On the motion of a compressible fluid in a rotating cylinder

The secondary flow of an incompressible fluid and of a perfect gas in a rotating cylinder is considered, by applying a linearised analysis to a small perturbation on the isothermal state of rigid body rotation. In chapter 2 we apply an order of magnitude consideration to the linerised dimensionless conservation equations. In section 2.1 the incompressible fluid is treated assuming a small Ekman number E based on the radius of the cylinder. The importance of the various viscous terms is investigated increasing the length-to-radius ratio L from unit magnitude to infinity. As a result, three types of flow can be distinguished which correspond to the L-ranges: E ~ / ~