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motion of the propagating front [5]: while the vortices move in the axial direction, they also circle around the cylinder with azimuthal velocity. At lower temperatures the front moves at constant velocity with a stable time average structure. This steady state of vortex propagation displays an increasing influence from turbulent fluctuations with decreasing temperature. Here the energy difference across the front, between the high-energy state of vortex-free flow ahead of the front and the twisted vortex state behind the front, is dissipated by the losses in vortex motion. The axial velocity of the front is obtained from its flight time while it travels the distance between the two NMR pick-up coils at each end of the long sample cylinder. In the laminar regime the losses prove to be caused by the well-known mutual friction dissipation while it acts on large length scales, comparable to the radius R of the rotating column. In contrast, at lower temperatures in the turbulent regime, owing to nonlinear interactions, the hydrodynamic energy flows to shorter length scales. Along this cascade it is dissipated by mutual friction and ultimately at the shortest length scales (on the order of the superfluid coherence length by some new mechanisms. Experimentally at low temperatures below 0.4 Tc, the total dissipation is observed to deviate orders of magnitude above the laminar extrapolation.

The velocity of the propagating vortex front has been compared to simulation calculations [2]. It has also led to a sophisticated analysis of the energy cascade which distributes the hydrodynamic kinetic energy in a Kolmogorov type of process over all length scales, starting from the largest hydrodynamic scale, given by the radius R of the column at which the energy is pumped into the cascade. The length scale comparable to the inter-vortex distance defines the crossover from classical to quantum scales. At the quantum scale the energy is dissipated by helical Kelvin-wave excitations which expand on individual vortex lines and, by means of nonlinear interactions, allow the energy to be transferred down to ever shorter wave lengths. In this regime of scales the ultimate limit is the radius of the vortex core which is comparable to the superfluid coherence length . The analysis by Victor L’vov [2] provides the first estimation of turbulent losses at the lowest temperatures, which is not restricted to isotropic homogeneous turbulence, but applies to flow with vortices constrained to an ordered configuration with high polarization along the rotation axis. The new element in this analysis is the appearance of a bottleneck in the energy cascade, in the transfer from the hydrodynamic scales larger than to the quantum scales smaller than where the Kelvin waves have to be excited. This model can now be fitted to the measurements of front propagation with a very reasonable choice of parameters.

Our measurements on the dissipation in vortex propagation in the turbulent temperature regime below 0.4 Tc depend on a number of new techniques, which have been developed in the course of this work. Among these are the NMR methods for counting vortices and for preparing states with a known number of vortices, the techniques to achieve high vortex-free counterflow and to inject vortex seed loops, and ways to reach and measure temperatures below 0.2 Tc in a long liquid 3He column. We now know how critical velocities, turbulent vortex formation, and vortex remanence can be dealt with to perform controlled measurements down to below 0.2 Tc. A number of further open questions can be answered utilizing these techniques: Is the turbulent dissipation converted directly to heat and if so, how does it happen? Does the loss of coupling to the external frame of reference change the nature of the critical velocity of various types of instabilities? Are new types of topological defects

Annual Report 2007