Axisymmetric flow within a torsionally oscillating sphere

The flow of an incompressible Newtonian fluid inside a torsionally oscillating spherical cavity is considered. The three-dimensional Navier-Stokes and continuity equations are solved by means of a Galerkin projection spectral method, based on a second-order incremental fractional-step approach. Legendre and Jacobi polynomial expansions are used in the zenithal and radial directions, respectively. Axisymmetric solutions are sought for a relatively wide set of the parameters controlling the flow, namely, the Rossby and the Womersley numbers. In particular, the behaviour of the flow for relatively large amplitudes of oscillation is studied, with emphasis on the generation of centrifugal instabilities. Numerical results are compared with experimental observations and semi-analytical solutions in the small-amplitude regime, showing good agreement