Transitions in overstable rotating magnetoconvection

TL;DR

This paper reports the novel observation of simultaneous subcritical and supercritical convection branches in overstable rotating magnetoconvection of liquid metals, supported by DNS and bifurcation analysis, revealing complex transition behaviors influenced by magnetic and rotational forces.

Contribution

It is the first to demonstrate the coexistence of subcritical and supercritical convection branches in overstable RBC with rotation and magnetic field, supported by detailed simulations and modeling.

Findings

Identification of simultaneous subcritical and supercritical convection branches.

Bifurcation analysis linking transitions to Hopf and pitchfork bifurcations.

Influence of Prandtl number on convection transition types.

Abstract

The classical Rayleigh-B\'{e}nard convection (RBC) system is known to exhibit either subcritical or supercritical transition to convection in the presence or absence of rotation and/or magnetic field. However, the simultaneous exhibition of subcritical and supercritical branches of convection in plane layer RBC depending on the initial conditions, has not been reported so far. Here, we report the phenomenon of simultaneous occurrence of subcritical and supercritical branches of convection in overstable RBC of electrically conducting low Prandtl number fluids (liquid metals) in the presence of an external uniform horizontal magnetic field and rotation about the vertical axis. Extensive three dimensional (3D) direct numerical simulations (DNS) and low dimensional modeling of the system, performed in the ranges $750 \leq \mathrm{Ta} \leq 3000$ and $0 < \mathrm{Q} \leq 1000$ of the Taylor number ($\mathrm{Ta}$, strength of the Coriolis force) and the Chandrasekhar number ($\mathrm{Q}$, strength of the Lorenz force) respectively, establish the phenomenon convincingly. Detailed bifurcation analysis of a simple three dimensional model derived from the DNS data reveals that a supercritical Hopf bifurcation and a subcritical pitchfork bifurcation of the conduction state are responsible for this. The effect of Prandtl number on these transitions is also explored in detail.