Predicting Magnetic Fields for the Three-Meter Spherical Couette Experiment*

The magnetohydrodynamics of Earth has been explored through experiments, numerical models, and machine learning. The interaction between Earth's magnetic fields and its outer core is replicated in a laboratory using the three-meter spherical Couette device filled with liquid sodium driven by two independently rotating concentric shells and an external dipole magnetic field. Recently, this experiment has been modified to come closer to replicating the convection-driven flows of Earth. The experiment takes sparse measurements of the external magnetic field. XSHELLS solves the coupled Navier-Stokes and induction equations numerically to give the full velocity and magnetic field up to a turbulent limit due to resolution. In these studies, we compare the experimental magnetic field measurement with the extrapolated surface magnetic field measurements in simulations using principal component analysis by matching all parameters but the level of turbulence. Our goal is to see if (i) the eigenvectors corresponding to the largest eigenvalues are comparable and (ii) how then the surface measurements of the simulation couple with the internal measurements, which are not accessible in the experiment. These studies provide insight on the measurements required to predict Earth's magnetic field.