  In superfluid $^3$He turbulence is carried predominantly by the superfluid
component. To explore the statistical properties of this quantum turbulence and
its differences from the classical counterpart we adopt the time-honored
approach of shell models. Using this approach we provide numerical simulations
of a Sabra-shell model that allows us to uncover the nature of the energy
spectrum in the relevant hydrodynamic regimes. These results are in qualitative
agreement with analytical expressions for the superfluid turbulent energy
spectra that were found using a differential approximation for the energy flux.
