Quantised Vortex Densities in Rotating Condensates and the Shear Bound

A rotating superfluid mimics solid-body rotation through an array of quantised vortices whose areal density is fixed by the Feynman relation. This paper computes vortex densities, intervortex spacings and the associated gradient scales for rotating rubidium-87 condensates and rotating helium-4 across experimentally accessible rotation rates, and compares them with the shear ceiling from the spin-torsion bound. Rubidium-87 rotating at 10 hertz carries 2.74e+10 vortices per square metre with a spacing of 6.0 micrometres; helium-4 at 10 radians per second carries 2.01e+08 per square metre with a spacing of 70.60 micrometres. The largest gradient associated with the array, set by the inverse spacing, stands at a ratio of 1.23e-11 to the torsion ceiling. Vortex arrays therefore reproduce the kinematics of rotation at densities of circulation that remain vastly below any fundamental shear limit, and the practical ceiling on vortex density is set by core overlap and condensate depletion, not by the bound. This study is computed from stated assumptions, not measured.