Magnetic fields in the universe are ubiquitous and are often in equipartition with the fluid motions,
thus playing an important dynamical role. The understanding of such flows is to be reached by
a combination of observations (say, in the solar and galactic environment, from the liquid core of
the Earth to the geosphere and heliosphere to the interstellar medium), of laboratory experiments
(hard in the MHD case) and of theory and modeling, including numerical simulations. In the
latter case, because geophysical and astrophysical flows have a huge number of interacting scales,
one indeed may need the adjunction of proper modeling to direct numerical simulations (DNS)
in order to gather a better understanding of such complex flows [1]. The models allow for a
signicant reduction of computer resources at a given Reynolds number; for example, one can
satisfactorily reproduce small-scale features of MHD turbulence in two dimensions, or the growth
rate of magnetic energy due to stretching by velocity gradients, and the saturation level of the
dynamo instability in 3D.
In this context, a few examples of where MHD turbulence is found and what properties it has will
be given with perhaps special emphasis on the Solar Wind. The reason why we need to model
turbulent flows and the diverse rationale behind such models together with a brief description of
their implementation will then be outlined.
Finally, if time permits, the problem of generation of magnetic fields in a fluid with a small
magnetic Prandlt number PM (ratio of the viscosity to the resistivity) – as encountered in the
liquid core of the Earth, in the solar convection zone or in laboratory experiments– will be evoked.
Combining DNS and modeling, one can show that a dynamo in such a flow is possible, at least
when one has well defined structures at large scales together with strong turbulent fluctuations;
in that case, dynamos are observed down to roughly PM 10−3. The critical magnetic Reynolds
number for dynamo action to occur increases sharply with 1/PM as turbulence sets in and then
it saturates [2]. Finally, one can note that the LES developed most recently [3] seems to better
model the flow than traditional eddy-viscosity types of modeling.
[1] A. Pouquet, A. Alexandros, P. Mininni & D. Montgomery, Y. Kaneda Editor, IUTAM Book Series
(Springer -Verlag), 4, 305 (2008).
[2] Y. Ponty, P. Mininni, J-F. Pinton, H. Politano & A. Pouquet, New J. Phys., 9, 296 (2007) [see also
Y. Ponty et al., Phys. Rev. Lett. 94 164502 (2005)].
[3] J. Baerenzung, H. Politano, Y. Ponty & A. Pouquet, Phys. Rev. E (2008), arXiv:0707.0642.
