Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces

Abstract

The response to librational forcing of a cube in rapid rotation about a diagonal axis is explored. In this orientation, the faces of the cube are all oblique to the rotation axis. The system supports inertial waves, which predominantly comprise beams emitted from the edges and vertices of the cube. Which ones emit and the resulting complicated pattern of three-dimensional reflections and subsequent focusing depend on the libration frequency. Direct numerical simulations of the Navier–Stokes flows with no-slip boundary conditions at low Ekman number ( $\text{E}=10^{-7}$ ) and small libration amplitude ( $\unicode[STIX]{x1D716}=10^{-7}$ ) exhibit complicated spatio-temporal structure that is remarkably well described by considerations of the inviscid reflections of wavebeams over the whole range of libration frequencies from zero to twice the mean rotation rate of the cube.