Transition to chaos in magnetized rotating Rayleigh-Bénard convection

Abstract

Transition to chaos and magnetic field generation are investigated in numerical simulations of three-dimensional rotating Rayleigh-Bénard convection. The behavior of the system is explored as a function of the rotation speed, measured by the Taylor number, the thermal buoyancy strength, measured by the Rayleigh number, and the magnetic Prandtl number. In the absence of magnetic field, a detailed exploration of the space of parameters reveals a sequence of Hopf bifurcations leading to quasiperiodicity and chaos. It is shown that rotation can dampen convection for low values of the Rayleigh number, but if buoyancy is strong enough to keep the convection, then rotation facilitates transition to chaos. In the presence of a weak seed magnetic field, convective motions may trigger a nonlinear dynamo that converts kinetic energy into magnetic energy, leading to an exponential increase of the magnetic energy. A nonhysteretic blowout bifurcation is shown to be responsible for the onset of the dynamo regime for a critical magnetic Prandtl number, whose value depends on the rotation rate.