  This study presents numerical simulations and experiments considering the
flow of an electrically conducting fluid inside a cube driven by a rotating
magnetic field (RMF). The investigations are focused on the spin-up, where a
liquid metal (GaInSn) is suddenly exposed to an azimuthal body force generated
by the RMF, and the subsequent flow development. The numerical simulations rely
on a semi-analytical expression for the induced electromagnetic force density
in an electrically conducting medium inside a cuboid container with insulating
walls. Velocity distributions in two perpendicular planes are measured using a
novel dual-plane, two-component ultrasound array Doppler velocimeter (UADV)
with continuous data streaming, enabling long term measurements for
investigating transient flows. This approach allows to identify the main
emerging flow modes during the transition from a stable to unstable flow
regimes with exponentially growing velocity oscillations using the Proper
Orthogonal Decomposition (POD) method.
  Characteristic frequencies in the oscillating flow regimes are determined in
the super critical range above the critical magnetic Taylor number $Ta_c
\approx 1.26 \times 10^5$, where the transition from the steady double vortex
structure of the secondary flow to an unstable regime with exponentially
growing oscillations is detected.
  The mean flow structures and the temporal evolution of the flow predicted by
the numerical simulations and observed in experiments are in very good
agreement.
