Local and nonlocal energy spectra of superfluid He 3 turbulence

Below the phase transition temperature Tc ≃ 10−3 K 3He-B has a mixture of normal and super- fluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the time-honored Hall-Vinen-Bekarevich- Khalatnikov coarse-grained equations of superfluid turbulence. We combine pseudo-spectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid 3He-B turbulence. For T < 0.37 Tc, with relatively weak mutual friction, we confirm the previously found “subcritical” energy spectrum E(k), given by a superposition of two power laws that can be approximated as E(k) ∝ k−x with an apparent scaling exponent 53 < x(k) < 3. For T > 0.37 Tc and with strong mutual friction, we observed numerically and confirmed analytically the scale-invariant spectrum E(k) ∝ k−x with a (k-independent) expo- nent x > 3 that gradually increases with the temperature and reaches a value x ∼ 9 for T ≈ 0.72 Tc. In the near-critical regimes we discover a strong enhancement of intermittency which exceeds by an order of magnitude the corresponding level in classical hydrodynamic turbulence.