Helicity-based analysis of vortex breakdown in spherical Couette flows

This study examines the bubble-like vortex breakdown within the azimuthal vortices of a spherical Couette flow (SCF). The analysis investigates flow topology for gap ratios of 0.5, 1, and 1.5 and Reynolds numbers up to 3000. The system displays steady and unsteady breakdown topologies depending on the gap ratio. The non-dimensionalized governing equations are solved in spherical coordinates using Dedalus, which employs a sparse spectral method. The three-dimensional flow is decomposed into a two-dimensional velocity field and an out-of-plane velocity. Helicity is also decomposed into planar helicity and out-of-plane components. The analysis reveals a correlation between planar helicity and the vortex breakdown bubble. The topology of the breakdown bubble is reconstructed using the iso-surface of planar helicity for axisymmetric, steady, and unsteady cases. This detailed investigation provides insights into the complex dynamics of vortex breakdown in SCF and contributes to the understanding of breakdown mechanisms.