Effect of oblique horizontal magnetic field on convection rolls

Abstract

We investigate the effect of external horizontal magnetic field applied on the convection rolls obliquely (at an angle $ϕ$ 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 ($\mathrm{Q}$) and the reduced Rayleigh number $r$ (ratio of Rayleigh number to critical Rayleigh number), are varied in the ranges $0 \leq \mathrm{Q} \leq 1000$ and $1 \leq r \leq 20$ for the Prandtl numbers $\mathrm{Pr} = 0.1$ and $0.2$ by considering three horizontal aspect ratios ($Γ$): $\frac{1}{2}$, $1$ 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 $ϕ\in (0^\circ, ~90^\circ]$ 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 in the form of steady rolls. 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 either be oriented along the $x$-axis (steady parallel rolls, SPR) or oriented at an angle $45^\circ$ (steady oblique rolls, SOR$^+$) with the $x$-axis depending on the choices of the parameters. A rich bifurcation structure with standing and traveling patterns emerges at higher $r$. The oscillatory instability of steady rolls scales as \( \mathrm{Q}^α\) with distinct exponents for weak and strong magnetic fields. Additionally, heat transfer decreases with increasing \( ϕ\) for given \( \mathrm{Q} \) and \( \mathrm{Pr} \).