field induction. The $j$–summation is over the sites of vortex lines. Note that Eq. (\[eq:AS:curlv\]) treats the vortex cores as singularities in the plane orthogonal to $ \nu_{\tau}$, which is justified on scales larger than the coherence length of a condensate. The crossover from the local hydrodynamic scale to the microscopic scale can be studied within the Ginzburg-Landau theory as we briefly discuss below.

For a single vortex the integral of Eq. (\[eq:AS:curlv\]) completely determines the superfluid pattern; as this equation is linear, for larger number of vortices the superfluid pattern is a superposition of the flows induced by each vortex. The resulting net flow, obviously, depends on the arrangement of the vortices. It turns out that the integral of Eq. (\[eq:AS:curlv\]) on the local hydrodynamic scale is radically different from the one on the scales involving larger number of vortices in a rotating superfluid.

To appreciate the difference in superfluid patterns on different scales let us look for vortex solutions in a neutral condensate in cylindrical geometry. The condensate wave function has the form $\psi({\bf x}) =  f(r) e^{i\theta}$ in the polar-cylindrical coordinates $(r,\theta, z)$; the neutron superfluid velocity upon integrating Eq. (\[eq:AS:curlv\]) becomes $$\begin{aligned}
\label{eq:AS:vn}
{\bf v}_n = 