Transitions near the onset of stationary rotating magnetoconvection: Role of magnetic Prandtl number

We investigate the instabilities and associated bifurcation structure near the onset of rotating magnetoconvection of low Prandtl number fluids by performing three-dimensional direct numerical simulations. Previous studies considered zero magnetic Prandtl number (Pm) limit for the investigation of bifurcation structure near the onset of convection. Here, we numerically investigate the effect of Pm on the bifurcation structure. The classical Rayleigh–Bénard convection setup in the presence of a horizontal magnetic field and rotation about the vertical axis is considered for the study. The control parameters, including the Taylor number (Ta), the Chandrasekhar number (Q), the reduced Rayleigh number (r), and the magnetic Prandtl number (Pm), are varied in the ranges 1≤Ta≤500, 0<Q≤1000, 0.8≤r≤3.7, and 10−4≤Pm≤0.5 by considering Prandtl numbers Pr=0.025 and 0.1. The investigation reveals the presence of supercritical, subcritical, and hybrid transitions to convection. These transitions lead to infinitesimal and finite amplitude fluid patterns at the onset of convection. The finite amplitude solutions can be both stationary and time-dependent. The bifurcation structures associated with these flow patterns at the onset are studied in detail. For very small Pm, the bifurcation structure is found to be qualitatively similar to the ones observed in the Pm→0 limit. However, as Pm is increased, several new solutions appear at the onset, and the resulting bifurcation structures are greatly modified.