Eigenfrequencies of inertial oscillations in a rotating fluid via a numerical simulation

An understanding of the instability of a spinning liquid-filled projectile requires a knowledge of the wave system in the rotating fluid. The axisymmetric wave system in a cylinder is studied by a numerical simulation; the particular case of perturbed solid body rotation is treated. Finite-difference solutions to the Navier-Stokes equations provide data from which wave frequencies and damping can be extracted using Fourier transform and digital filter techniques. The frequency and damping are compared with the values computed from a linearized eigenvalue analysis. It is found that the latter can be used with confidence for Reynolds number as low as 1,000.