Differentially rotating split-cylinder flow: Responses to weak harmonic forcing in the rapid rotation regime

The flow in a rapidly rotating cylinder is studied numerically. The cylinder is split in half, and the rapid rotation in the two halves is modulated harmonically with a small amplitude. We consider modulation frequencies ranging from zero to twice the background rotation frequency, so that the system supports inertial waves. The split in the cylinder at midheight provides a localized perturbation from which inertial wave beams emanate, but so too do the corners where the endwalls and the sidewall meet. There is no discontinuity in the boundary condition at these corners, but the thin modulated endwall and sidewall boundary layers meet at the corners, and this leads to a localized perturbation to the rapid background rotation. This interaction produces inertial wave beams that over wide parameter regimes are more intense than those from the split at the cylinder midheight. Due to finite viscosity and nonlinear flow conditions, the wave beams produce intricate patterns formed by constructive and destructive interference as they self-intersect and reflect off cylinder boundaries and the axis. These patterns are very sensitive to the modulation frequency. Additionally, a phase difference between the modulations of the two cylinder halves was imposed. The phase difference impacts the symmetries of the system and its response to the modulations. In particular, some low-order Kelvin modes are driven resonantly, and their selection depends not only on the frequency but also on the phase of the differential modulation.