Surface Oscillations of a Rotating Liquid

The free oscillations of a fluid in a rotating, axially symmetric container are investigated under the assumption that the equilibrium motion of the fluid be a rigid-body rotation. Gravitational forces are neglected. The resulting boundary-value problem leads to an elliptic or hyperbolic partial differential equation, depending on the frequency/angular velocity ratio. The problem is solved for a cylindrical container and discussed exhaustively. Due to the Coriolis force, there exist modes with the radial velocity component vanishing inside the fluid (“nodal cylinders”), besides the usual nodes in axial and azimuthal direction. The oscillations in the neighborhood of critical container dimensions are analyzed. Numerical results are presented in graphs.