= Line vortex
{title2=$\mathbf u=\frac{\Gamma}{2\pi}\frac{\mathbf e_z\times(\mathbf r-\mathbf r_0)}{|\mathbf r-\mathbf r_0|^2}$}
= Point vortex
{synonym}
= Point vortices
{synonym}
An ideal straight <line vortex> in a two-dimensional <incompressible flow> has <circulation> $\Gamma$ and induces velocity
$$
\mathbf u(\mathbf r)=\frac{\Gamma}{2\pi}\frac{\mathbf e_z\times(\mathbf r-\mathbf r_0)}{|\mathbf r-\mathbf r_0|^2}.
$$
Its <stream function>, with $\mathbf u=(\psi_y,-\psi_x)$, is $\psi=-\Gamma\log|\mathbf r-\mathbf r_0|/(2\pi)$. Positive $\Gamma$ means counterclockwise <circulation>. In an ideal point-vortex description, the vortex position is advected by the regular velocity produced by the other vortices and the boundaries; its own singular velocity is excluded.
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