Energy spectrum of thermal counterflow turbulence in superfluid helium-4

Abstract

Recent preliminary experiments (Marakov et al Phys. Rev. B 91, 094503 (2015)), using tripletstate He2 excimer molecules as tracers of the motion of the normal fluid, have shown that, in thermal counterflow turbulence in superfluid 4 He, small scale turbulence in the superfluid component is accompanied, above a critical heat flux, by partially-coupled large-scale turbulence in both fluids, with an energy spectrum proportional to k −m , where m is greater than the Kolmogorov value of 5/3. Here we report the results of a more detailed study of this spectrum, over a range of temperatures and heat fluxes, using the same experimental technique. We show that the exponent m varies systematically with heat flux, but is always greater than 5/3. We interpret this as arising from the steady counterflow, which causes large-scale eddies in the two fluids to be pulled in opposite directions, giving rise to dissipation by mutual friction at all wave numbers, mutual friction tending also to oppose the effect of the counterflow. Comparison of the experimental results with a simple theory suggests that this process may be more complicated than we might have hoped, but experiments covering a wider range of heat fluxes, which are technically very difficult, will probably be required before we can arrive at a convincing theory.

Strong anisotropy of superfluid He4 counterflow turbulence

“…The trace S j (R) ≡ α S αα j (R) is a measure of the kinetic energy of turbulent (normal or superfluid) velocity fluctuations on scale R. Recently, the streamwise normal velocity across a channel, v x (y, t) was measured using thin lines of the triplet-state He 2 molecular tracers created by a femptosecond-laser field ionization of He atoms 42 across the channel. This way, the transversal 2 nd -order structure functions 11,12 of the normal-fluid velocity differences S xx n (R y ) were obtained. Similarly, one can use two or more tracer lines, separated in the streamline direction x, to measure the longitudinal structure function S xx n (R x ) and even inclined structure function S xx n (R x , R y ).…”

Characterizing vortex tangle properties in steady-state He II counterflow using particle tracking velocimetry

“…provided the counterflow velocity ρv n /ρ s exceeds a small critical velocity v 0 . To illustrate agreement with σ G1 , we computed v 2 L 1/2 using values for γ (a temperature-dependent parameter relating L to v ns ), v 0 , and the parameter c 2 reported in the recent work of Gao et al [27,28], and we approximated the mean vortex line spacing ℓ = L −1/2 across the entire parameter space. Since the agreement between σ G1 and v 2 L 1/2 appeared to be reasonable, we can use measured G1 velocity fluctuations to represent v 2 L 1/2 , and apply Eqn.…”

“…(2) to calculate its average value across the imaging plane. We begin by obtaining values for ℓ, γ, and v 0 using our own apparatus, employing both flow visualization and second sound attenuation according to the procedures outlined by Gao et al [27]. The results for each temperature are tabulated in Table I.…”

Fully Coupled Two-Fluid Dynamics in Superfluid He4 : Anomalous Anisotropic Velocity Fluctuations in Counterflow

“…Visualization experiments were performed to observe the normal-fluid flow [27][28][29][30]. Marakov et al visualized the velocity profile of the normal fluid by using He * 2 molecules [30], and the characteristic energy spectra were analyzed [31,32]. A particle tracking velocimetry (PTV) experiment provides insights on statistical properties and indicated that the velocity fluctuations of the normal fluid are anisotropic in contrast to classical fluid [33,34].…”