetic flux tubes in the solar convection zone. Astron. Astrophys. 56, 439–442.Google Scholar
Schüssler, M. 1984 On the structure of magnetic fields in the solar convection zone. In The Hydromagnetics of the Sun (ed.T. D. Guyenne & J. J. Hunt), pp. 67–75. ESA SP-220.
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.Google Scholar
Toomre, J., Zahn, J.-P., Latour, J. & Spiegel, E. A. 1976 Stellar convection theory. II. Single-mode study of the second convection zone in an A-type star. Astrophys. J. 207, 545–563.Google Scholar
Vainshtein, S. I. & Zeldovich, Ya. B. 1972 Origin of magnetic fields in astrophysics. Sov. Phys. Usp. 15, 159–172.Google Scholar
Valdettaro, L. & Meneguzzi, M. 1991 Turbulent dynamos driven by convection inside spherical shells The Sun and Cool Stars: Activity, Magnetism, Dynamos (ed. I. Tuominen, D. Moss & G. Rüdiger). Lecture Notes in Physics, vol. 380, pp. 80–85. Springer.
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20.Google Scholar
Vincent, A. & Meneguzzi, M. 1994 On the dynamics of vortex tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254.Google Scholar
Zeldovich, Ya. B., Molchanov, S. A., Ruzmaikin, A. A. & Sokoloff, D. D. 1987 Intermittency in random media. Sov. Phys. Usp. 30, 353–369.Google Scholar
Zeldovich, Ya. B., Ruzmaikin, A. A. & Sokoloff, D. D. 1990 The Almighty Chance. World Scientific.