Magnetohydrodynamics and dynamo effect

The dynamo effect is an instability that, in an electrically conductive fluid, converts kinetic energy into magnetic energy. It is this process that generates the magnetic field of astrophysical objects (planets, stars, galaxies). In a liquid metal, dynamo instability occurs in highly turbulent flows. We are therefore dealing with an instability in which the unstable field (the magnetic field) is forced by a highly fluctuating field (the velocity field). Even though the idea of dynamo instability was presented by Larmor more than hundred years ago, no experimental observation was achieved until the early 2000s.

Selected results :
Experimental observation of the dynamo effect and of spontaneous reversals of the magnetic field in a turbulent flow of liquid sodium (VKS collaboration)

vksf1 — Time series of the magnetic field measured in the VKS experiment. The magnetic field remains of same direction for hundreds of seconds and abruptly reverses in an apparently random manner.

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium
Monchaux R., Berhanu M., Bourgoin M., Moulin M., Odier Ph ., Pinton J. -F., Volk R., Fauve S., Mordant N., Pétrélis F, Chiffaudel A. , Daviaud F., Dubrulle B., Gasquet C., Marie L., Ravelet F.
Physical Review Letters 98 (4) 044502 (2007)

Magnetic field reversals in an experimental turbulent dynamo
Berhanu M, Monchaux R, Fauve S, Mordant N, Pétrélis F, Chiffaudel A, Daviaud F, Dubrulle B, Marié L, Ravelet F, Bourgoin M, Odier P, Pinton JF, Volk R
Europhysics Letters 77, 59001 (2007)

Model for the reversals of the magnetic field

A low dimensional model based on the competition between two modes of magnetic field captures the variety of regimes observed in the VKS experiment as well as what is known of the Earth magnetic field and other astrophysical objets.

QBO3 — Comparison between the time series of reversing magnetic field as observed in the VKS experiment, the low dimensional model and the Earth magnetic field.

Experimental dynamos: from models to applications to the geodynamo
F. Pétrélis,
Comptes Rendus. Physique, 1-17 (2024)

Mechanisms for magnetic field reversals
Pétrélis F, Fauve S
Philosophical Transactions of the Royal society A (368), 1595-1605 (2010)

From Reversing to Hemispherical Dynamos
Gallet B, Pétrélis F
Physical Review E (80) 035302 (2009)

Simple Mechanism for Reversals of Earth’s Magnetic Field
Pétrélis F, Fauve S, Dormy E, Valet J-P
Physical Review Letters (102), 144503 (2009)

Chaotic dynamics of the magnetic field generated by dynamo action in a turbulent flow
Pétrélis F, Fauve S,
J. Phys. : Condens. Matter (20) 494203 (2008)

Observation in numerical dynamos

Magnetic reversals in a geodynamo model with a stably-stratified layer
N. Muller, C. Gissinger, F. Pétrélis,
Physics of the Earth and Planetary Interiors, 371, 107502 (2026)

Relating Earth reversal frequency and plate tectonics

Plate tectonics may control geomagnetic reversal frequency
F. Pétrélis, J. Besse, J-P Valet
Geophysical Research Letters (38), L19303 (2011)

Dynamo due to variations of electrical conductivity or magnetic permeability

Fluctuations of electrical conductivity: a new source for astrophysical magnetic fields
Francois Petrelis, Alexandros Alexakis, Christophe Gissinger
Phys. Rev. Lett. 116, 161102 (2016)

Optimum reduction of the dynamo threshold by a ferromagnetic layer located in the flow
J. Herault, F. Pétrélis
Physical Review E 90, 033015 (2014)

Spatial variations of magnetic permeability as a source of dynamo action
B. Gallet, F. Pétrélis, S. Fauve
Journal of Fluid Mechanics 727, 161-190 (2013)

Dynamo action due to spatially dependent magnetic permeability
B. Gallet, F. Pétrélis, S. Fauve
Europhysics Letters (97), 69001 (2012)