The saturation of decaying counterflow turbulence in helium II

TL;DR

This paper investigates the decay behavior of quantized vortex tangles in superfluid helium II, proposing a theoretical model that explains different observed decay regimes and reconciles previous experimental findings.

Contribution

A simple theoretical model is introduced that captures the complex decay dynamics of vortex tangles in helium II, explaining various experimental decay regimes.

Findings

The model reproduces the observed $t^{-1}$ decay of vortex line density.

It explains the transition to a $t^{-3/2}$ decay in certain conditions.

The model accounts for both rapid initial decay and slower long-term decay.

Abstract

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L \sim t^{-1}$. Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf 44}, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found an initial transient followed by the same classical $t^{-3/2}$ scaling observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.