Potential dipole
= Potential dipole
{title2=$\phi=\mathbf d\cdot\mathbf x/r^3$}
A potential dipole in three dimensions is the <potential flow> $\mathbf u=\nabla\phi$ with $\phi=\mathbf d\cdot\mathbf x/r^3$. Away from the origin its potential is a <harmonic function>, so it is also a constant-<pressure> <Stokes flow>. Its <velocity> decays as $r^{-3}$ and its <vorticity> is zero. It is distinct from a <stresslet>, whose leading <velocity> decays as $r^{-2}$.