Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T11:16:24.690Z Has data issue: false hasContentIssue false

9 - MHD Dynamos and Turbulence

Published online by Cambridge University Press:  05 February 2013

By
S.M. Tobias ,
F. Cattaneo  and
S. Boldyrev
Edited by
Peter A. Davidson ,
Yukio Kaneda  and
Katepalli R. Sreenivasan
S.M. Tobias
Affiliation:
University of Leeds
F. Cattaneo
Affiliation:
University of Chicago
S. Boldyrev
Affiliation:
University of Wisconsin – Madison
Peter A. Davidson
Affiliation:
University of Cambridge
Yukio Kaneda
Affiliation:
Aichi Institute of Technology, Japan
Katepalli R. Sreenivasan
Affiliation:
New York University
Get access

Summary

Introduction

Magnetic fields are ubiquitous in the universe (Parker (1979); Zeldovich et al. (1983)). Their interaction with an electrically conducting fluid gives rise to a complex system–a magnetofluid-whose dynamics is quite distinct from that of either a non conducting fluid, or that of a magnetic field in a vacuum (Cowling (1976)). The scales of these interactions vary in nature from metres to megaparsecs and in most situations, the dissipative processes occur on small enough scales that the resulting flows are turbulent. The purpose of this review is to discuss a small fraction of what is currently known about the properties of these turbulent flows. We refer the reader to several recent reviews for a broader view of the field (Biskamp (2003); Galtier (2008, 2009); Lazarian (2006); Lazarian & Cho (2005); Müller & Busse (2007); Kulsrud & Zweibel (2008), Bigot et al. 2008, Sridhar 2010, Brandenburg & Nordlund 2010). The electrically conducting fluid most commonly found in nature is ionized gas, i.e. a plasma, and its description in terms of all its fundamental constituents is extremely complex (see e.g. Kulsrud (2005)). In many circumstances, however, these complexities can be neglected in favour of a simplified description in term of a single fluid interacting with a magnetic field. Formally, this approach is justifiable when the processes of interest occur on timescales long compared with the light-crossing time, and on spatial scales much larger that any characteristic plasma length.

Type
Chapter
Information
Ten Chapters in Turbulence , pp. 351 - 404
Publisher: Cambridge University Press
Print publication year: 2012

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

Aluie, H. and Eyink, G. L. 2010 Scale locality of magnetohydrodynamic turbulence. Physical Review Letters 104, 081101.Google Scholar
Arponen, H. & Horvai, P. 2007 Dynamo effect in the Kraichnan magnetohydrodynamic turbulence. Journal of Statistical Physics 129, 205–239.Google Scholar
Balbus, S. A. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I – Linear analysis. II – Nonlinear evolution. Astrophysical Journal 376, 214–233.Google Scholar
Balbus, S. A. & Hawley, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Reviews of Modern Physics 70, 1–53.Google Scholar
Balmforth, N. J. & Korycansky, D. G. 2001 Non-linear dynamics of the corotation torque. Mon. Not. Roy. Ast. Soc. 326, 833–851.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge: Cambridge University Press.
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. Journal of Fluid Mechanics 5, 113–133.Google Scholar
Beresnyak, A. & Lazarian, A. 2006 Polarization intermittency and its influence on MHD turbulence. Astrophysical Journal Letters 640, L175–L178.Google Scholar
Beresnyak, A. & Lazarian, A. 2008 Strong imbalanced turbulence. Astrophys. J. 682, 1070–1075.Google Scholar
Beresnyak, A., Lazarian, A. & Cho, J. 2005 Density scaling and anisotropy in supersonic magnetohydrodynamic turbulence. Astrophysical Journal Letters 624, L93–L96.Google Scholar
Berger, M. & Rosner, R. 1995 The evolution of helicity in the presence of turbulence. Geophysical and Astrophysical Fluid Dynamics 81, 73–99.Google Scholar
Bhattacharjee, A. & Ng, C. S. 2001 Random scattering and anisotropic turbulence of shear Alfvén wave packets. Astrophys. J. 548, 318–322.Google Scholar
Bigot, B., Galtier, S. & Politano, H. 2008 Development of anisotropy in incompressible magnetohydrodynamic turbulence. Physical ReviewE 78 066301.Google Scholar
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge: Cambridge University Press.
