Role of partial stable stratification on the onset of rotating magnetoconvection with a uniform horizontal field

TL;DR

This study investigates how partial stable stratification modifies the onset of rotating magnetoconvection under a uniform horizontal magnetic field in a 2D plane-layer model. By combining linear stability analysis and direct numerical simulations across regimes of rotation ($E$), magnetic strength ($\Lambda$), diffusivity ratio ($q$), and stratification height ($h$), the authors derive local scaling laws for the critical Rayleigh number $Ra_c$ and the critical wavenumber $k_c^x$, and quantify the depth of convective penetration into the stable layer. Key findings show that stable stratification lowers $Ra_c$, raises $k_c^x$, and enables penetrative convection whose extent is curtailed by stronger magnetic fields and faster rotation; the effects are strongest in rotation-dominated regimes and weaken under strong magnetism, with pronounced diffusion-dependence (notably at $q=10$). The results yield regime-dependent scaling laws, reveal how stratification interacts with rotation and Lorentz forces, and have implications for core dynamics and geomagnetic variability in planetary interiors. Overall, the work advances understanding of how a stably stratified top layer can influence the onset and structure of convection in rapidly rotating, magnetized fluids relevant to planetary dynamos.

Abstract

To explore the combined effects of partial thermal stable stratification and magnetic back-reaction within Earth's tangent cylinder, we study the onset of magnetoconvection in an infinite plane layer subject to horizontal magnetic field imposed perpendicular to the rotation axis. Three stratification models-fully unstable, weakly stable, and strongly stable-are considered to examine their influence on convective onset. A broad range of rotation rates and diffusivity ratios captures the effects of rotation and thermal-to-magnetic diffusivity contrast, while magnetic back-reaction is analyzed by varying the imposed magnetic field strength. To assess the impact of stratification on convection threshold and flow structure, we derive local scaling laws for critical onset parameters and compute penetration percentages to quantify convective intrusion into the stable layer. Results show that stable stratification promotes earlier onset and smaller-scale flows, with stronger effects in rotation-dominated regimes-hallmarks of penetrative convection. In weak magnetic fields, faster rotation enhances columnarity and intensifies stratification effects while delaying onset. Under strong magnetic fields, thicker rolls persist even at rapid rotation, with limited but noticeable penetration into the stable layer. Magnetic stabilization is more effective at low to moderate diffusivity ratios but weakens at high diffusivity ratio. Penetration decreases with stronger magnetic fields and rotation, especially under strong stratification, but varies non-monotonically with rotation in weak stratification and magnetic regimes. These findings highlight the complex interplay among stratification, rotation, and magnetic field strength in setting the onset and structure of rotating convection relevant to planetary interiors.

Figures (12)

• Figure 1: Schematic diagram of 2-D rotating plane layer convection model subject to background magnetic field ($\mathbf{B}^*$), background rotation ($\bm{\Omega}$) directed in opposite direction of gravity ($\mathbf{g}$), and background temperature profiles, ($a$) for the reference case without thermal stable stratification (temperature profile: blue solid line), ($b$) for the case of partial stable stratification (temperature profile: red solid line).
• Figure 2: (a) Background temperature profile($T^*$ vs. $z$), (b) Background axial temperature gradient profile ($\frac{\partial T^*}{\partial z}$ vs. $z$), and (c) Variation of normaliszed buoyancy frequency with interface height ($h$).
• Figure 3: Axial velocity perturbation ($u_z^{\prime}$) contours (a)-(d) for $h = \infty$, (i)-(l) for $h = 0.8$, and (q)-(t) for $h = 0.6$, respectively. Temperature perturbation contours (e)-(h) for $h = \infty$, (m)-(p) for $h = 0.8$, and (u)-(x) for $h = 0.6$, respectively. The first column indicates the non-magnetic case at $\Lambda = 0$. The second, third, and fourth columns indicate increasing strength of background magnetic field as $\Lambda = 0.01, 1, 5$, respectively. Parameter regime is chosen as $E = 10^{-4}$, $q = 1 (Pr = Pm = 1)$.
• Figure 4: Variation of critical Rayleigh number, $Ra_c$, with Elsasser number, $\Lambda$, (a) for $E = 10^{-5}$, (b) for $E = 10^{-4}$, (c) for $E = 10^{-3}$ for different $h = \infty$ (Largest), $h = 0.8$ (Moderate), and $h = 0.6$ (Smallest). Variation of critical horizontal wave number, $k_c^x$, with Elsasser number, $\Lambda$, (a) for $E = 10^{-5}$, (b) for $E = 10^{-4}$, (c) for $E = 10^{-3}$ for different $h = \infty$ (Red), $h = 0.8$ (Green), and $h = 0.6$ (Blue) for $q = 0.01 (Pm = 0.005, Pr = 0.5)$.
• Figure 5: Variation of critical Rayleigh number, $Ra_c$, with Elsasser number, $\Lambda$, (a) for $E = 10^{-5}$, (b) for $E = 10^{-4}$, (c) for $E = 10^{-3}$ for different $h = \infty$ (Largest), $h = 0.8$ (Moderate), and $h = 0.6$ (Smallest). Variation of critical horizontal wave number, $k_c^x$, with Elsasser number, $\Lambda$, (a) for $E = 10^{-5}$, (b) for $E = 10^{-4}$, (c) for $E = 10^{-3}$ for different $h = \infty$ (Red), $h = 0.8$ (Green), and $h = 0.6$ (Blue) for $q = 1 (Pm = 1, Pr = 1)$.