Below the phase transition temperature Tc ≃ 10 −3 K 3 He-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 3 He-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 5 3 < 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) exponent 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.

We perform gas flow experiments in a shallow microchannel, 1.14±0.02 μm deep, 200 μm wide, etched in glass and covered by an atomically flat silicon wafer. The dimensions of the channel are accurately measured by using profilometry, optical microscopy and interferometric optical microscopy. Flow-rate and pressure drop measurements are performed for helium and nitrogen, in a range of averaged Knudsen numbers extending up to 0.8 for helium and 0.6 for nitrogen. This represents an extension, by a factor of 3 or so, of previous studies. We emphasize the importance of the averaged Knudsen number which is identified as the basic control parameter of the problem. From the measurements, we estimate the accommodation factor for helium to be equal to 0.91±0.03 and that for nitrogen equal to 0.87±0.06. We provide estimates for second-order effects, and compare them with theoretical expectations. We estimate the upper limit of the slip flow regime, in terms of the averaged Knudsen number, to be 0.3±0.1, for the two gases.

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