Boldyrev, S. 2001 A solvable model for nonlinear mean field dynamo. Astrophysical Journal 562, 1081–1085.Google Scholar
Boldyrev, S. 2005 On the spectrum of magnetohydrodynamic turbulence. Astrophys. J. Lett. 626, L37–L40.Google Scholar
Boldyrev, S. 2006 Spectrum of magnetohydrodynamic turbulence. Physical Review Letters 96, 115002.Google Scholar
Boldyrev, S. & Cattaneo, F. 2004 Magnetic field generation in Kolmogorov turbulence. Physical Review Letters 92, 144501.Google Scholar
Boldyrev, S. & Perez, J. C. 2009 Spectrum of weak magnetohydrodynamic turbulence. Physical Review Letters 103, 225001.Google Scholar
Boldyrev, S., Cattaneo, F. & Rosner, R. 2005 Magnetic field generation in helical turbulence. Physical Review Letters 95, 255001.Google Scholar
Boldyrev, S., Mason, J. & Cattaneo, F. 2009 Dynamic alignment and exact scaling laws in magnetohydrodynamic turbulence. Astrophys. J. Lett. 699, L39–L42.Google Scholar
Bracco, A., Chavanis, P. H., Provenzale, A. & Spiegel, E. A. 1999 Particle aggregation in a turbulent Keplerian flow. Physics of Fluids 11, 2280–2287.Google Scholar
Brandenburg, A. & Nordlund, A. 2010 Astrophysical turbulence. Reports on Progress in Physics 74, 046901.Google Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and non-linear dynamo theory. Physics Reports 417, 1–209.Google Scholar
Busse, F. H. 2002 Convective flows in rapidly rotating spheres and their dynamo action. Physics of Fluids 14, 1301–1314.Google Scholar
Carati, D., Debliquy, O., Knaepen, B., Teaca, B. & Verma, M. 2006 Energy transfers in forced MHD turbulence. Journal of Turbulence 7, 51.Google Scholar
Cattaneo, F. 1999 On the origin of magnetic fields in the quiet Photosphere. Astrophys. J. lett. 515, L39–L42.Google Scholar
Cattaneo, F. & Hughes, D. W. 2009 Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers. Mon. Not. Roy. Ast. Soc. 395, L48–L51.Google Scholar
Cattaneo, F. & Tobias, S. M. 2005 Interaction between dynamos at different scales. Phys. Fluids 17, 127105.Google Scholar
Cattaneo, F. & Tobias, S. M. 2009 Dynamo properties of the turbulent velocity field of a saturated dynamo, JFM 621, 205–214.Google Scholar
Chandran, B. D. G. 2008a Strong Anisotropic MHD Turbulence with Cross Helicity. Astrophys. J. 685, 646–658.Google Scholar
Chandran, B. D. G. 2008b Weakly Turbulent Magnetohydrodynamic Waves in Compressible Low-β Plasmas. Physical Review Letters 101 235004.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. International Series of Monographs on Physics, Oxford: Clarendon Press.
Chertkov, M., Falkovich, G., Kolokolov, I. & Vergassola, M. 1999 Small-scale turbulent dynamo. Physical Review Letters 83, 4065–4068.Google Scholar
Childress, S. & Gilbert, A. D. 1995 Stretch, Twist, Fold: The Fast Dynamo. Berlin: Springer-Verlag.
Cho, J., Lazarian, A. & Vishniac, E. T. 2002 Simulations of magnetohydrodynamic turbulence in a strongly magnetized medium. Astrophys. J. 564, 291–301.Google Scholar
Cho, J. & Vishniac, E. T. 2000 The anisotropy of Magnetohydrodynamic alfvénic turbulence. Astrophys. J. 539, 273–282.Google Scholar
Christensen, U., Olson, P. & Glatzmaier, G. A. 1999 Numerical modelling of the geodynamo: a systematic parameter study. Geophysical Journal International 138, 393–409.Google Scholar
Cowling, T. G. 1933 The magnetic field of sunspots. Mon. Not. Roy. Ast. Soc. 94, 39–48.Google Scholar
Cowling, T. G. 1976 Magnetohydrodynamics. Bristol: Adam Hilger.
Davidson, P. A. 2004 Turbulence : an Introduction for Scientists and Engineers. Oxford: Oxford University Press.
