The dependence of inertial oscillation frequency on time since a cylindrical container began rotating from rest is established experimentally for several axially symmetric modes of oscillation. The oscillations were excited by including a sinusoidal perturbation in the rotation speed of the container which served to establish an exchange of fluid between the viscous boundary layers and the interior. The interior is set into oscillation by the boundary layer flow and the resulting axial pressure differences are used to establish the amplitude of the inertial oscillation.

This research has been primarily concerned with the excitation and detection of inertial waves in a fluid contained in a rotating cylindrical cavity during spin-up of the fluid from rest. Application of this work is to the study of fluid filled projectiles and their stability in free flight. It is well known that a projectile containing fluid will be subject to instability if its nutational frequency is near one of the eigenfrequencies of the contained fluid. Our work has centered on finding these time dependent eigenfrequencies for a fluid which completely fills a cylindrical cavity. Also of interest in the application of our work is the rate at which these waves decay once they are excited during the spin-up period. Included in our experimental work was a study of decay rates for several inertial waves during spin-up from rest. (Author).

For application to liquid-filled shell problems, the natural frequencies and decay rates of oscillations of liquids during spin-up in filled rotating cylinders are calculated. In this first part only the fully spun-up flow, i.e., solid-body rotation, is considered. Nevertheless, this part describes in detail the method of solution for the general case of spin-up, and presents results which check with experimental and previous theoretical data closely enough to confirm the reliability of the computational procedure. Data are shown which illustrate the variation of the eigenfrequencies of a disturbance mode with Reynolds number and aspect ratio of the cylinder. This work treats the viscous perturbation equations for flow of a rotating fluid. An eigenvalue problem results, defined by a sixth-order system which is integrated using the orthonormalization technique. (Author).