Geomagnetic signatures of the slurry F-layer inferred from dynamo simulations

Abstract

Seismic observations indicate that the lowermost portion of Earth's liquid core is density stratified. The existence of this so-called F-layer challenges classical theories of core dynamics, where the geodynamo process that generates Earth's main magnetic field is assumed to be powered by heat and light element release at the inner core boundary. The seismically-inferred thickness, density, and velocity anomaly can be reproduced by a dynamical model that represents the F-layer as a two-phase two-component slurry on the liquidus, with a ``snow'' of solid iron particles falling through a quasi-static iron-oxygen liquid. Here, we present the first fluid dynamical simulations of thermochemically driven rotating convection and dynamo action that include a simple representation of the stratified slurry F-layer at the base of the spherical shell geometry. We show that the F-layer can create a barrier to columnar quasi-geostrophic flow, which is expressed near the core surface as a migration of peak radial and azimuthal flow speeds to lower latitudes as the thickness and stratification strength increase. In dynamo simulations, this effect induces polar minima in the radial magnetic field at the outer boundary ($B_r$) that strengthen and deepen with increasing stratification, and peaks in latitudinal profiles of $B_r$ moving to lower latitudes with reduced temporal variability. The geomagnetic signature of the F-layer is most prominent in time-averaged $B_r$, when resolved to at least spherical harmonic degree 5, and a trend of increasingly negative zonal degree 3 and 5 Gauss coefficients as the F-layer thickness and stratification strength increase. Our results suggest that an F-layer thickness of 600~km is incompatible with geomagnetic observations and favour weak stratification (normalised Brunt-Väisälä frequency $<1$) and a layer $<400$~km thick.

Figures (12)

• Figure 1: Pseudo isometric plot of instantaneous $u_r$ (top row), time and azimuthal average of $u_\phi$ (middle row), and time and azimuthal average of $\mathcal{N}^2$ (bottom row). Columns show four simulations: C02 ($\mathrm{Ra}_{T} = 55 \times 10^6;\, C_{\mathrm{i}}^{\prime}=-0.4725$), C18 ($\mathrm{Ra}_{T} = 55 \times 10^6;\, C_{\mathrm{i}}^{\prime}=10$), C19 ($\mathrm{Ra}_{T} = 12 \times 10^7;\, C_{\mathrm{i}}^{\prime}=10$), C34 ($\mathrm{Ra}_{T} = 12 \times 10^7;\, C_{\mathrm{i}}^{\prime}=100$). In the bottom row, the blue line denotes the iso-contour for $\partial C/\partial r= 0$, and the light blue area denotes the stable region with $\mathcal{N}^2>0$. Vertical dotted lines indicate the tangent cylinder of the inner core. Black dashed lines show the radius for which $\mathcal{N}^2= 0$ when averaged in time, $\phi$ and $\theta$, white dashed lines correspond to the radius $r_\mathrm{s}$ in the reference state.
• Figure 2: Radial profiles of the dimensionless Brunt-Väisälä ($\mathcal{N}^2$) (a, b, c), of the square of radial velocity ($u_r^2$) (d, e, f), and of the square of azimuthal velocity ($u_\phi^2$) (g, h, i). Each colour denotes a different value of $C_{\mathrm{i}}^{\prime}$. Columns from left to right correspond to $\mathrm{Ra}_{T}=90 \times 10^5$, $55 \times 10^6$ and $12 \times 10^7$, respectively. For comparison, $\mathcal{N}^2$ is normalised by its absolute value at the inner core boundary (where it is maximum and set by the imposed by $C_{\mathrm{i}}^{\prime}$). Vertical dotted lines denote the radius $r_\mathrm{s}$ in the reference state. In the middle and right columns, 4 simulations correspond to the ones shown in Fig.\ref{['fig:nonmag_merid']}.
• Figure 3: Profiles of $u_r$ (a) and $u_\phi$ (b) as a function of co-latitude at a radius just below the outer core boundary (i.e., below the boundary layer which is defined by a local maximum of horizontal velocity $\sqrt{\vec{u}_h^2}$, near the core mantle boundary). Plotted velocities are normalised by their respective maximum value, and for different values of $C_{\mathrm{i}}^{\prime}$, a vertical offset is applied to each case to introduce visual separation of the profiles. For these thermochemical simulations, $\mathrm{Ra}_{T}$ is $55 \times 10^6$. Vertical dotted lines denote the tangent cylinder. Red dots indicate the position of the minimum of $u_r$ (a), which corresponds to a down-welling outside the TC, and the position of the minimum of $u_\phi$ (b), which corresponds to westward flow outside the TC. Dashed black and solid brown lines correspond to simulations C02 and C18 seen in Fig.\ref{['fig:nonmag_merid']}).
• Figure 4: Co-latitudinal distance between the minimum of $u_r$ and the tangent cylinder of the inner core as a function of the thickness of the stable F-layer for simulations with $\mathrm{Ra}_{T}= 55 \times 10^6$. Filled and empty circles denote dynamo and thermochemical simulations, respectively. Triangles, squares, and upside-down triangles denote source radius $r_s= 0.63,\, 0.83,\, 1.03$, respectively. Thin and thick circles denote no-F-layer simulations (with $r_s= 0$) for two different inner core radii ($r_\mathrm{i}=0.538\textrm{ or }\, 0.83$), respectively. Six colours show the different values of the strength of the stratification $C_{\mathrm{i}}^{\prime}$. The black dashed line denotes the position of the tangent cylinder of the F-layer relative to the inner core tangent cylinder. Dotted lines highlight the effect of varying $C_{\mathrm{i}}^{\prime}$ with all other parameters fixed.
• Figure 5: Time-averaged radial magnetic field (normalised by its maximum) at $r_\mathrm{o}$ truncated at $\ell_{\rm max}=14$. (a) No F-layer (case DC02), (b) F-layer (case DC05) with $C_{\mathrm{i}}^{\prime}=20$ and (c) F-layer (case DC08) with $C_{\mathrm{i}}^{\prime}=100$. DC05 and DC08 have $\mathcal{N}^2_\mathrm{i}=0.34$ and $H_\mathrm{F}=389$ km, and $\mathcal{N}^2_\mathrm{i}=2.06$ and $H_\mathrm{F}=612$ km, respectively. All other parameters are fixed: $\mathrm{Ra}_{T}=12 \times 10^7$, $r_{s}=0.83$. The red, orange, and blue circles in the right-hand panel mark the tangent cylinder, F-layer radius determined by the $\mathcal{N}^2 = 0$, and the radius $r_\mathrm{s}$ in the reference state. Time has been rescaled to dimensional units using the magnetic diffusion time $D^2/\eta$ with $\eta = 1.6$ m$^{2}\,\textrm{s}^{-1}$.