Periodic and quasiperiodic vortex shedding in the wake of a rotating sphere

The flow past a sphere rotating about an axis aligned with the streamwise direction is numerically investigated. The dynamics is governed by the incompressible Navier–Stokes equations and depends on two control parameters: the Reynolds number Re and rotation rate ΩΩ. The present investigation systematically covers the range Re≤350Re≤350 and Ω≤2Ω≤2. First, the axisymmetric steady base flow (whether stable or not) is computed for all values of the control parameters. Then, after linearisation of the equations about the base flow, the growth rates and frequencies of the leading eigenmodes are obtained. Fully nonlinear direct numerical simulations yield the detailed flow fields and hydrodynamic forces acting on the sphere. Different wake modes (low-frequency periodic helical, quasi-periodic shedding and high-frequency periodic helical) are identified and their characteristic frequencies precisely determined.