Macroscopic dynamics of the vortex tangle in He II

Abstract

The problem of unsteady superfluid turbulence is considered. Vinen's phenomenological formulation of the vortex-line-density evolution equation encounters a number of difficulties. Some of them are intrinsic in the Feynman-Vinen approach, e.g., the question of an unambiguous choice of the relevant equation. Recent investigations of turbulent unsteady flows and of the vortex-tangle structure lead to new problems. In particular Schwarz suggested that the vortex-line-density evolution equation has the form of the Vinen equation but the physical mechanisms leading to it differ from those suggested by Feynman and Vinen. Reviewing the relevant problems we show that the different concepts concerning macroscopic vortex-tangle dynamics lead to differences in the hydrodynamic equations of the superfluid turbulent flows. Using this fact we devised and performed a special experiment in which a region of strongly nonequilibrium superfluid turbulence was probed by a second-sound pulse. Results of this experiment allowed us to draw two main conclusions: (i) Vinen's vortex-line-density evolution equation is valid. (ii) Schwarz's recent interpretation of the physical mechanisms leading to Vinen's equation seems to be more plausible.