= Two-dimensional vortex dynamics
{title2=$\zeta_t+J(\psi,\zeta)=0,\quad\nabla^2\psi=\zeta$}
For inviscid planar <incompressible flow>, write <velocity> as $(-\psi_y,\psi_x)$ and <vorticity> as $\zeta=\nabla^2\psi$. Taking <curl> of the <Euler equations for an inviscid fluid> removes <pressure> and gives the displayed transport equation, with $J(\psi,\zeta)=\psi_x\zeta_y-\psi_y\zeta_x$. The <Poisson equation> then recovers the <streamfunction> at each instant. A velocity tangent to the plane cannot stretch its perpendicular <vorticity> vector.
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