The role of thermal buoyancy in stabilizing the axial dipole field in rotating two-component convective dynamos

Abstract

Two-component convection driven by both compositional and thermal buoyancy within the fluid core of a rapidly rotating planet produces a predominantly axial dipole field. In a dynamo driven by strong compositional buoyancy that by itself destabilizes the axial dipole, the addition of relatively weak thermal buoyancy establishes the dipole field through the spontaneous generation of slow magnetostrophic waves produced by balances between the magnetic, buoyancy and Coriolis (MAC) forces at several locations within the core. A substantially higher compositional buoyancy is then required to trigger polarity transitions, since the dipolar regime is extended in two-component convection, as predicted by a linear magnetoconvection model that analyses the long-time evolution of a density disturbance. The existence of the axial dipole also prescribes a lower bound for the fraction of the total power contributed by thermal buoyancy, $\approx$ 10%, above which the two-component dynamo with homogeneous boundary heat flux lies deep within the dipolar regime. Two-component convection has implications for Earth's core dynamo: dominant compositional buoyancy ensures the observed polar circulation speed, and a large heterogeneity in the lower-mantle heat flux induces magnetic field excursions and occasional polarity reversals.

Figures (12)

• Figure 1: Initial state of a density perturbation $\rho^{\prime}$ in an unstably stratified fluid subject to background rotation $\bm{\varOmega} = \varOmega \hat{\bm{e}}_z$, a uniform magnetic field $\bm{B}_0 = B_0 \hat{\bm{e}}_y$ and gravity $\bm{g} = -g \hat{\bm{e}}_y$, in Cartesian coordinates $(x, y, z)$.
• Figure 2: (a) Absolute values of the squared fundamental frequencies are shown as functions of $Ra_{\ell}^C$ for one-component compositional convection. The dashed vertical line indicates the value of $Ra_{\ell}^C$ at which the slow MAC wave frequency $\omega_s$ approaches zero, corresponding to the condition $\omega_{M} \approx \omega_{A}$. (b) Ratio of $B_0^2$ at the slow MAC wave suppression points for one- and two-component convection, plotted against the ratio of their local Rayleigh numbers. The subscript ' 1' for $B_0^2$ and $Ra_\ell$ denotes the values for one-component compositional convection. The thermal power ratios at these suppression points for the two-component models are also indicated. (c) Variation of the square of the axial velocity of the slow MAC waves $u_{z,s}^2$ and (d) square of the axial induced magnetic field $b_{z}^2$ as a function of $Ra_{\ell}$ and $|\omega_{A}/\omega_{M}|$ for one- and two-component convection. The colour codes are the same as in (b). The parameters used are $E_\eta = 1 \times 10^{-5}$ and $t/t_\eta = 7.2 \times 10^{-3}$.
• Figure 3: Contour plots of the square of the axial ($z$) velocity of the slow ($s$) MAC waves on the $y$--$z$ plane at $x = 0$, for single-component (a--b) and two-component (c--d) convection with $f^T = 5\%$. The corresponding values of $Ra_\ell^C$ ($|\omega_A/\omega_M|$) are (a) 70 (0.3), (b) 440 (0.96), (c) 444 (0.3) and (d) 1900 (0.97). The other parameters are $E_\eta = 1 \times 10^{-5}$ and $t/t_\eta = 7.2 \times 10^{-3}$.
• Figure 4: Evolution of the dipole colatitude and the ratio of the root mean square value of the axial magnetic field ($\bar{B}_{10}$) to the root mean square value of the total magnetic field ($\bar{B}$) with magnetic diffusion time. Panels (a) and (b) show two dynamo simulations initiated from a seed magnetic field for (a) $Ra^T = 0$, $Ra^C = 3000$ and (b) $Ra^T = 220$, $Ra^C = 3000$. Panel (c) corresponds to a simulation initiated from a reversing state with $Ra^T = 0$, $Ra^C = 3000$, where at time ' A' (dashed vertical line) thermal buoyancy with $Ra^T = 220$ is introduced, contributing $\approx 20\%$ of the total convective power. The dotted vertical lines in panels (b) and (c) indicate the time of dipole formation. (d) & (e): Contours of the radial magnetic field at the outer boundary at time ' B' and ' C' are shown. The dynamo parameters are $E = 6 \times 10^{-5}$, $Pm = Sc = 5$, and $Pr = 0.5$.
• Figure 5: Helicity isosurfaces (contour level $\pm 7 \times 10^5$) at times ' A', ' B' and ' C' (marked in figure \ref{['tiltfdip']} c) for $l \leq 17$. The other dynamo parameters are $Ra^T=220$, $Ra^C=3000$, $E = 6 \times 10^{-5}$ and $Pm = Sc = 5$.