Dmitruk, P., Gómez, D. O. & Matthaeus, W. H. 2003 Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics. Physics of Plasmas 10, 3584–3591.Google Scholar
Dobrowolny, M., Mangeney, A. & Veltri, P. 1980 Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Physical Review Letters 45, 144–147.Google Scholar
Dormy, E. & Soward, A. M., ed. 2007 Mathematical Aspects of Natural Dynamos. CRC Press/Taylor & Francis.
Elskens, Y. & Escande, D. F. 2003 Microscopic Dynamics of Plasmas and Chaos. Bristol: Institute of Physics Publishing.
Finn, J. M. & Ott, E. 1988 Chaotic flows and fast magnetic dynamos. Physics of Fluids 31, 2992–3011.Google Scholar
Frick, P. & Sokoloff, D. 1998 Cascade and dynamo action in a shell model of magnetohydrodynamic turbulence. Physical ReviewE 57, 4155–4164.Google Scholar
Frisch, U. 1995 Turbulence: the Legacy of A. N. Kolmogorov. Cambridge: Cambridge University Press.
Galtier, S. 2008 Magnetohydrodynamic turbulence. In SF2A-2008 ed. C. Charbonnel, F.Combes, , & R., Samadi, pp. 313–326.
Galtier, S. 2009 Wave turbulence in magnetized plasmas. Nonlinear Processes in Geophysics 16, 83–98.Google Scholar
Galtier, S. & Chandran, B. D. G. 2006 Extended spectral scaling laws for shear Alfvén wave turbulence. Physics of Plasmas 13 11, 114505.Google Scholar
Galtier, S., Nazarenko, S. V., Newell, A. C. & Pouquet, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. Journal of Plasma Physics 63, 447–488.Google Scholar
Galtier, S., Nazarenko, S. V., Newell, A. C. & Pouquet, A. 2002 Anisotropic turbulence of shear Alfvén waves. Astrophys. J. Lett. 564, L49–L52.Google Scholar
Godon, P. & Livio, M. 2000 The formation and role of vortices in protoplanetary disks. Astrophys. J. 537, 396–404.Google Scholar
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence. Astrophys. J. 438, 763–775.Google Scholar
Goldreich, P. & Sridhar, S. 1997 Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680–688.Google Scholar
Grappin, R., Leorat, J. & Pouquet, A. 1983 Dependence of MHD turbulence spectra on the velocity field-magnetic field correlation. Astron. Astrophys. 126, 51–58.Google Scholar
Haugen, N. E., Brandenburg, A. & Dobler, W. 2004 Simulations of nonhelical hydromagnetic turbulence. Phys. Rev.E 70, 016308.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2006 Astrophysical gyrokinetics: basic equations and linear theory. Astrophysical Journal 651, 590–614Google Scholar
Iroshnikov, P. S. 1963 Turbulence of a conducting fluid in a strong magnetic field. Astronomicheskii Zhurnal 40, 742–750.Google Scholar
Iskakov, A. B., Schekochihin, A. A., Cowley, S. C., McWilliams, J. C. & Proctor, M. R. E. 2007 Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers. Physical Review Letters 98 20, 208501.Google Scholar
Kadomtsev, B. B. & Pogutse, O. P. 1974 Nonlinear helical perturbations of a plasma in the tokamak. Soviet Journal of Experimental and Theoretical Physics 38, 283.Google Scholar
Kazantsev, A. P. 1968 Enhancement of a magnetic field by a conducting fluid. Soviet Journal of Experimental and Theoretical Physics 26, 1031–1034.Google Scholar
Kim, E. & Hughes, D. W. 1997 Flow helicity in a simplified statistical model of a fast dynamo. Physics Letters A 236, 211–218.Google Scholar
Klapper, I. & Young, L. S. 1995 Rigorous bounds on the fast dynamo growth-rate involving topological entropy. Comm. Math. Phys. 175, 623–646.Google Scholar
Kleeorin, N. & Rogachevskii, I. 1997 Intermittency and anomalous scaling for magnetic fluctuations. Phys. Rev.E 56 417.Google Scholar
Kleeorin, N., Rogachevskii, I. & Sokoloff, D. 2002 Magnetic fluctuations with a zero mean field in a random fluid flow with a finite correlation time and a small magnetic diffusion. Phys. Rev.E 65, 036303.Google Scholar
Kraichnan, R. H. 1965 Inertial-Range Spectrum of Hydromagnetic Turbulence. Physics of Fluids 8, 1385–1387.Google Scholar
Krause, F. & Raedler, K. 1980 Mean-Field Magnetohydrodynamics and Dynamo Theory. Oxford, Pergamon Press, Ltd., 1980.
