- Liquid metal magnetohydrodynamic flow driven by a system of rotating permanent magnets in a container of orthogonal cross-section has been studied. The main objective of the work is to research the impact of magnetic forcing parameters (magnetic field value, magnets arrangement, and angular velocity of their rotation) on the generated hydrodynamic structures and flow modes. On this basis, we contemplate realizing required flow features by setting certain parameters of the driving magnetic system. A numerical study of the problem in the induction-free approximation without taking into account the effect of the variable component of electromagnetic force is presented. The parameters of spin-up modes and steady-state flow regimes have been calculated by three-dimensional direct numerical simulation based on COMSOL Multiphysics 4.3a software and experimentally verified on a specially designed setup using noninvasive Doppler ultrasound technique.