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Since we are dealing with a multiple connected region, the velocity field is not determined uniquely by the boundary condition and the specification of the vorticity field alone. This is reflected by the fact that the vortex centered at the origin can have arbitrary circulation without affecting the boundary condition. We choose the central vortex to have the circulation stated in the text, to prevent ring currents. Fixing in that way the circulation of the vortex at the origin sets the so-called cyclic constant of the velocity field to zero. With this additional information the velocity field is determined uniquely [23].
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