Magnetic fields are ubiquitous in the cosmos and play an important dynamical role, as in the solar wind, in stars or in the interstellar medium. In planets and stars, magnetic fields are believed to be generated by a dynamo instability, in which the stretching of magnetic field lines by vigorous motions of electrically conducting fluids exceeds the Joule dissipation. Such magnetohydrodynamic (MHD) flows have large Reynolds numbers and thus nonlinear mode coupling leads to multi-scale interactions and to the formation of complex flows with, in the small scales, the presence of strong intermittent structures. Moreover, tearing mode instabilities develop and reconnection takes place, as in the magnetopause, or in the heating of solar and stellar corona.

At what rate does dissipation occur, as the Reynolds number increases? What is the origin of these structures, and how fast are they formed? What is the origin of such magnetic fields (the dynamo problem)? How does the dynamo work when the magnetic Prandtl number P_M—the ratio of viscosity to magnetic diffusivity—differs substantially from unity? For example, in the interstellar medium, it can be as large as 10¹⁴, whereas in stars such as the Sun and for planets such as Earth, it can be very low (lower than 10⁻⁵, the value for the Earth fluid core); similarly, in liquid breeder reactors and in laboratory experiments with liquid metals, P_M  1. Huge scale separation is needed, and several dynamical regimes have been identified, depending on turbulence, rotation, flow helicity, wave interactions, etc.

The progress reported in this invited focus issue of New Journal of Physics concerns observations, experiments, modeling, theory and direct numerical simulations. It is the hope of the editors of this collection that a general overview of where this dynamic scientific field is presently, and where it is going in the near future (with several large-scale projects, from detailed satellite observations to experiments and petascale computing), will be valuable to our readers.

Focus on Magnetohydrodynamics and the Dynamo Problem Contents

Toward coupling flow driven and magnetically driven dynamos
Eric G Blackman

Bifurcations and dynamo action in a Taylor–Green flow
B Dubrulle, P Blaineau, O Mafra Lopes, F Daviaud, J-P Laval and R Dolganov

2D enslaving of MHD turbulence
Sergey Nazarenko

Numerical insights into magnetic dynamo action in a turbulent regime
Sasa Kenjeres and Kemal Hanjalic

Magnetic helicity effects in astrophysical and laboratory dynamos
A Brandenburg and P J Käpylä

Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
D Rosenberg, A Pouquet and P D Mininni

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere
P D Mininni, D C Montgomery and L Turner

Structure and stability of the magnetic solar tachocline
G Rüdiger and L L Kitchatinov

Interactive desktop analysis of high resolution simulations: application to turbulent plume dynamics and current sheet formation
John Clyne, Pablo Mininni, Alan Norton and Mark Rast

Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
A A Schekochihin, A B Iskakov, S C Cowley, J C McWilliams, M R E Proctor and T A Yousef

Theory of the Lorentz force flowmeter
André Thess, Evgeny Votyakov, Bernard Knaepen and Oleg Zikanov

Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics
A Alexakis, P D Mininni and A Pouquet

Global solar dynamo models: simulations and predictions of cyclic photospheric fields and long-term non-reversing interior fields
M Dikpati and P A Gilman

Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions
Y Ponty, P D Mininni, J-F Pinton, H Politano and A Pouquet

Experiments on the magnetorotational instability in helical magnetic fields
Frank Stefani, Thomas Gundrum, Gunter Gerbeth, Günther Rüdiger, Jacek Szklarski and Rainer Hollerbach

A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence
F Plunian and R Stepanov

Shell models for Hall effect induced magnetic turbulence
Peter Frick, Rodion Stepanov and Matthias Rheinhardt

Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
J D Gibbon and D D Holm

Magnetic field generation by coherent turbulence structures
D Kivotides, A J Mee and C F Barenghi

Kinematic dynamos in multiple scale flows
A Tilgner

Steve Cowley, Imperial College, London, UK and University of California, Los Angeles, USA
Jean-François Pinton, Ecole Normale Supérieure de Lyon, France
Annick Pouquet, National Center for Atmospheric Research, Boulder, Colorado, USA