= Hydrodynamic Biot-Savart kernel
{title2=$\mathbf u(\mathbf x)=\frac1{4\pi}\int\frac{\boldsymbol\omega(\mathbf y)\times(\mathbf x-\mathbf y)}{|\mathbf x-\mathbf y|^3}\,d^3y$}
In an unbounded incompressible <fluid> with localized <vorticity> and no added harmonic background, <velocity> is reconstructed by $\mathbf u(\mathbf x)=(4\pi)^{-1}\int\boldsymbol\omega(\mathbf y)\times(\mathbf x-\mathbf y)/|\mathbf x-\mathbf y|^3\,d^3y$. Its <multipole expansion> relates <hydrodynamic impulse> to a dipolar far-field <velocity>.
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