Simulations of Axisymmetric Inertial Waves in a Rotating Container of Fluid

Coriolis accelerations in a rotating body of fluid produce restoring forces for disturbances that depart from solid-body rotation, resulting in wave-like motion known as inertial waves. This kind of behaviour can be important in geophysical and technological applications (e.g. planetary core dynamics, instabilities in spinning rocket fuel tanks). For simple container shapes and for solid-body rotations, the frequencies and mode shapes of inertia waves can be readily calculated following the assumptions of linearity and potential flow. Our simulations seek to recreate the classic experiments of Fultz (1959) in which inertial waves within a cylindrical container of spinning fluid were driven via an axially oscillating disk situated on the container axis. Fultz found that the mode shapes and frequencies observed matched the linear inviscid predictions well, although it was unclear how exact resonance was assessed. We have employed a spectral element DNS method to carry out axisymmetric simulations with dimensionless parameters chosen to match those of Fultz’s experiment, with varying cylinder geometries, and where the paddle motion was simulated by a fixed boundary within the fluid on which oscillatory boundary conditions were imposed. Resonance is assessed on the basis of maxima in the peak amount of flow kinetic energy for fixed paddle motion amplitude, or alternatively on the basis of minimum peak-to-peak force exerted on the paddle boundary. In general the mode shapes and resonance frequencies agree well with both the inviscid theoretical predictions and Fultz’s published results