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

TL;DR

This study experimentally investigates inertial waves and modes in a rotating cube subjected to libration, revealing how specific inertial modes are excited at resonant frequencies and how they propagate within the fluid.

Contribution

It provides the first detailed experimental characterization of inertial waves and modes excited by libration in a cubic container, including resonance phenomena and mode selection based on symmetry.

Findings

Inertial waves propagate obliquely from cube edges during libration.

Resonant inertial modes are selectively excited based on symmetry.

Comparison with numerical models confirms mode excitation conditions.

Abstract

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 $\sigma_0$ is smaller than twice the mean rotation rate $\Omega_0$, inertial waves can propagate in the interior of the fluid. At arbitrary excitation frequencies $\sigma_0<2\Omega_0$, 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, Fluid Dyn. Res. \textbf{33}, 373 (2003)], we show that only a subset of inertial modes, matching the symmetries of the forcing, can be excited by the libration.