Eur. Phys. J. E (2017) 40: 13
https://doi.org/10.1140/epje/i2017-11499-2

Regular Article

Magnetoconvection transient dynamics by numerical simulation

¹ Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS-INPT-UPS, Toulouse, France
² CEA, DEN, Cadarache, SMTA/LPMA, F13108 St, Paul lez Durance, France

^* e-mail: srenaudi@imft.fr

Received: 1 September 2016
Accepted: 5 January 2017
Published online: 30 January 2017

Abstract

We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 10³-10⁶, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.