Eur. Phys. J. B 50, 639-652 (2006)
https://doi.org/10.1140/epjb/e2006-00171-4

Magnetic field generation by convective flows in a plane layer

¹ International Institute of Earthquake Prediction Theory and Mathematical Geophysics, 79 bldg. 2, Warshavskoe ave., 117556 Moscow, Russian Federation
² Laboratory of General Aerodynamics, Institute of Mechanics, Lomonosov Moscow State University, 1, Michurinsky ave., 119899 Moscow, Russian Federation
³ Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France

Corresponding author: ^a olgap@mitp.ru

Received: 10 July 2005
Revised: 17 October 2005
Published online: 17 May 2006

Abstract

Hydrodynamic and magnetohydrodynamic convective attractors in a plane horizontal layer 0≤z≤1 are investigated numerically. We consider Rayleigh-Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period L in the x and y directions. Computations have been performed for the Prandtl number P=1 for and Rayleigh numbers 0<R≤4000, and for L=4, 0<R≤2000. Fifteen different types of hydrodynamic attractors are found, including two types of steady states distinct from rolls, travelling waves, periodic and quasiperiodic flows, and chaotic attractors of heteroclinic nature. Kinematic dynamo problem has been solved for the computed convective attractors. Out of the 15 types of the observed attractors only 6 can act as kinematic dynamos. Nonlinear magnetohydrodynamic regimes have been explored assuming as initial conditions convective attractors capable of magnetic field generation, and a small seed magnetic field. After initial exponential growth, in the saturated regime magnetic energy remains much smaller than the flow kinetic energy. The final magnetohydrodynamic attractors are either quasiperiodic or chaotic.