Kulsrud, R. M. 2005 Plasma Physics for Astrophysics. Princeton: Princeton University Press.
Kulsrud, R. M. & Anderson, S. W. 1992 The spectrum of random magnetic fields in the mean field dynamo theory of the galactic magnetic field. Astrophysical Journal 396, 606–630.Google Scholar
Kulsrud, R. M. & Zweibel, E. G. 2008 On the origin of cosmic magnetic fields. Reports on Progress in Physics 71, 046901.Google Scholar
Lazarian, A. 2006 Intermittency of magnetohydrodynamic turbulence: an astro-physical perspective. International Journal of Modern PhysicsD 15, 1099–1111.Google Scholar
Lazarian, A. & Cho, J. 2005 Scaling, Intermittency and decay of MHD turbulence. Physica Scripta T116, 32–37.Google Scholar
Li, P. S., McKee, C. F., Klein, R. I. & Fisher, R. T. 2008 Sub-Alfvénic nonideal MHD turbulence simulations with ambipolar diffusion. I. Turbulence statistics. Astrophysical Journal 684, 380–394.Google Scholar
Lithwick, Y. & Goldreich, P. 2003 Imbalanced Weak Magnetohydrodynamic Turbulence. Astrophys. J. 582, 1220–1240.Google Scholar
Lithwick, Y., Goldreich, P. & Sridhar, S. 2007 Imbalanced Strong MHD Turbulence. Astrophys. J. 655, 269–274.Google Scholar
Malyshkin, L. & Boldyrev, S. 2007 Magnetic dynamo action in helical turbulence. Astrophysical Journal Letters 671, L185–L188.Google Scholar
Malyshkin, L. & Boldyrev, S. 2008 Amplification of magnetic fields by dynamo action in Gaussian-correlated helical turbulence. Physica Scripta T132, 014028.Google Scholar
Malyshkin, L. & Boldyrev, S. 2009 On magnetic dynamo action in astrophysical turbulence. Astrophys. J. 697, 1433–1438.Google Scholar
Malyshkin, L. & Boldyrev, S. 2010 Magnetic Dynamo action at Low Magnetic Prandtl Numbers. Physical Review Lett. 105, 215002Google Scholar
Maron, J. & Goldreich, P. 2001 Simulations of Incompressible Magnetohydrodynamic Turbulence. Astrophys. J. 554, 1175–1196.Google Scholar
Maron, J., Cowley, S. & McWilliams, J. 2004 The Nonlinear Magnetic Cascade. Astrophysical Journal 603, 569–583.Google Scholar
Mason, J., Cattaneo, F. & Boldyrev, S. 2006 Dynamic Alignment in Driven Magnetohydrodynamic Turbulence. Physical Review Letters 97, 255002.Google Scholar
Mason, J., Cattaneo, F. & Boldyrev, S. 2008 Numerical measurements of the spectrum in magnetohydrodynamic turbulence. Physical ReviewE 77, 036403.Google Scholar
Mason, J., Malyshkin, L., Boldyrev, S. & Cattaneo, F. 2011 Magnetic Dynamo Action in Random Flows with Zero and Finite Correlation Times. Astrophysical Journal 730, 86.Google Scholar
Matthaeus, W. H., Pouquet, A., Mininni, P. D., Dmitruk, P. & Breech, B. 2008 Rapid Alignment of Velocity and Magnetic Field in Magnetohydrodynamic Turbulence. Physical Review Letters 100, 085003.Google Scholar
Mininni, P. D. 2006 Turbulent magnetic dynamo excitation at low magnetic Prandtl number. Physics of Plasmas 13, 056502.Google Scholar
Mininni, P. D., Ponty, Y., Montgomery, D. C., Pinton, J.-F., Politano, H. & Pouquet, A. 2005 Dynamo Regimes with a Nonhelical Forcing. Astrophys. J. 626, 853–863.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge: Cambridge University Press.
