Transitions in electromagnetically-driven 2D flows with random forcing configurations

Two-dimensional (2D) flows offer a convenient platform for testing new theoretical approaches for predicting turbulent flow. Compared to 3D flows, 2D flows have faster numerical simulations and are less technically challenging to measure experimentally. We present a combined numerical and experimental study of quasi-2D flows in a shallow electrolyte layer driven by Lorentz forces produced by electric current interacting with a magnetic field generated by a random array of permanent magnets. The simulations are based on a 2D model which is derived by depth-averaging the three-dimensional Navier-Stokes equations. Ensembles of simulations and experiments are carried out with different random magnet arrangements to study the transitions the flow undergoes as the forcing is increased. These transitions are sensitive to the forcing profile which varies with different magnet arrangements. In this work, we predict flow dynamics for different magnet arrangements using machine learning based algorithms, including physics-informed neural networks (PINNs), and present preliminary results comparing different approaches. Our research will provide a foundational stepping stone toward machine learning-based predictions of (quasi-2D) geophysical flows, 3D turbulence, and more.