= Kutta condition
The <Kutta condition> selects the circulation of an idealized <potential flow> past a body with a sharp trailing edge by requiring finite limiting velocity at that edge. For the <Joukowski map> $z=\zeta+a^2/\zeta$, the trailing edge $z=2a$ corresponds to a simple zero of $dz/d\zeta$ at $\zeta=a$. If $W$ is the <complex potential of a two-dimensional potential flow>[complex potential] in the circle plane, then $dw/dz=W'(\zeta)/(1-a^2/\zeta^2)$ is finite there only if $W'(a)=0$. For a <uniform flow> of speed $U$ at angle $\alpha$ and a <point vortex> of circulation $\Gamma$, this gives $\Gamma=-4\pi Ua\sin\alpha$, and cancellation of the simple zeros gives the tangential trailing-edge velocity $U\cos\alpha$. The opposite endpoint can retain a leading-edge singularity.
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