Predicting the magnetic field of the three-meter spherical Couette experiment

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The magnetohydrodynamics of Earth have been explored at the University of Maryland and the Institute of Geosciences in Grenoble, France through experiments, numerical models, and machine learning. The interaction between Earth's magnetic fields and its outer core is emulated 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, the experiment has undergone modifications to increase the helical flows in the poloidal direction to bring it closer to the convection-driven geodynamo flows of Earth. The experiment has 31 surface Hall probes measuring sparsely the external magnetic field. The numerical model, XSHELLS, solves the coupled Navier-Stokes and induction equations numerically to give a full picture of the internal velocity and magnetic field, however, it cannot resolve all the turbulence. In this thesis we aim to improve the prediction of magnetic fields in the experiment by performing studies both on experimental data and simulation data. First, we analyze the simulation data to assess the viability of using the measured external magnetic field to represent the internal dynamics of the velocity and magnetic field. These simulations also elucidate the internal behavior of the experiment for the first time. Next, we compare the experimental magnetic field measurements 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. Next, we perform several machine learning techniques to see the feasibility of using the current probe setup to predict the magnetic fields in time. In the second to last chapter, we assess the potential locations for magnetic field measurements. These studies provide insight on the measurements required to predict Earth's magnetic field.