Dipolar velocity field of a localized eddy (${\mathbf{u}}_{\mathrm{far}}=[3\mathbf{n}(\mathbf{I}\cdot \mathbf{n})-\mathbf{I}]/(4\pi r^3)$)

A localized vorticity distribution with nonzero hydrodynamic impulse induces $\mathbf{u}\sim [3\mathbf{n}(\mathbf{I}\cdot \mathbf{n})-\mathbf{I}]/(4\pi r^3)$. This curl-free exterior velocity can remain long-ranged even when the vorticity is localized. In a random ensemble it produces dipolar longitudinal and transverse correlation tails.