Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry, and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements. Motivated by designed examples for superfluids, we numerically consider the influence of a geometric potential on vortices for fluids with finite viscosity and show examples in which a change in the geometry is used to manipulate the flow field.
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Reuther et al. (2015) studied this question.
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