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| Numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing are presented. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. The driving mechanism is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom endwalls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves. The system losses stability to a complicated three-dimensional flow when the sidewall oscillation displacement amplitude is of the order of the cylinder radius, but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques. |
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