= Velocity field of a dense coaxial vortex-ring array
{title2=$u_{\rm inside}\simeq\Gamma/l$}
A long array of equal co-oriented <vortex rings>, spaced by $l\ll r$, approximates an azimuthal <vortex sheet> on a cylinder of radius $r$. The <circulation> per unit axial <length> is $\Gamma/l$. The conditions $\nabla\cdot\mathbf u=0$ and $\nabla\times\mathbf u=\boldsymbol\omega$ are mathematically analogous to the magnetostatic equations for a <solenoid>. Away from its ends, an array long compared with $r$ produces nearly uniform axial flow $\Gamma/l$ inside and weak flow outside. A finite array has return flow outside connecting its two ends. The uniform-core approximation fails close to individual vortex cores and near the ends, and the field requires a stated <circulation> orientation and background flow.
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