Higher-order statistics and intermittency of a two-fluid HVBK quantum turbulent flow

The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model is widely used to study quantum turbulence in superfluid helium numerically. 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.



Budget equations are assessed through Direct Numerical Simulations of the HVBK flow based on accurate pseudo-spectral methods. Values from 0.1 to 10 are considered for the ratio of the normal and superfluid densities. We analyze the importance of each term in budget equations and emphasize their role in energy exchange between normal and superfluid components.



Some interesting features are observed: i) transport and pressure-related terms are dominant, similar to single-fluid turbulence; ii) the mathematical signature of the FRN (finite Reynolds number) effect is weak in the transport of the third-order moment, despite the low value of the Reynolds number; iii) for very low temperatures, the normal fluid behaves as a fluid of vanishing viscosity, since the mutual friction annihilates the effects of viscosity. We also derive an equation for the velocity flatness F for small scales. We show that the F of both the normal fluid and superfluid gradually increases when temperature decreases, thus corroborating the picture of the locking between the two fluids.