  Turbulence in superfluid helium~II is a tangle of quantized vortex lines
which interact via the classical Biot-Savart law. We show that vortex tangles
with the same vortex line density will have different energy spectra, depending
on the normal fluid which feeds energy into the superfluid component, and
identify the spectral signature of two forms of superfluid turbulence:
Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity
field into local and nonlocal contributions, we find that in Vinen tangles the
motion of vortex lines depends mainly on the local curvature, whereas in
Kolmogorov tangles the long-range vortex interaction is dominant and leads to
the formation of clustering of lines, in analogy to the 'worms` of ordinary
turbulence.
