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

TL;DR

This study addresses how partial stable stratification alters the onset of rotating magnetoconvection under a uniform axial magnetic field in a plane-layer setup. By performing DNS across a broad parameter space in rotation ($E$), magnetic back-reaction ($\Lambda$), diffusivity ratio ($q$), and SSL strength ($h$), the authors quantify critical thresholds ($Ra_c$, $k_c^x$), convective structures, symmetry breaking, and penetration depth ($\delta_N$). Key findings show that SSL promotes earlier onset, increases the dominant horizontal scale, and induces axial-symmetry breaking that weakens with stronger magnetic fields; penetration into the SSL is enhanced in the rotation-dominated regime and suppressed in the magnetically dominated regime, with critical Ekman numbers $E_c$ marking maximum penetration that depend on SSL strength. The results illuminate the interplay among rotation, magnetic fields, and stratification relevant to geophysical and astrophysical interiors, such as Earth's outer core and planetary dynamos, and provide scaling insights for onset under mixed diffusion regimes and SSL configurations.

Abstract

This study examines the onset of rotating magnetoconvection under an axially imposed magnetic field in the presence of partial thermal stable stratification. Three stratification models-fully unstable, weakly stable, and strongly stable-are analyzed across Ekman numbers $E = 10^{-3}, 10^{-4}$, and $10^{-5}$ (rotation rates) and Roberts numbers $q = 0.01, 1$ and $10$ (diffusivity ratios). Magnetic back-reaction is explored by varying the Elsasser number ($Λ$) from 0 to 10. Symmetry-breaking effects of stable layer are assessed via an asymmetry index. Additionally, local scaling laws are derived for onset parameters and convective penetration is quantified numerically. Results show that stable stratification promotes earlier onset and smaller-scale flows, with stronger effects in weak field regimes-hallmarks of penetrative convection. In weak magnetic fields, symmetry breaking is pronounced but weakens for strong field regime. Convective roll thickening peaks at $Λ= 1$, while columnarity persists in both weak and strong field regimes due to rotational constraints and elongation effects along imposed field direction, respectively. Magnetic stabilization is most effective at low to moderate values of $q$ but weakens in high $q$ regimes. Penetration depth is inversely related to the magnetic field strength and rotation rates, particularly under strong stratification, but varies non-monotonically with rotation in weakly stratified cases. In the non-magnetic limit, the critical Ekman number $E_c$, exhibiting maximum penetration effects, is obtained as $E_c = 10^{-4}$ for weak stable stratification and $E_c = 10^{-3}$ for strong stable stratification. Obtained results can provide insights into the complex interplay of various geophysical effects on planetary interiors.

Figures (11)

• Figure 1: Schematic diagram of 2-D rotating plane layer convection model subject to background magnetic field ($\mathbf{B}^*$) in vertical direction, 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) Buoyancy profiles and (b) vertical temperature gradient profiles for three stratification cases: fully unstable stratification ($h = \infty$), weakly stable stratification ($h = 0.8$), and strongly stable stratification ($h = 0.6$). Panels (c) and (d) show the basic state temperature field $T^*(x, z)$ and its vertical gradient $\frac{\partial T^*}{\partial z}(x, z)$, respectively, for the strongly stable stratification case ($h = 0.6$). The dashed line marks the interface between the unstable and stable layers at $z = 0.6$.
• 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: Axial profiles of time- and horizontally-averaged (a, b) axial velocity perturbation ($\langle \bar{u}^{\prime}_z \rangle$) and (c, d) temperature perturbation ($\langle \bar{T}^{\prime} \rangle$) for $E = 10^{-4}$ and $q = 1$. The left column (a, c) corresponds to the weak magnetic field regime ($\Lambda = 0.01$), while the right column (b, d) corresponds to the strong magnetic field regime ($\Lambda = 5$). Line colors indicate stratification strength: black — fully unstable stratification ($h = \infty$), blue — weak stable stratification ($h = 0.8$), and red — strong stable stratification ($h = 0.6$).
• Figure 5: Plots of the critical Rayleigh number ($Ra_c$) and horizontal wavenumber ($k_c^x$) as functions of $\Lambda$. Panels (a), (b), and (c) show $Ra_c$ vs. $\Lambda$ for $q = 0.01$, $q = 1$, and $q = 10$, respectively. Similarly, panels (d), (e), and (f) show $k_c^x$ vs. $\Lambda$ for the same values of $q$. Each marker represents a different rotational regime: filled circles for rapid rotation ($E = 10^{-5}$), filled diamonds for moderate rotation ($E = 10^{-4}$), and filled hexagons for slow rotation ($E = 10^{-3}$). Colors denote stratification strength: red for fully unstable stratification ($h = \infty$), green for weak stable stratification ($h = 0.8$), and blue for strong stable stratification ($h = 0.6$).