= Source dipole
{title2=$\mathbf u=[3(\mathbf M\cdot\mathbf r)\mathbf r/r^5-\mathbf M/r^3]/(4\pi)$}
= Source doublet
{synonym}
A source dipole is the limit of an equal source and sink brought together with their source-strength times separation vector fixed at $\mathbf M$. Differentiating the <three-dimensional point source> field gives $\mathbf u=-(\mathbf M\cdot\nabla)[\mathbf r/(4\pi r^3)]$. It has <velocity potential> $-\mathbf M\cdot\mathbf r/(4\pi r^3)$, zero total <volume flux>, and $r^{-3}$ far-field decay. Unlike a <stresslet>, it is an irrotational potential singularity rather than a <force-dipole flow>.
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