The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions

Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual timescale range where Earth's core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth's core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth's core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfven torsional waves, and non-axisymmetric, quasi-geostrophic Alfven and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal timescales, thereby providing a constraint on the extent of the f(-4) range observed in the geomagnetic frequency power spectrum. As the model approaches Earth's core conditions, this spectral broadening arises because the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also extract an increasing amount of energy from the underlying convection as their key timescale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion timescale to the Alfven timescale, highlighting the dominance of Alfven waves in the signal and the stabilizing control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth's core conditions supports the detectability of Alfven waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.

Automated summary

The study uses a geodynamo simulation model to analyze the interactions between slow convective motions and fast hydromagnetic waves in Earth's core, identifying three classes of fluid dynamic and hydromagnetic waves. These waves enrich and flatten the energy density spectrum of geomagnetic acceleration at decadal timescales, providing constraints on the observed frequency power spectrum.