Effective viscosity of superfluid turbulence at zero temperature
In plain words
Even at absolute zero, where superfluid helium has no viscosity, a vortex tangle decays as if the fluid had an effective viscosity. Its size, and why it differs between kinds of tangles, has not been calculated.
Precise statement
For a homogeneous vortex tangle in 4He at $T\to 0$ with line density $L$, define the effective kinematic viscosity nu' by the energy decay rate $\epsilon=\nu'(\kappa L)^2$, with $\kappa=h/m_4$. Calculate $\nu'/\kappa$ from the microscopic dissipation channels (reconnections, Kelvin-wave cascade, phonon emission) for quasiclassical (Kolmogorov) and ultraquantum (Vinen) tangles, and explain why the measured values differ between the two (Walmsley and Golov 2008).
What would settle it
A calculation from vortex-filament or Gross-Pitaevskii dynamics reproducing measured $\nu'/\kappa$ for both tangle types within a factor of 2.