  We carry out an in-depth analysis of a recently introduced vortex gas model
of homogeneous and isotropic turbulence. Direct numerical simulations are used
to provide a concrete physical interpretation of one of the model's constituent
fields: the degree of vortex polarization. Our investigations shed light on the
complexity underlying vortex interactions and reveal, furthermore, that despite
some striking similarities, classical and quantum turbulence exhibit distinct
structural characteristics, even at inertial range scales. Crucially, these
differences arise due to correlations between the polarization and circulation
intensity within vortex clusters.
