Transition to chaos and magnetic field generation in rotating Rayleigh-B\'enard convection

Abstract

Hydrodynamic and magnetohydrodynamic convective attractors in three-dimensional rotating Rayleigh-B\'enard convection are studied numerically by varying the Taylor and Rayleigh numbers as control parameters. First, an analysis of hydrodynamic attractors and their bifurcations is conducted, where routes to chaos via quasiperiodicity are identified. Second, the behaviour of the magnetohydrodynamic system is investigated by introducing a seed magnetic field and measuring its growth or decay as a function of the Taylor number, while keeping the Rayleigh number fixed. Analysis of the attractors shows that rotation has a significant impact on magnetic field generation in Rayleigh-B\'enard convection, with the critical magnetic Prandtl number changing nonmonotonically with the rotation rate. It is argued that a nonhysteretic blowout bifurcation with on-off intermittency is responsible for the transitions to dynamo.