Effect of horizontal magnetic field on K\"{u}ppers-Lortz instability

TL;DR

This study explores how an external horizontal magnetic field influences the K"{u}ppers-Lortz instability in rotating Rayleigh-Bénard convection, revealing magnetic inhibition effects and the coexistence of different instabilities depending on parameters.

Contribution

It provides a detailed analysis of magnetic field effects on KLI across various Prandtl, Taylor, and Chandrasekhar numbers using weakly nonlinear and linear theories.

Findings

Magnetic field inhibits KLI at high Prandtl number by increasing critical Taylor number.

KLI is favored at low Q and inhibited at high Q for finite Prandtl numbers.

Small angle instability appears for Pr < 50, coexisting with KLI depending on parameters.

Abstract

We investigate the effect of an external horizontal magnetic field on the K\"{u}ppers-Lortz instability (KLI) in rotating Rayleigh-B\'{e}nard convection of Boussinesq fluids using weakly nonlinear theory along with linear theory. By KLI, we mean the instability where the two-dimensional roll solutions of the system occurring at the onset of convection becomes unstable against the perturbations by rolls oriented at different angle with the previous one as the rotation rate exceeds a critical value. The governing parameters, namely, the Prandtl number ($\mathrm{Pr}$), Taylor number ($\mathrm{Ta}$) and Chandrasekhar number ($\mathrm{Q}$) are varied in the ranges $0.8 \leq \mathrm{Pr} < \infty$, $0 < \mathrm{Ta} \leq 10^4$ and $0 \leq \mathrm{Q} \leq 10^4$ respectively by considering the vanishingly small magnetic Prandtl number limit. In the $\mathrm{Pr}\rightarrow \infty$ limit, magnetic field is found to inhibit the KLI by enhancing the critical Taylor number ($\mathrm{Ta}_c$) for its onset. On the other hand, for finite Prandtl number fluids, KLI is favored for lower $\mathrm{Q}$, and it is inhibited for higher $\mathrm{Q}$. Interestingly, in the finite Prandtl number range both KLI and small angle instability are manifested depending on the Prandtl number. No small angle instability is observed for $\mathrm{Pr} \geq 50$ and the rotation induced KLI is inhibited predominantly by the magnetic field. While, for $\mathrm{Pr} < 50$, along with the K\"{u}ppers-Lortz instability, small angle instability is also observed. However, in this case, KLI is favored for lower $\mathrm{Q}$, while it is inhibited for higher $\mathrm{Q}$.