Quasiclassical and ultraquantum decay of superfluid turbulence

Abstract

We address the question which, after a decade-long discussion, still remains open: what is the nature of the ultraquantum regime of decay of quantum turbulence? The model developed in this work reproduces both the ultraquantum and the quasiclassical decay regimes and explains their hydrodynamical natures. In the case where turbulence is generated by forcing at some intermediate lengthscale, e.g. by the beam of vortex rings in the experiment of Walmsley and Golov [Phys. Rev. Lett. 100, 245301 (2008)], we explained the mechanisms of generation of both ultraquantum and quasiclassical regimes. We also found that the anisotropy of the beam is important for generating the large scale motion associated with the quasiclassical regime.PACS numbers: 67.25.dk, 67.30.he, 47.27.Gs The existence of a macroscopic complex order parameter in superfluid helium ( 4 He and 3 He) constrains the vorticity to vortex lines, each line carrying one quantum of circulation κ. This is in sharp contrast to ordinary fluids, where vorticity is continuous. An important question is how quantum turbulence compares to classical turbulence [1]. Experiments in helium have revealed two regimes [2-4] of turbulent decay characterized by L ∼ t −1 (ultraquantum) and L ∼ t −3/2 (quasiclassical) behaviour, where t is time and the vortex line density (vortex length per unit volume) L measures the turbulence's intensity. In these two regimes the kinetic energy (per unit mass) decays as E ∼ t −1 and E ∼ t −2 , respectively. (Here it seems appropriate to point to the detailed theoretical analysis [5] of energy decay in classical, viscous, uniform and isotropic turbulence.) The second regime is thought to be associated with the classical Kolmogorov distribution of kinetic energy over the length scales, but the nature of the first regime is still a mystery. Here we show that the first regime, associated entirely with the Kelvin wave cascade along individual vortex lines, takes place when the energy input at some intermediate lengthscale is insufficient to induce the large-scale motion which is associated with quasiclassical, "Kolmogorov" turbulence. In other words, the first regime is a transient turbulent state which decays before energy can be transferred to large scales by vortex reconnections, which play a key role in this reverse energy transfer.Theoretical and experimental studies have revealed analogies between superfluid turbulence and classical turbulence, notably the same Kolmogorov energy spectrum in continually forced turbulence [6][7][8][9][10], as well as many dissimilarities and new effects. Our concern is the decay of pure superfluid turbulence at temperatures small enough that thermal excitations are negligible; in the absence of viscous forces, in 4 He the only mechanism [1] to dissipate kinetic energy is phonon emission at length scales much shorter than the average intervortex distanceHe-B, which is a fermionic superfluid, the dissipation is thought to be associated with the CaroliMatricon mechanism [11] of energy loss from short Kelvin w...

Introduction to quantum turbulence

“…The main experimental evidence (26,66) is that, if the vortex tangle is left to decay, the vortex line density decreases as L ∼ t −1 , in agreement with a phenomenological model of Vinen (7), which indeed assumes a random, homogeneous, and isotropic vortex configuration. The same L ∼ t −1 decay has been observed in numerical simulations (67), which also confirmed that the energy spectrum remains broadly concentrated near k ≈ 1=ℓ.…”

Local and nonlocal dynamics in superfluid turbulence

“…Models based on this property describe fairly well the pioneering experiments of Vinen 6 , in which an applied heat flux drives the superfluid and the normal fluid in opposite directions (thermal counterflow). More recently, such 'Vinen' tangles were created at very low temperatures by short injections of ions 7 , exhibiting the characteristic decay L ∼ t −1/2 predicted by Vinen 8 . Under different conditions, however, the experimental evidence is consistent with a more structured vortex tangle 4,9 , where the kinetic energy is distributed over a range of length scales according to the same Kolmogorov law which governs ordinary turbulence.…”

Quantum turbulence generated by oscillating structures

“…The way in which this type of turbulence evolves and decays is of great interest (see, for example, ref. 41). …”