Statistics of Quantum Turbulence in Superfluid He

TL;DR

This paper reviews the statistical properties of quantum turbulence in superfluid helium, covering energy spectra, velocity correlations, dissipation mechanisms, energy exchange, and intermittency across various flow types.

Contribution

It provides a comprehensive overview of the current understanding and recent results on the statistical characteristics of quantum turbulence in superfluid helium.

Findings

Analysis of energy spectra in different flow regimes

Insights into mutual friction and viscosity effects

Observations of intermittency and high-order statistics

Abstract

Based on our current understanding of statistics of quantum turbulence as well as on results of intensive ongoing analytical, numerical and experimental studies we overview here the following problems in the large-scale, space-homogeneous, steady-state turbulence of superfluid $^4$He and $^3$He: 1) Energy spectra of normal and superfluid velocity components; 2) Cross-correlation function of normal and superfluid velocities; 3) Energy dissipation by mutual friction and viscosity; 4) Energy exchange between normal and superfluid components; 5) High-order statistics and intermittency effects. The statistical properties are discussed for turbulence in different types of flows: coflow of $^4$He; turbulent $^3$He with the laminar normal fluid; pure superflow and counterflow in He-4.