A study of the critical layer in a rotating liquid payload

The unsteady motion of a fluid which fills a spinning cylinder is considered. Spin-up of the fluid is the basic flow which is perturbed. Non-axisymmetric, viscous perturbations are used to study the wave motion and critical layer. The frequencies and decay rates are determined by the eigenvalues of the system of perturbation equations. For large time the fluid approaches solid body rotation; for this state there is no critical layer and the eigenvalue problem is considerably simpler. The critical layer always exists for small time; it ceases to exist at a time which depends on the parameters of the basic flow and the wave motion. Time histories of the eigenvalues and of the critical layer are given for two cases and two radial modes. The effects of the critical layer on the eigenfunctions and the phase of the velocity are presented. Comparison with the experiment is discussed.