CLOSE INTERACTION BETWEEN A VORTEX FILAMENT AND A RIGID SPHERE

The evolution of a linear vortex filament close to a rigid sphere is investigated at high Reynolds number. The limiting evolution in an ideal flow, is analysed using a cutoff method and the results are compared with those of a singular vortex approach able to account for a viscous effect on the vortex structure evolution. The computed results show the creation of a closed vortex structure in ideal flow and also, at low Reynolds number, an unrealistic reattachment of the vortex to the surface of the body. The nature of the boundary-layer development, when the no-slip condition is satisfied, is calculated near the symmetry plane. The solutions show the development of an unsteady, vortex-driven, separating boundary layer with the three-dimensional separations dependent on the initial distance of the filament from the wall. All the solutions ultimately show a rapid growth of the secondary vorticity field near the surface and suggest an ejection from the boundary layer, followed by a strong viscous-inviscid interaction.