Abstracts - KTH Mechanics

ix
Generation of magnetic fields by turbulent flows
S. Fauve ∗ ,F.Pétrélis †
The generation of a magnetic field by the flow of an electrically conducting fluid,
i.e. the dynamo effect, has been first considered to explain the origin of the magnetic
fields of planets, stars and galaxies. It has been also studied in relation with several
applied problems such as liquid metal cooling of nuclear reactors, liquid metal
electromagnets and instabilities in toroidal plasmas. Magnetic field generation by
laminar flows is fairly well understood and dynamos generated by simple but clever
flow geometries have been successfully observed in experiments performed a few years
ago in Karlsruhe and Riga.
However, the effect of turbulence on dynamo threshold and saturation still involves
many open problems. We have shown that small scale turbulent fluctuations
only slightly modify the dynamo threshold predicted as if the mean flow were acting
alone, in agreement with the Karlsrhue and Riga experimental observations 1 . On
the contrary, large scale fluctuations of eddies generating the field can strongly inhibit
the dynamo effect, as shown in an analytically tractable example. Thus, the
behaviour of the dynamo threshold of strongly turbulent flows as a function of the kinetic
Reynolds number, is still an open problem involving many conflicting statements
in the literature.
The nonlinearly saturated dynamo regime also depends on the Reynolds number
of the flow generating the magnetic field. We show that different scaling laws can
be obtained for the magnetic energy generated in the vicinity of the threshold 2 and
compare them to the values measured in Karlsruhe and Riga. The importance of
the Coriolis force, crucial for astrophysical or geophysical dynamos, is also shortly
discussed.
Dynamos generated by strongly turbulent flows of liquid metal as well as astrophysical
or geophysical dynamos, cannot be studied with direct numerical simulations
of the equations of magnetohydrodynamics in a realistic parameter range. Progress in
this direction thus strongly relies on experimental observations and several groups in
the world are trying to generate a turbulent dynamo 3 . We will shortly review these
efforts and show how the study of fluctuations and transport of a magnetic field by
the flow of a liquid metal can give insights in the relevant mechanisms of turbulent
dynamos 4 5 .
∗ Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond 75005 Paris,
France.
† Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond 75005 Paris,
France.
1 Fauve and Pétrélis, Peyresq Lectures on Nonlinear Phenomena, Ed. J-A Sepulchre, World
Scientific 2, 1 (2003).
2 Pétrélis and Fauve, Eur. Phys. J. B 22, 273 (2001).
3 Fauve and Lathrop, Fluid Dynamics and Dynamos in Astrophysics and Geophysics, A. Soward
et al., Eds. 393 (2005).
4 Bourgoin et al., Phys. Fluids 14, 3046 (2002).
5 Pétrélis et al., Phys. Rev. Lett. 90, 174501 (2003).