Oscillations of a liquid in a rotating cylinder. Part 2: Spin-up

The unsteady motion of a fluid which fills a cylindrical container in a spinning projectile is considered. The spin is imparted impulsively to the cylinder and spin-up of the fluid is the basic flow which is perturbed to study the waves in the rotating fluid. The core flow is perturbed, not the Ekman layer flow. This is called the spin-up eigenvalue problem which is solved with modal solutions. Viscous perturbations are needed because of the boundary layer and critical layer. A numerical method of solution is given and several results shown. There are two times at which projectile instability might occur. The results of the theory and method are validated by comparison with experimental results.