Overstable rotating convection in the presence of a vertical magnetic field

Abstract

We present the results of our investigation on nonlinear overstable rotating magnetoconvection (RMC) in presence of vertical external magnetic field. We focus on the dynamics appearing near the onset of convection by varying the system control parameters, namely, the Taylor number ($\mathrm{Ta}$), the Chandrasekhar number ($\mathrm{Q}$) and the Prandtl number ($\mathrm{Pr}$) in the ranges $750\leq\mathrm{Ta}\leq10^6$, $0 < \mathrm{Q} \leq 10^3$ and $0 < \mathrm{Pr} \leq 0.5$. Three dimensional (3D) direct numerical simulations (DNS) of the governing equations and low-dimensional modeling of the system are performed for this purpose. Extensive DNS in the specified parameter space shows two qualitatively different onsets depending on $\mathrm{Ta}$, $\mathrm{Q}$ and $\mathrm{Pr}$. In the first one, bistability appears at the onset, where both subcritical and supercritical convection coexist, while only supercritical convection is observed in the second one. Analysis of the low-dimensional model reveals that a supercritical Hopf bifurcation is responsible for the supercritical onset and a subcritical pitchfork bifurcation is responsible for the subcritical onset. It is also observed that appearance of subcritical convection at the onset has strong dependence on all three control parameters $\mathrm{Ta}$, $\mathrm{Q}$ and $\mathrm{Pr}$. The scenario of subcritical convection is found to disappear as $\mathrm{Pr}$ is increased for fixed $\mathrm{Ta}$ and $\mathrm{Q}$. However, most striking findings of the investigation is that the increment in $\mathrm{Ta}$ for fixed $\mathrm{Q}$ and $\mathrm{Pr}$ opposes the subcritical convection, whereas the increment in $\mathrm{Q}$ for fixed $\mathrm{Ta}$ and $\mathrm{Pr}$ favors it. This is in sharp contrast with the earlier results reported in RMC.