Statistics of turbulence and intermittency enhancement in superfluid $^4$He counterflow

TL;DR

This paper analyzes turbulence and intermittency in superfluid helium-4 counterflow, revealing scale-dependent energy spectra and enhanced intermittency at small scales, with findings aligning with recent theoretical predictions.

Contribution

It provides detailed experimental measurements of energy spectra and structure functions in superfluid helium-4 counterflow, identifying distinct scale regimes and their turbulence characteristics.

Findings

Two distinct spectral regimes with different power-law exponents

Intermittency is modestly enhanced in cascade and mutual friction intervals

Small scales exhibit much stronger intermittency than classical turbulence

Abstract

We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid $^4$He counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum $E_{xz} (k_y)$ (averaged over the $xz$-plane, parallel to the channel wall), directly measured as a function of the wall-normal wave-vector $k_y$, gives more detailed information on the energy distribution over scales than the corresponding second-order structure function $S_{2}(\delta_y)$. In particular, we discover two intervals of $k_y$ with different apparent exponents: $E_{xz} (k_y)\propto k_y^{-m_C}$ for $k\lesssim k_\times$ and $E_{xz} (k_y)\propto k_y^{-m_F}$ for $k\gtrsim k_\times$. Here $k_\times$ denotes wavenumber that separate scales with relatively strong (for $k\lesssim k_\times$) and relatively weak (for $k\gtrsim k_\times$) coupling between the normal-fluid and superfluid velocity components. We interpret these $k$-ranges as cascade-dominated and mutual friction-dominated intervals, respectively. General behavior of the experimental spectra $E_{xz}(k_y)$ agree well with the predicted spectra [Phys. Rev. B 97, 214513 (2018)]. Analysis of the $n$-th order structure functions statistics shows that in the energy-containing interval the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade- and mutual friction-dominated intervals we found some modest enhancement of intermittency with respect of its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.