Coherent flow structures and magnetic field patterns in rotating spherical shell convective dynamos: A data-driven approach

The Earth's outer core dynamics involve convective fluid motion generating an observable geomagnetic field. The velocity and magnetic fields exhibit characteristic spatiotemporal features possessing geophysical significance for which extensive datasets are available from direct observations and computational simulations. This study demonstrates the robustness of proper orthogonal decomposition (POD), a data-driven technique, in detecting prominent and relevant features in these datasets. Improvising on previous practices, the POD efficiently detects infinitesimal instabilities at the onset of convection, providing an accurate and objective methodology to determine the convective threshold, even for heterogeneous buoyancy forcing. Time evolution of paired, phase-shifted modes efficiently reconstructs the azimuthally drifting of traveling wave instabilities. Simultaneously reduced order modeling of velocity components clearly distinguish the equatorial and polar coherent flow structures. Supercritical convection-driven magnetic field data over long periods, generated using numerical simulations, produce dominant modes that are more accurately representative of time-averaged patterns than geocentric axial dipole patterns. Moreover, the quantitative significance of the dominant modes determines the extent of dimensional reduction complementing established diagnostics for dipolarity. Finally, analysis of observational geomagnetic field data reveals long-lived dominant patterns influenced by thermal core–mantle interaction consistent with numerical models employing tomographic heat flux boundary conditions in present as well as previous studies.