This study aims to investigate the intricate interaction between fluid flow and magnetic fields, known as magnetohydrodynamic (MHD) phenomena, within a hemispherical container filled with conducting gallium–indium–tin (Ga-In-Sn) liquid. The primary objective is to explain the influence of the external magnetic field and electric current intensities on the flow structure. Novel insights into the emergence of Lorentz forces that drive the flow dynamics are pursued by varying these parameters. The motivation for this investigation is rooted in the desire to deepen our understanding and uncover new insights into magnetohydrodynamic (MHD) phenomena within a specific experimental setup. Specifically, we aim to understand how swirl velocity is generated and altered by fluctuations in magnetic field strength and electric current intensity within the system. Our investigation reveals a transformation in the flow pattern in a hemispherical pool as the magnetic field strength increases while maintaining a constant electric current intensity. Sequential transformations from a rope tornado to a tornado, cyclone, and finally an inverted tornado are observed, shedding light on the complex behavior of the system. On the other hand, under fixed external magnetic field conditions, it is observed that, as the electric current intensifies, the flow pattern evolves from a tornado to a rope tornado or from a cyclone to a tornado. Furthermore, once the electric current intensity exceeds a specific threshold, the flow pattern remains unchanged, providing valuable insights for process optimization and control. This study contributes to a deeper understanding of MHD phenomena and offers practical implications for optimizing processes such as electroslag remelting (ESR) and vacuum arc remelting (VAR) that involve a similar hemispherical pool of conductive liquid. The simulation results are validated against experimental measurements, ensuring the reliability and accuracy of our findings.