  Interfacial waves arising in a two-phase swirling flow driven by a
low-frequency rotating magnetic field (RMF) are studied. At low RMF
frequencies, of the order of 1-10 Hz, the oscillatory part of the induced
Lorenz force becomes comparable to the time-averaged one, and cannot be
neglected. In particular, when free surfaces or two-liquid stably stratified
systems are subject to a low-frequency RMF, induced pressure variations
necessarily excite free-surface/interfacial waves, which can improve mass
transfer in different metallurgical processes. In this paper, we formulate a
linear wave model and derive explicit analytical solutions predicting
RMF-driven wave patterns that closely resemble hyperbolic paraboloids. These
theoretical predictions are validated against experiments based on a
non-intrusive acoustic measurement technique, which measures liquid-liquid
interface elevations in a two-phase KOH-GaInSn stably stratified system. A good
quantitative agreement is found for non-resonant wave responses in the vicinity
of the fundamental resonance frequency. The experiments reveal the additional
excitation of several higher harmonics superimposing the fundamental wave
oscillation, which are visible even in the linear wave regime.
