Effect of horizontal magnetic field on Küppers–Lortz instability

Abstract

We investigate the effect of an external horizontal magnetic field on the Küppers–Lortz instability (KLI) in rotating Rayleigh–Bénard convection of Boussinesq fluids using weakly nonlinear theory along with linear theory. By the KLI, we mean the instability where the two-dimensional roll solutions of the system occurring at the onset of convection become unstable against the perturbations by rolls oriented at different angles with the previous one as the rotation rate exceeds a critical value. The governing parameters, namely, the Prandtl number (Pr), the Taylor number (Ta), and the Chandrasekhar number (Q), are varied in the ranges 0.8≤Pr<∞, 0<Ta≤104, and 0≤Q≤104, respectively, by considering the vanishingly small magnetic Prandtl number limit. In the Pr→∞ limit, magnetic field is found to inhibit the KLI by enhancing the critical Taylor number (Tac) for its onset. On the other hand, for finite Prandtl number fluids, the KLI is favored for lower Q, and it is inhibited for higher 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 Pr≥50, and the rotation-induced KLI is inhibited predominantly by the magnetic field, while, for Pr<50, along with the Küppers–Lortz instability, small-angle instability is also observed. However, in this case, the KLI is favored for lower Q, while it is inhibited for higher Q.