Dependence of magnetic field generation by thermal convection on the rotation rate: a case study

TL;DR

This study investigates how the magnetic field generation by thermal convection depends on the rotation rate through direct numerical simulations, revealing complex bifurcation structures and the nuanced influence of rotation on magnetic dynamo action.

Contribution

It provides a detailed analysis of the bifurcation scenarios and attractor types in magnetohydrodynamic convection across a range of rotation rates, highlighting new global bifurcations influenced by symmetry.

Findings

Identification of 21 nonlinear convective MHD attractors.

Discovery of two novel global bifurcations similar to SNIC bifurcations.

Demonstration that the effect of rotation rate on magnetic field generation is more complex than previously understood.

Abstract

Dependence of magnetic field generation on the rotation rate is explored by direct numerical simulation of magnetohydrodynamic convective attractors in a plane layer of conducting fluid with square periodicity cells for the Taylor number varied from zero to 2000, for which the convective fluid motion halts (other parameters of the system are fixed). We observe 5 types of hydrodynamic (amagnetic) attractors: two families of two-dimensional (i.e. depending on two spatial variables) rolls parallel to sides of periodicity boxes of different widths and parallel to the diagonal, travelling waves and three-dimensional "wavy" rolls. All types of attractors, except for one family of rolls, are capable of kinematic magnetic field generation. We have found 21 distinct nonlinear convective MHD attractors (13 steady states and 8 periodic regimes) and identified bifurcations in which they emerge. In addition, we have observed a family of periodic, two-frequency quasiperiodic and chaotic regimes, as well as an incomplete Feigenbaum period doubling sequence of bifurcations of a torus followed by a chaotic regime and subsequently by a torus with 1/3 of the cascade frequency. The system is highly symmetric. We have found two novel global bifurcations reminiscent of the SNIC bifurcation, which are only possible in the presence of symmetries. The universally accepted paradigm, whereby an increase of the rotation rate below a certain level is beneficial for magnetic field generation, while a further increase inhibits it (and halts the motion of fluid on continuing the increase) remains unaltered, but we demonstrate that this "large-scale" picture lacks many significant details.