Effect of oblique horizontal magnetic field on convection rolls

We investigate the effect of external horizontal magnetic field applied on the convection rolls obliquely (at an angle $\varphi$ with the $x$-axis) in electrically conducting low Prandtl number fluids under the paradigm of the Rayleigh–Bénard convection by performing three-dimensional direct numerical simulations. The control parameters, namely, the Chandrasekhar number ($Q$) and the reduced Rayleigh number $r$ (ratio of Rayleigh number to critical Rayleigh number), are varied in the ranges $0\le Q\le 1000$ and $1\le r\le 20$ for the Prandtl numbers $\mathrm{Pr}=0.1$ and 0.2 by considering three horizontal aspect ratios ($\Gamma$): $\frac{1}{2}$, 1 and 2. In the absence of the magnetic field, the convection starts in the form of steady rolls including the one parallel to the $x$-axis. As the oblique horizontal magnetic field is switched on at an angle $\varphi \in (0^{\circ },90^{\circ }]$ with the $x$-axis, it is observed that the Lorentz force generated by the component of the magnetic field transverse to the axis of the convection rolls inhibits convection. Thus, with the application of the magnetic field, the convection is suppressed and restarts for a higher Rayleigh number in the form of steady convection rolls. The rolls can be oriented at angles 0° (steady parallel rolls, SPR) or 45° (steady oblique rolls, SOR${}^{+}$) or 135° (steady oblique rolls, SOR${}^{-}$) with the $x$-axis depending on the choices of the parameters. A rich bifurcation structure consisting of standing and traveling flow patterns associated with these steady flow patterns for higher values $r$ is investigated in detail. The oscillatory instability of the steady rolls is found to scale as $Q^{\alpha }$ with two distinct exponents, one each for weaker and stronger magnetic fields. The investigation reveals that for a given set of values of $Q$ and $\mathrm{Pr}$, the heat transfer is inhibited with the increase of $\varphi$.