 Line vortex

An ideal straight line vortex in a two-dimensional incompressible flow has circulation $\Gamma$ and induces velocityIts 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.