= Irrotational circulation in an exterior domain
In smooth barotropic inviscid flow with conservative <body force>, <Kelvin's circulation theorem> preserves circulation of <material curves>. Initially zero <vorticity> therefore gives zero circulation on contractible loops for all times. A loop winding around an excluded obstacle can have a nonzero constant circulation: the planar field $\mathbf u=\Gamma\mathbf e_\theta/(2\pi r)$ is <irrotational> outside the origin but has circulation $\Gamma$ on a positively oriented enclosing loop.
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