  Superfluid helium consists of two inter-penetrating fluids, a viscous normal
fluid and an inviscid superfluid, coupled by a mutual friction. We develop a
two-fluid shell model to study superfluid turbulence. We investigate the energy
spectra and the balance of fluxes between the two fluids as a function of
temperature in continuously forced turbulence, and, in the absence of forcing,
the decay of turbulence. We furthermore investigate deviations from the
$k^{-5/3}$ spectrum caused by the mutual friction force. We compare our results
with experiments and existing calculations. We find that, at sufficiently low
temperatures a build-up of energy develops at high wavenumbers suggesting the
need for a further dissipative effect, such as the Kelvin wave cascade and
phonon emission.
