Abstract
We investigate dynamics of a vortex ring encountering a coaxial spherical obstacle in Bose-Einstein condensates. For a perfect spherical obstacle, the vortex ring would first expand and then shrink when passing over the obstacle. For the case of a periodically modified spherical obstacle, the circular vortex ring is deformed to be gear shaped during the passing-over process. This gear-shaped vortex ring can evolve into a helical Kelvin-wave state, or split into several smaller vortex rings. In the latter situation, these split vortex rings would travel some distances forwards and then reconnect with each other, forming one new forward-moving Kelvin wave, or two Kelvin waves of different sizes, with the bigger one moving forwards and the smaller one moving backwards.
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