Scanning Superfluid-Turbulence Cascade by its Low-Temperature Cutoff

Abstract

On the basis of a recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, L, controlled by the frictional coefficient, alpha(T)<<1, responsible for the cutoff. The curve ln L(lnalpha) is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wave number regions. Excellent agreement with a recent experiment by Walmsley et al. [Phys. Rev. Lett. 99, 265302 (2007)] -- in which L(T) has been measured down to T ~ 0.08 K -- implies that the scenario of low-temperature superfluid turbulence is now experimentally validated and allows to quantify the Kelvin-wave cascade spectrum.

Quantum turbulence—from superfluid helium to atomic Bose–Einstein condensates

“…On the other hand, at length scales smaller than the mean vortex spacing the energy is transferred along each vortex through a Kelvin-wave cascade; this regime has no classical analog and can be called quantum. Several theoretical considerations of the classical-quantum crossover have been proposed [58,59,60], but this topic is not yet settled and remains controversial.…”

Quantum turbulence in superfluids with wall-clamped normal component

“…Here the anomaly in the temperature dependence of the effective turbulent viscosity ν′ was observed, in a way similar to the shoulder in the front velocity V f in our experiments. The current explanation of this effect is linked to the physics of the crossover region in the turbulent energy cascades (46). We note, however, that the decrease of ν′ is observed in the temperature region where Re α ∼ Re λ ∼ 10 3 , and thus the influence of the decoupling cannot be a priori excluded.…”

ExcimersHe2*as Tracers of Quantum Turbulence inHe4in theT=Zmeev1, Pakpour2, Walmsley3 et al. 2013Phys. Rev. Lett.580410View full textAdd to dashboardCite

“…Within the former (coarse-grained flow on length scales greater than the mean separation between vortex lines), the regions of enhanced vorticity, i.e., those with an enhanced density of vortex lines, will be most visible. Within the latter (small length scales that resolve discrete vortex lines), one will be able to observe such processes as vortex reconnections, Kelvin waves, and the emission and absorption of small vortex loops-which are believed to be responsible for the quantum cascade of energy and control the dissipation of the vortex tangle [3,4].Micron-sized particles of solid hydrogen have already been used to tag vortex cores at high temperatures, T $ 2 K [5,6]; however, the invasive means of introduction and relatively large particle size preclude implementation of this technique for low temperatures and small length scales. Potentially ideal tracers would be metastable molecules He à 2 in the spin triplet state, which have a relatively long lifetime of ð13 AE 2Þ s [7].…”

“…Each molecule can be visualized many times by laser fluorescence [10], and single-molecule resolution is, in principle, possible. It was shown that the excimers can serve as tracers of the normal component in superfluid 4 He at temperatures above 1 K [11], and visualization has been successfully demonstrated [12].…”

“…and M ¼ V 2 þ 2m 4 ¼ 71 amu is the effective mass of the molecule 4 He à 2 (the product V is expected to be nearly pressure independent because of the opposite dependences ðPÞ and VðPÞ: between pressures P ¼ 0:1 bar and P ¼ 5:0 bar used in our experiment, the helium density increases by 5% [20] while the bubble's volume V / R 3 à is expected to decrease by 5% [14]). In reality, the singularity in UðrÞ at r ¼ 0 is replaced by a finite minimum of width $R à , which would allow the particle eventually to escape (effectively undergoing scattering by a large angle)-provided little energy was dissipated on its way to r $ R à .…”