Chaotic quantized vortices and hydrodynamic processes in superfluid helium

Superfluid turbulence in He II flows appears as a stochastic tangle of quantized vortex lines. Interest in this system extends beyond the field of superfluid helium to include the study of statistical physics of extended objects and classical turbulence. A wealth of information concerning the vortex tangle has been supplied by experiments, by phenomenological models, and by numerical simulation. In the restricted case of stationary homogeneous flows, a good correlation between theory and experiment has already been demonstrated. This review therefore concentrates on nonstationary and nonhomogeneous processes with the goal of understanding the dynamical properties of the vortex tangle. The first part of this paper reviews the concept of the stochastic vortex tangle with emphasis on the work of Vinen and Schwarz. Special attention is given to justifying Vinen's equation as a basis for the study of nonstationary processes. This analysis reveals that the interpretation of experimental results requires a careful account of the mutual influence of the vortex tangle and the flow of the supefluid. The second part of this paper reviews the development of the required hyrodynamic equations of superfluid turbulence. These equations are applied to a number of examples such as linear and nonlinear sound, heat pulses, and fluctuations. The role of stochastic vortices in the phase-transition problem is discussed. Attention is focused on the relation between hydrodynamic effects and the vortex tangle properties. Finally, the main results concerning the stochastic vortex tangle are resumed and some of the important questions are pointed out.