The theory of homogeneous turbulence in superfluid He-3-B

Recent studies have shown that the structure of homogeneous grid turbulence in superfluid He-4 is quite similar to that of its classical counterpart. Both the normal component and the superfluid component are turbulent. On length scales greater than the spacing, l, of the quantized vortex lines that allow the superfluid component to undergo turbulent (rotational) motion, the velocity fields in the two components are practically identical and are consistent with the existence an inertial regime with an energy spectrum of the Kolmogorov form. This type of turbulence is possible because the normal component has a very small viscosity, so that the Reynolds number for the normal fluid can be very high. In the case of superfluid He-3-B, the superfluid component can be turbulent in much the same way as in He-4, but turbulence in the normal fluid is inhibited by a very large viscosity. An outline is given of a theory of homogeneous grid turbulence in this case. Because the velocity fields in the two fluids can no longer be the same, a force of mutual friction must act between the two fluids. It is shown that this frictional force damps turbulent motion, by an amount that depends on the dimensionless parameter, alpha, that characterizes the magnitude of the mutual friction. If alpha > 1 turbulence on all length scales greater than l is strongly damped, but for smaller values of a the damping is confined to larger eddies, the smaller eddies still exhibiting an inertial regime with a Kolmogorov spectrum. Comparison is made with recent theoretical work by Volovik and his co-workers and with the experiments of Finne et al on the way in which He-3-B is brought into rotation with a containing vessel for different values of alpha. The presentation emphasizes the physical principles involved, the mathematical details having been set out in another paper. (c) 2005 Elsevier Ltd. All rights reserved.