The viscous flow inside a closed rotating cylinder of gas subject to periodic axial compression is investigated numerically. The numerical method is based on a spectral Galerkin expansion of the velocity field, assuming axisymmetry of the flow. If the forcing amplitude is weak and the angular forcing frequency is less than twice the rotation rate, inertial waves emanate from the corners, forming conical oscillatory jets which undergo reflections at the walls. Their thickness is O(E1/3), or O(E1/4) for particular forcing frequencies, where E is the Ekman number. For larger forcing amplitudes, the conical pattern breaks down. When the forcing frequency is resonant with a low-order inertial mode, the flow can undergo two types of parametric instabilities: a mode-triad resonance, and a subharmonic instability. The combination of both these mechanisms provides a possible route to quasiperiodicity of the flow.