SINDy Modeling of Velocity and Magnetic Fields Interactions in the Three-Meter Liquid Sodium Spherical Couette Experiment

The 3-m experiment is a spherical Couette device designed to understand the dynamo action that generates the geomagnetic field, a process through which a magnetic field is amplified and sustained by rotating, convecting, and conducting fluid. The experiment consists of two concentric and independently rotating spherical shells filled with liquid sodium in between. The radii of the inner (0.51m) and outer (1.46m) spheres are chosen for a radius ratio dimensionally similar to Earth’s core. We measure the radial component of the magnetic field with 31 Hall sensors located on the outer sphere, the azimuthal, and the cylindrical radial components with four Hall sensors inserted into the liquid sodium through one instrumentation port. The radial magnetic field measurements are presented in terms of Gauss coefficients up to degree and order of four. Laboratory models of the geodynamo such as our 3-m system have yet to allow direct measurements of velocity fields within the turbulently flowing metal. The Sparse Identification of Nonlinear Dynamics (SINDy) is a technique to discover dynamic systems models from data. We produce SINDy models of the spherical Gauss coefficients, which are interpreted approximately based on Bullard and Gellman-type interactions, thus allowing us to understand the interactions between the fluid velocity fields and the magnetic fields.