Numerical investigation of the collision of a vortex ring with a wavy sphere

The numerical investigation of vortex dynamics resulting from the collision of a vortex ring with a wavy sphere of various wavenumbers (n) at a Reynolds number of 1000 was conducted using a developed remeshed vortex particle method.The influence of the wall's wavenumber on vortex dynamic mechanisms, such as the primary vortex ring's deformation, the boundary layer's separation, and the formation, interaction, and reconnection of secondary and tertiary vortices, was analysed.When the primary ring collides with a smooth sphere (n=0), secondary and tertiary rings are formed, and their interaction with the primary ring is similar to that observed with a flat plate.In the case of the wavy sphere, the boundary layer separates from the wall's hills more rapidly than from the valleys, leading to the boundary layer rolling up into the secondary vortex in a wavy pattern.The segments of the secondary vortex originating from the hills move around the primary ring, while those from the valleys convect upwards, forming incomplete vortex loops at n=5.However, at n=9, the reconnection of segments from the valleys results in the formation of a chain of small-scale rings.Furthermore, tertiary vortices are generated from the valleys due to the additional separation of the wall boundary layer induced by the secondary vortex segments in the valleys.These vortices dissipate rapidly at n=5, whereas reconnection occurs to form additional vortex loops at n=9.