Counter-flow Induced Decoupling in Super-Fluid Turbulence

TL;DR

This paper reveals that in thermally driven superfluid turbulence with counterflow, the normal and superfluid velocity fluctuations are nearly decoupled across most scales, contrasting with the coupled fluctuations observed in mechanically driven turbulence.

Contribution

The study introduces an analytic model showing decoupling of velocity fluctuations in thermally driven superfluid turbulence with counterflow, differing from previous coupled fluctuation models.

Findings

Normal and superfluid velocity fluctuations are decoupled across most scales.

Decoupling occurs in thermally driven turbulence with counterflow.

Contrast with coupled fluctuations in mechanically driven turbulence.

Abstract

In mechanically driven superfluid turbulence the mean velocities of the normal- and superfluid components are known to coincide: $\mathbf U_{\text{n}} =\mathbf U_{\text{s}}$. Numerous laboratory, numerical and analytical studies showed that under these conditions the mutual friction between the normal- and superfluid velocity components couples also their fluctuations: $\mathbf u'_{\text{n}}(\mathbf r,t) \approx \mathbf u'_{\text{s}}(\mathbf r,t)$ almost at all scales. In this paper we show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity $\mathbf U_{\text{ns}}\equiv \mathbf U_{\text{n}} -\mathbf U_{\text{s}}\ne 0$. We suggest a simple analytic model for the cross correlation function $\left\langle \mathbf u'_{\text{n}}(\mathbf r,t) \cdot \mathbf u'_{\text{s}}(\mathbf r',t)\right \rangle$ and its dependence on $U_{\text{ns}}$. We demonstrate that $\mathbf u'_{\text{n}}(\mathbf r,t)$ and $ \mathbf u'_{\text{s}}(\mathbf r,t)$ are decoupled almost in the entire range of separations $|\mathbf r-\mathbf r'|$ between the energy containing scale and intervortex distance.