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.

We investigate the dynamics of flow reversals close to the onset of Rayleigh-Bénard convection (RBC) of electrically conducting low Prandtl number (Pr) Boussinesq fluids in the presence of an external vertical magnetic field. The investigation is carried out by performing three-dimensional (3D) direct numerical simulations (DNS) of the related mathematical model considering the quasi-static approximation. The numerical investigation reveals a rich dynamics of the flow reversals close to the onset of convection. Three qualitatively different kinds of flow reversals, namely chaotic, intermittent and periodic are identified and all are found to occur in the presence of weak magnetic field, measured in terms of the Chandrasekhar number (Q). Explored ranges of the Prandtl number (Pr), the Rayleigh number (Ra) and the Chandrasekhar number are 0 < Pr ≤ 0.03, 6.5 × 10 2 ≤ Ra ≤ 7 × 10 3 and 0 < Q ≤ 100, respectively. Out of the three different types of flow reversals, intermittent flow reversal is new and has not been reported so far in convective system to the best of our knowledge. The probability density function of the time interval of occurrences of chaotic flow reversals is found to decay exponentially. The heat transfer properties of the system are also numerically investigated and it is observed that magnetic field facilitates the heat transfer in the considered ranges of the parameter space.focus article

The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenario near the onset of rotating convection of low Prandtl number fluids is not well understood. Here we investigate the transition scenario in rotating Rayleigh-B\'{e}nard convection with no slip boundary conditions by performing 3D direct numerical simulations (DNS) and low dimensional modeling. The governing parameters, namely, the Taylor number ($\mathrm{Ta}$), Rayleigh number ($\mathrm{Ra}$) and Prandtl number ($\mathrm{Pr}$) are varied in the ranges $0&lt; \mathrm{Ta}\leq 8\times 10^3$, $0 &lt;\mathrm{Ra} &lt; 1\times 10^4$ and $0 &lt;\mathrm{Pr} \leq 0.35$, where convection appears as stationary cellular pattern. In DNS, for $\mathrm{Pr} &lt; 0.31$, supercritical or subcritical onset of convection appears, according as $\mathrm{Ta} &gt; \mathrm{Ta_c}(\mathrm{Pr})$ or $\mathrm{Ta} &lt; \mathrm{Ta_c}(\mathrm{Pr})$, where $\mathrm{Ta_c}(\mathrm{Pr})$ is a $\mathrm{Pr}$ dependent threshold of $\mathrm{Ta}$. On the other hand, only supercritical onset of convection is observed for $\mathrm{Pr}\geq 0.31$. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as $\mathrm{Ra}$ is increased beyond the onset of convection, the system becomes time dependent and depending on $\mathrm{Pr}$, standing and traveling wave solutions are observed. For very small $\mathrm{Pr}$ ($\leq 0.045$), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher $\mathrm{Ta}$.