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The large scale turbulent statistics of mechanically driven superfluid $^4$Hewas shown experimentally to follow the classical counterpart. In this paper weuse direct numerical simulations to study the whole range of scales in a rangeof temperatures $T \in[1.3,2.1]$K. The numerics employ self-consistent andnon-linearly coupled normal and superfluid components. The main results arethat (i) the velocity fluctuations of normal and super components arewell-correlated in the inertial range of scales, but decorrelate at smallscales. (ii) The energy transfer by mutual friction between components isparticularly efficient in the temperature range between 1.8K and 2K, leading toenhancement of small scales intermittency for these temperatures. (iii) At low$T$ and close to $T_{\lambda}$ the scaling properties of the energy spectra andstructure functions of the two components are approaching those of classicalhydrodynamic turbulence.

Turbulent statistics and intermittency enhancement in coflowing superfluid $^4$He