Vortical structures behind a sphere at subcritical Reynolds numbers

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Abstract
Large eddy simulations of turbulent flow over a sphere are conducted at subcritical Reynolds numbers (Re=3700 and 104) based on the freestream velocity and sphere diameter. At Re=3700, the separating shear layer persists downstream to form a cylindrical vortex sheet and its instability becomes manifest at x≈2d. The flow right behind the sphere contains only a few vortices. On the other hand, at Re=104, the shear-layer instability occurs right behind the sphere in a form of vortex rings, and the flow becomes turbulent in the near wake. Therefore, at Re=104, the size of the recirculation region is smaller and the wake recovers more quickly than at Re=3700. At both Reynolds numbers, large-scale waviness of vortical structures is observed in the wake and the plane containing the large-scale waviness changes quasirandomly in time. This waviness is more pronounced at Re=104 than at Re=3700. The mechanism responsible for this large-scale waviness of vortical structures is shown to be closely associated with the temporal evolution of vortices generated by the shear-layer instability.