Sloshing dynamics of a viscous liquid in a spinning horizontal cylindrical tank

The natural frequencies and the slosh dynamics are obtained numerically for a viscous liquid in a partially filled spinning horizontal cylindrical tank. The tank spins with constant angular velocity around its axial direction and is placed perpendicularly to its rotational axis in an outer gravity field. The fundamental slosh frequencies are obtained for both longitudinal and transverse modes as function of filling level, viscosity and gravity acceleration. For sufficient high angular velocities the phenomenon of second-harmonic generation is observed in the response spectrum.