Numerical simulations and proper orthogonal decomposition are used to identify the fundamental mechanism of magnetic field reversals in the von Kármán sodium experiment with ferromagnetic impellers close to contrarotation. Two numerical solvers are used and agree well on the resulting mechanism. The reversal dynamics rely on the interaction of four dominant axisymmetric modes: the magnetic dipole mode $D$ and quadrupole mode $Q$, as well as the zonal velocity mode $V$ and the $R_{\pi }$-symmetric mode $U$. This hierarchy leads to a reduced-order $DQVU$ Galerkin model derived from the magnetohydrodynamic equations. The model improves upon previous three-variable versions by adding a velocity variable $U$ and related interactions, which are shown to be essential for reproducing the main features of magnetic field dynamics.

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• Dynamo theory
• Flow instability
• Magnetohydrodynamic turbulence
• Direct numerical simulations
• Large eddy simulations