An iterative study of time independent induction effects in magnetohydrodynamics

Mickaël Bourgoin (1) , Philippe Odier (1) , Jean-François Pinton (1) , Yanick Ricard (2)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 LST - Laboratoire de Sciences de la Terre

We introduce a new numerical approach to study magnetic induction in flows of an electrically conducting fluid submitted to an external applied field B-0. In our procedure the induction equation is solved iteratively in successive orders of the magnetic Reynolds number Rm. All electrical quantities such as potential, currents, and fields are computed explicitly with real boundary conditions. We validate our approach on the well known case of the expulsion of magnetic field lines from large scale eddies. We then apply our technique to the study of the induction mechanisms in the von Karman flows generated in the gap between coaxial rotating disks. We demonstrate how the omega and alpha effects develop in this flow, and how they could cooperate to generate a dynamo in this homogeneous geometry. We also discuss induction effects that specifically result from boundary conditions.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Mickaël Bourgoin, Philippe Odier, Jean-François Pinton, Yanick Ricard. An iterative study of time independent induction effects in magnetohydrodynamics. Physics of Fluids, 2004, 16 (7), pp.2529-2547. ⟨10.1063/1.1739401⟩. ⟨hal-00492367⟩