Monchaux, R., Berhanu, M., Bourgoin, M., Moulin, M., Odier, P., Pinton, J.-F., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., Chiffaudel, A., Daviaud, F., Dubrulle, B., Gasquet, C., Marié, L. & Ravelet, F. 2007 Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium. Physical Review Letters 98 4, 044502.Google Scholar
Müller, W. & Busse, A. 2007 Recent developments in the theory of magnetohydrodynamic turbulence. In Turbulence and Nonlinear Processes in Astrophysical Plasmas, D., Shaikh & G. P., Zank, (eds.) American Institute of Physics Conference Series, vol. 932, pp. 52–57.
Müller, W. & Grappin, R. 2005 Spectral Energy Dynamics in Magnetohydrodynamic Turbulence. Physical Review Letters 95, 114502.Google Scholar
Müller, W., Biskamp, D. & Grappin, R. 2003 Statistical anisotropy of magnetohydrodynamic turbulence. Phys. Rev.E 67, 066302.Google Scholar
Newell, A. C., Nazarenko, S. & Biven, L. 2001 Wave turbulence and intermittency. Physica D Nonlinear Phenomena 152, 520–550.Google Scholar
Ng, C. S. & Bhattacharjee, A. 1996 Interaction of Shear-Alfven Wave Packets: Implication for Weak Magnetohydrodynamic Turbulence in Astrophysical Plasmas. Astrophys. J. 465, 845–854.Google Scholar
Ng, C. S., Bhattacharjee, A., Germaschewski, K. & Galtier, S. 2003 Anisotropic fluid turbulence in the interstellar medium and solar wind. Physics of Plasmas 10, 1954–1962.Google Scholar
Oughton, S., Dmitruk, P. & Matthaeus, W. H. 2004 Reduced magnetohydrodynamics and parallel spectral transfer. Physics of Plasmas 11, 2214–2225.Google Scholar
Parker, E. N. 1979 Cosmical Magnetic Fields: their Origin and their Activity. Oxford, Clarendon Press; New York, Oxford University Press.
Perez, J. C. & Boldyrev, S. 2008 On Weak and Strong Magnetohydrodynamic Turbulence. Astrophys. J. Lett. 672, L61–L64.Google Scholar
Perez, J. C. & Boldyrev, S. 2009 Role of Cross-Helicity in Magnetohydrodynamic Turbulence. Physical Review Letters 102, 025003.Google Scholar
Perez, J. C. & Boldyrev, S. 2010a Numerical simulations of imbalanced strong magnetohydrodynamic turbulence. Astrophys. J. Lett. 710, L63–L66.Google Scholar
Perez, J. C. & Boldyrev, S. 2010b Strong magnetohydrodynamic turbulence with cross helicity. Physics of Plasmas 17, 055903.Google Scholar
Pétrélis, F. & Fauve, S. 2008 Chaotic dynamics of the magnetic field generated by dynamo action in a turbulent flow. Journal of Physics Condensed Matter 20, 494203.Google Scholar
Podesta, J. J. & Bhattacharjee, A. 2010 Theory of incompressible MHD turbulence with cross-helicity. Astrophys. J. 718, 1151–1157.Google Scholar
Podesta, J. J., Chandran, B. D. G., Bhattacharjee, A., Roberts, D. A. & Goldstein, M. L. 2009 Scale-dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence. Journal of Geophysical Research Space Physics 114, A01107.Google Scholar
Politano, H. & Pouquet, A. 1998 Dynamical length scales for turbulent magnetized flows. Geophys. Res. Lett. 25, 273–276.Google Scholar
Ponty, Y., Mininni, P. D., Pinton, J.-F., Politano, H. & Pouquet, A. 2007 Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions. New Journal of Physics 9, 296–305.Google Scholar
Pouquet, A., Frisch, U. & Leorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. Journal of Fluid Mechanics 77, 321–354.Google Scholar
Rappazzo, A. F., Velli, M., Einaudi, G. & Dahlburg, R. B. 2007 Coronal Heating, Weak MHD Turbulence, and Scaling Laws. Astrophysical Journal Letters 657, L47–L51.Google Scholar
Rappazzo, A. F., Velli, M., Einaudi, G. & Dahlburg, R. B. 2008 Nonlinear Dynamics of the Parker Scenario for Coronal Heating. Astrophys. J. 677, 1348–1366.Google Scholar
