Matteo Giacobello

Wake structure of a transversely rotating sphere at moderate Reynolds numbers

The uniform flow past a sphere undergoing steady rotation about an axis transverse to the free stream flow was investigated numerically. The objective was to reveal the effect of sphere rotation on the characteristics of the vortical wake structure and on the forces exerted on the sphere. This was achieved by solving the time-dependent, incompressible Navier–Stokes equations, using an accurate Fourier–Chebyshev spectral collocation method. Reynolds numbers Re of 100, 250 and 300 were considered, which for a stationary sphere cover the axisymmetric steady, non-axisymmetric steady and vortex shedding regimes. The study identified wake transitions that occur over the range of non-dimensional rotational speeds Ω* = 0 to 1.00, where Ω* is the maximum velocity on the sphere surface normalized by the free stream velocity. At Re = 100, sphere rotation triggers a transition to a steady double-threaded structure. At Re = 250, the wake undergoes a transition to vortex shedding for Ω* ≥ 0.08. With an increasing rotation rate, the recirculating region is progressively reduced until a further transition to a steady double-threaded wake structure for Ω* ≥ 0.30. At Re = 300, wake shedding is suppressed for Ω* ≥ 0.50 via the same mechanism found at Re = 250. For Ω* ≥ 0.80, the wake undergoes a further transition to vortex shedding, through what appears to be a shear layer instability of the Kelvin–Helmholtz type.

Superfluid spherical Couette flow

We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor-Couette flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap width δ and rotational shear ΔΩ. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is patchy; that is, it takes different forms in different parts of the vessel, a surprising new result.