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arXiv:1506.00464 · Physical Review B

Coupled normal fluid and superfluid profiles of turbulent helium II in channels

Luca Galantucci, Michele Sciacca, Carlo F. Barenghi

Published Nov 30, 2015• 25 citations
arXivHTMLPDF

Abstract

We perform fully coupled two-dimensional numerical simulations of plane channel helium II counterflows with vortex-line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three dimensions. We focus on the coarse-grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser-induced fluorescence of metastable helium molecules.

DOI
10.1103/physrevb.92.174530

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We perform fully coupled two-dimensional numerical simulations of plane channel helium II counterflows with vortex-line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three dimensions. We focus on the coarse-grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser-induced fluorescence of metastable helium molecules.
We describe a technique, using thin lines of triplet-state He2∗\mathrm{He}_{2}^{*}He2∗​ molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid 4He^{4}\mathrm{He}4He, together with its application to thermal counterflow in a channel. We show that, at relatively small velocities, where the superfluid is already turbulent, the flow of the normal fluid remains laminar, but with a distorted velocity profile, while at a higher velocity there is a transition to turbulence. The form of the structure function in this turbulent state differs significantly from that found in types of conventional turbulence. This visualization technique also promises to be applicable to other fluid dynamical problems involving cryogenic helium.
Metastable helium molecules generated in a discharge near a sharp tungsten tip immersed in superfluid 4He are imaged using a laser-induced-fluorescence technique. By pulsing the tip, a small cloud of He(2*) molecules is produced. We can determine the normal-fluid velocity in a heat-induced counterflow by tracing the position of a single molecule cloud. As we run the tip in continuous field-emission mode, a normal-fluid jet from the tip is generated and molecules are entrained in the jet. A focused 910 nm pump laser pulse is used to drive a small group of molecules to the first excited vibrational level of the triplet ground state. Subsequent imaging of the tagged molecules with an expanded 925 nm probe laser pulse allows us to measure the flow velocity of the jet. The techniques we developed provide new tools in quantitatively studying the normal fluid flow in superfluid helium.
Describing superfluid turbulence at intermediate scales between the intervortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines L\mathcal{L}L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides L\mathcal{L}L and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter Il0{I}_{l0}Il0​. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the vortex line density and the anisotropy parameter Il0{I}_{l0}Il0​ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.
Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi-two-dimensional system exhibiting a split cascade, is observed. The findings of this work could motivate new experimental settings to study quasi-two-dimensional superfluid turbulence in the bulk of three-dimensional experiments. They might also find applications beyond superfluids in systems described by more than one fluid component.