Schekochihin, A. A., Cowley, S. C., Hammett, G. W., Maron, J. L. & McWilliams, J. C. 2002 A model of nonlinear evolution and saturation of the turbulent MHD dynamo. New Journal of Physics 4, 84.Google Scholar
Schekochihin, A. A., Boldyrev, S. A. & Kulsrud, R. M. 2002 Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers. Astrophys. J. 567, 828–852.Google Scholar
Schekochihin, A. A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2004 Critical Magnetic Prandtl Number for Small-Scale Dynamo. Physical Review Letters 92 5, 054502.Google Scholar
Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Hammett, G. W., Maron, J. L. & McWilliams, J. C. 2004 Saturated State of the Nonlinear Small-Scale Dynamo. Physical Review Letters 92 8, 084504.Google Scholar
Schekochihin, A. A., Haugen, N. E. L., Brandenburg, A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2005 The Onset of a Small-Scale Turbulent Dynamo at Low Magnetic Prandtl Numbers. Astrophysical Journal Letters 625, L115–L118.Google Scholar
Schekochihin, A. A., Iskakov, A. B., Cowley, S. C., McWilliams, J. C., Proctor, M. R. E. & Yousef, T. A. 2007 Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers. New Journal of Physics 9, 300.Google Scholar
Shebalin, J. V., Matthaeus, W. H. & Montgomery, D. 1983 Anisotropy in MHD turbulence due to a mean magnetic field. Journal of Plasma Physics 29, 525–547.Google Scholar
Sridhar, S. 2010 Magnetohydrodynamic turbulence in a strongly magnetised plasma. Astronomische Nachrichten 331, 93–100.Google Scholar
Strauss, H. R. 1976 Nonlinear, three-dimensional magnetohydrodynamics of non-circular tokamaks. Physics of Fluids 19, 134–140.Google Scholar
Steenbeck, M. and Krause, F. & Rädler, K.-H. 1966 Zeitschrift Naturforschung TeilA 21, 369.
Subramanian, K. 1999 Unified Treatment of Small- and Large-Scale Dynamos in Helical Turbulence. Physical Review Letters 83, 2957–2960.Google Scholar
Subramanian, K. 2003 Hyperdiffusion in Nonlinear Large- and Small-Scale Turbulent Dynamos. Physical Review Letters 90 24, 245003.Google Scholar
Tobias, S. M. & Cattaneo, F. 2008a Dynamo action in complex flows: the quick and the fast. Journal of Fluid Mechanics 601, 101–122.Google Scholar
Tobias, S. M. & Cattaneo, F. 2008b Limited Role of Spectra in Dynamo Theory: Coherent versus Random Dynamos. Physical Review Letters 101 12, 125003.Google Scholar
Tobias, S. M., Cattaneo, F. & Brummell, N.H. 2010 On the Generation of Organised Magnetic Fields. Astrophysical Journal 728, 153.Google Scholar
Vainshtein, S. I. & Kichatinov, L. L. 1986 The dynamics of magnetic fields in a highly conducting turbulent medium and the generalized Kolmogorov–Fokker– Planck equations. Journal of Fluid Mechanics 168, 73–87.Google Scholar
Verhille, G., Plihon, N., Bourgoin, M., Odier, P. & Pinton, J. 2010 Laboratory Dynamo Experiments. Space Science Reviews 152, 543–564.Google Scholar
Yousef, T. A., Brandenburg, A. & Rüdiger, G. 2003 Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations. Astronomy & Astrophysics 411, 321–327.Google Scholar
Zakharov, V. E., L'Vov, V. S. & Falkovich, G. 1992 Kolmogorov spectra of turbulence I: Wave turbulence.
Zel'dovich, Y. B. 1956 The magnetic field in the two dimensional motion of a conducting turbulent fluid. Zh. Exp. Teor. Fiz. SSSR 31, 154–155.Google Scholar
Zeldovich, I. B., Ruzmaikin, A. A. & Sokolov, D. D., eds. 1983 Magnetic Fields in Astrophysics, vol. 3. Heidelrberg: Springer-Verlag.
Zeldovich, Y. B., Ruzmaikin, A. A. & Sokoloff, D. D. 1990 The Almighty Chance. World Scientific Lecture Notes in Physics, Singapore: World Scientific Publishers, 1990.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×