Turbulent statistics and intermittency enhancement in coflowing superfluid $^4$He

TL;DR

This study uses direct numerical simulations to analyze turbulence in superfluid helium-4 across various temperatures, revealing correlated velocity fluctuations, temperature-dependent energy transfer, and intermittency enhancement at certain temperatures.

Contribution

It provides a comprehensive numerical analysis of superfluid turbulence, highlighting temperature-dependent behaviors and the role of mutual friction in intermittency enhancement.

Findings

Velocity fluctuations are correlated in the inertial range but decorrelate at small scales.

Mutual friction efficiently transfers energy between components at 1.8K-2K, boosting small-scale intermittency.

Energy spectra and structure functions approach classical turbulence behavior near Tλ and at low temperatures.

Abstract

The large scale turbulent statistics of mechanically driven superfluid $^4$He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures $T \in[1.3,2.1]$K. The numerics employ self-consistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particularly efficient in the temperature range between 1.8K and 2K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low $T$ and close to $T_{\lambda}$ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.