  The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model is widely used to
numerically study quantum turbulence in superfluid helium. Based on the
two-fluid model of Tisza and Landau, the HVBK model describes the normal
(viscous) and superfluid (inviscid) components of the flow using two
Navier-Stokes type equations, coupled through a mutual friction force term.
This feature makes the HVBK model very appealing in applying statistical tools
used in classical turbulence to study properties of quantum turbulence. A large
body of literature used low-order statistics (spectra, or second-order
structure functions in real space) to unravel exchanges between the two fluids
at several levels. The novelty in this study is to use a theoretical approach
based on first principles to derive transport equations for the third-order
moments for each component of velocity.
