The influence of a stably stratified layer on the hydromagnetic waves in the Earth's core and their electromagnetic torques

TL;DR

This study addresses whether a stably stratified layer at the top of the Earth's outer core can modify hydromagnetic waves and their coupling to the mantle. Using a 3D spherical Boussinesq MHD model with a quadrupolar background field and a thin conducting mantle layer, the authors solve a linear eigenvalue problem via a spectral method to obtain wave modes and their damping, across dimensionless parameters such as $Ek$, $Le$, $Em$, $Pr$, and the stratification strength $\tilde{N}$. They find that interannual torsional Alfvén waves are only marginally affected by weak to moderate stratification, while decadal MAC-like waves can become trapped within the stable layer and exert viscous and electromagnetic torques on the mantle that greatly exceed neutrally stratified values; strong stratification, however, suppresses the radial magnetic signal at the CMB. These results place constraints on the possible strength of a top stable layer and emphasize the importance of core–mantle coupling for interpreting length-of-day and polar-motion signals, guiding future assessments of the layer’s thickness, diffusivities, and geomagnetic implications.

Abstract

Evidence from seismic studies, mineral physics, thermal evolution models and geomagnetic observations is inconclusive about the presence of a stably stratified layer at the top of the Earth's fluid outer core. Such a convectively stable layer could have a strong influence on the internal fluid waves propagating underneath the core-mantle boundary (CMB) that are used to probe the outermost region of the core through the wave interaction with the geomagnetic field and the rotation of the mantle. Here, we numerically investigate the effect of a top stable layer on the outer core fluid waves by calculating the eigenmodes in a neutrally stratified sphere permeated by a magnetic field with and without a top stable layer. We use a numerical model, assuming a flow with an m-fold azimuthal symmetry, that allows for radial motions across the lower boundary of the stable layer and angular momentum exchanges across the CMB through viscous and electromagnetic coupling. On interannual time-scales, we find torsional Alfvén waves that are only marginally affected by weak to moderate stratification strength in the outer layer. At decadal time-scales similarly weak stable layers promote the appearance of waves that propagate primarily within the stable layer itself and resemble Magneto-Archimedes-Coriolis (MAC) waves, even though they interact with the adiabatic fluid core below. These waves can exert viscous and electromagnetic torques on the mantle that are several orders of magnitude larger than those in the neutrally stratified case.

Figures (13)

• Figure 1: Illustration of the radial (a) and latitudinal (b) dependence of the background magnetic field $\boldsymbol{\mathbf{B}}_{0,r}$ determined by eq. \ref{['eq:B0']}. The left plot shows the field strength $\boldsymbol{\mathbf{B}}_{0,r}$ as a function of radius $r$ for an arbitrary choice of $\theta,\phi$, divided by its maximum value $\max_r|\boldsymbol{\mathbf{B}}_{0,r}|$. The right plot shows the field strength $\boldsymbol{\mathbf{B}}_{0,r}$ as a function of latitude $\theta$ for an arbitrary choice of $r,\phi$, divided by its maximum value. $\max_\theta|\boldsymbol{\mathbf{B}}_{0,r}|$
• Figure 2: Illustration of the radial profile of the Brunt-Väisälä frequency $N(r)$ determined by the stratification strength $N_0$, smoothness parameter $h$ and layer thickness $d$ in eq.\ref{['eq:BV_profile']}.
• Figure 3: Eigenvalue spectrum of the least-damped equatorially symmetric and axisymmetric ($m=0$) waves in a neutrally stratified core with $\mathrm{Ek} = 2 \times10^{-9}$, $\mathrm{Em} = 10^{-7}$, and $\mathrm{Le} = 10^{-3}$. Frequency $\omega$ on the $x$-axis and damping $\sigma$ on the $y$-axis are non-dimensional with characteristic time-scale $\tau_\mathrm{A}$. Dot colour gives the kinetic to magnetic energy ratio and differentiates between three branches of wave motion: orange for slow Magneto-Coriolis (MC) waves if the magnetic energy is dominant, blue for magnetically modified inertial waves (I) if the kinetic energy dominates and black for torsional Alfvén waves (TA) if the two energies are equal. The dashed line corresponds to $Q = |\omega|/2|\sigma| = 1$, waves above this line in the gray-shaded area have lower quality factors and waves below this line have higher quality factors.
• Figure 4: Meridonial cuts of the kinetic energy density in dimensionless units of the waves indicated with a star (a), square (b) and circle (c) in Figure \ref{['fig:kin2mag']}. Yellow and orange colours indicate regions with higher kinetic energy, while dark and purple colours indicate regions with lower kinetic energy.
• Figure 5: Viscous and electromagnetic torque produced by the least-damped equatorially symmetric axisymmetric waves in a neutrally stratified core with $\mathrm{Ek} = 2 \times10^{-9}$, $\mathrm{Em} = 10^{-7}$, and $\mathrm{Le} = 10^{-3}$. For each wave, depicted with a coloured marker, the torques $\mathit{\Gamma}_\nu$ and $\mathit{\Gamma}_\eta$ have been normalised using the r.m.s value of the wave induced radial magnetic field at the CMB. Light yellow colours and big markers (resp. dark purple colours and small markers) indicate higher normalised torques (resp. lower normalised torques).