The Null Dynamical Effect, and Some Frequency Spectra, of Resonant Inertial Pressure Waves in a Rapidly Rotating, Right Circular, Sectored Cylinder

Abstract

It is shown that inertial waves in the form of standing asymmetrical pressure waves can exist in an incompressible liquid in a rotating sectored cylinder in a rigid body (e.g., a top or a missile) executing a small amplitude gyroscopic motion about its center of mass. Some of the frequency spectra of these waves are presented along with the result that sectoring the cylinder into any number of equal sectors results in eliminating the destabilizing effect of these waves (i.e., the amplitude growth of the motion of the rigid container) when there is a “Stewartson” resonance between the frequency of one of the inertial modes and the frequency of the nutational component of the motion of the container. Experimental results are in reasonable agreement with the theory.