Determination of the effective kinematic viscosity for the decay of quasiclassical turbulence in superfluidHe4

Abstract

The energy dissipation of quasiclassical homogeneous turbulence in superfluid 4 He (He II) is controlled by an effective kinematic viscosity ν ′ , which relates the energy decay rate dE/dt to the density of quantized vortex lines L as dE/dt = −ν ′ (κL) 2 . The precise value of ν ′ is of fundamental importance in developing our understanding of the dissipation mechanism in He II, and it is also needed in many high Reynolds number turbulence experiments and model testing that use He II as the working fluid. However, a reliable determination of ν ′ requires the measurements of both E(t) and L(t), which was never achieved. Here we discuss our study of the quasiclassical turbulence that emerges in the decay of thermal counterflow in He II at above 1 K. We were able to measure E(t) using a recently developed flow visualization technique and L(t) via second sound attenuation. We report the ν ′ values in a wide temperature range determined for the first time from a comparison of the time evolution of E(t) and L(t).PACS numbers: 67.25.dk, 29.40.Gx, Below about 2.17 K, liquid 4 He transits to the superfluid phase (He II) in which an inviscid irrotational superfluid component (i.e. the condensate) coexists with a viscous normal-fluid component (i.e. the thermal excitations) [1]. The fraction of the normal fluid drops drastically with decreasing temperature and only amounts to about 0.7% of the total density at 1 K [2]. This quantum fluid system exhibits fascinating hydrodynamic properties. For instance, the rotational motion of the superfluid in a simply-connected volume can occur with the formation of topological defects in the form of vortex lines. These vortex lines all have identical cores with a radius a 0 ≃1Å and they each carry a single quantum of circulation κ=10 −3 cm 2 /s [3]. Turbulence in the superfluid therefore takes the form of an irregular tangle of vortex lines (quantum turbulence). Turbulence in the normal fluid is expected to be more similar to that in a classical fluid, but a force of mutual friction between the two fluids, arising from the scattering of thermal excitations by the vortex lines, can affect the flows in both fluids [4].At above 1 K, despite being a two-fluid system with many properties restricted by quantum effects, He II is observed to behave very similarly to classical fluids when a turbulent flow is generated by methods conventionally used in classical fluid research, such as by a towed grid [5] or a rotating propeller [6]. Even in a non-classical thermal counterflow induced by an applied heat current in He II, it has been revealed that quasiclassical turbulence can emerge during the decay of counterflow after the heat current is switched off [7][8][9]. The quasiclassical behavior * Corresponding: wguo@magnet.fsu.edu of He II is interpreted as the consequence of a strong coupling of the two fluids by mutual friction at large scales [10]. It is suggested that the turbulent eddies in the normal fluid are matched by eddies in the superfluid produced by polarized vortices [11,12], although ...

Exploration of thermal counterflow in He II using particle tracking velocimetry

“…More recently, a different approach to He II flow visualization has been introduced, making use of metastable He 2 * molecules as tracer particles [45]. Measurements of the turbulent normal fluid velocity with these particles have lead to non-classical forms of the second order transverse structure function [8], effective kinematic viscosity in decaying counterflow turbulence [46], and the energy spectrum in a sustained thermal counterflow [14]. These measurements are free of the ambiguity associated with PIV and PTV methods since the He 2 * molecules strictly trace the normal fluid for temperatures above about 1 K [45].…”

Dissipation in quantum turbulence in superfluid He4 above 1 K

“…That the variation with time of the slope of the line in Fig.5 is indeed due to the variation with time of the parameter c 2 is shown more strikingly in Fig.7, where we compare on the same graph the time dependence of the value χ 2 derived both by differentiating 1/L in Fig.5 with respect to time and by substituting the value of c 2 from Fig.6(a) into Eq. (12). Even the random fluctuations of c 2 are reflected to a significant degree in fluctuations in χ 2 derived from Fig.5.…”

“…The increase at times greater than about 1 s may be due in part to the vortex line density becoming too small (the ratio of line spacing to the spatial period has become greater than about 0.3), and in part to the effect of the logarithmic factor in Eq. (12). A possible explanation of the discrepancy at smaller times is that the parameter c 2 in Eq.…”

“…In the other case values of ν ′ were obtained from observations of the decay of vortex line density combined with questionable assumptions about the form of the large-scale energy spectrum as it relates to turbulence in a channel of finite crosssection. Only very recently has ν ′ been determined in a more satisfactory way for the case of decaying TCT [12], although the results have yet to be compared carefully with those obtained solely from the decay of vortex line density. The general aims of this paper are, as far as possible, to remedy these various shortcomings.…”

Quench-Spot Detection for Superconducting Accelerator Cavities Via Flow Visualization in Superfluid Helium-4

“…Typically, 5-6 imaging pulses are used to produce good quality images. This flow visualization technique has been successfully utilized in our quantitative studies of quantum turbulence in He II [29,[37][38][39][40][41].…”