Nonlinear flows driven by libration in a rotating half cone

We investigate the problem of nonlinear oscillatory flow of homogeneous fluid with viscosity $\nu$ confined in a half cone that rotates rapidly about a fixed axis with angular velocity ${\Omega}_0 $ and that undergoes weak longitudinal libration with amplitude $\epsilon {\Omega}_0$ and frequency $\hat{\omega} {\Omega}_0$, where $\epsilon$ is the Poincar\'{e} number and $\hat{\omega} $ is dimensionless frequency with $0< \hat{\omega}<2$. Two different methods are employed in this investigation: experimental studies and direct numerical simulation using a finite element method.