Inertial waves and modes excited by the libration of a rotating cube

We report experimental measurements of the flow in a cubic container submitted to a longitudinal libration, i.e., a rotation modulated in time. Velocity fields in a vertical and a horizontal plane are measured in the librating frame using a corotating particle image velocimetry system. When the libration frequency σ₀ is smaller than twice the mean rotation rate, Ω₀, inertial waves can propagate in the interior of the fluid. At arbitrary excitation frequencies σ₀ < 2Ω₀, the oscillating flow shows two contributions: (i) a basic flow induced by the libration motion, and (ii) inertial wave beams propagating obliquely upward and downward from the horizontal edges of the cube. In addition to these two contributions, inertial modes may also be excited at some specific resonant frequencies. We characterize in particular the resonance of the mode of lowest order compatible with the symmetries of the forcing, noted [2,1,+]. By comparing the measured flow fields to the expected inviscid inertial modes computed numerically [L. R. M. Maas, “On the amphidromic structure of inertial waves in rectangular parallelepiped,” Fluid Dyn. Res. 33, 373 (2003)] https://doi.org/10.1016/j.fluiddyn.2003.08.003, we show that only a subset of inertial modes, matching the symmetries of the forcing, can be excited by the libration.