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 $L(t)$.
By injecting negative ions in superfluid 4He in the zero-temperature limit (T < 0.5 K), we generated tangles of quantized vortex line with negligible large-scale flow. For this quantum regime of superfluid turbulence, the vortex line length L was found to decay at late time t as L proportional to t^{-1}; the prefactor being independent of the initial value of L. The corresponding effective kinematic viscosity is 0.1 kappa, where kappa is the circulation quantum. At T > 0.7 K, a jet of ions generates quasi-classical tangles identical to those produced by mechanical means.
We compare the decay of turbulence in superfluid $^4$He produced by a moving grid to the decay of turbulence created by either impulsive spin-down to rest or by intense ion injection. In all cases the vortex line density $L$ decays at late time $t$ as $L \propto t^{-3/2}$. At temperatures above 0.8 K, all methods result in the same rate of decay. Below 0.8 K, the spin-down turbulence maintains initial rotation and decays slower than grid turbulence and ion-jet turbulence. This may be due to a decoupling of the large-scale superfluid flow from the normal component at low temperatures, which cha…
We present a combined numerical and experimental study of Andreev scattering from quantum turbulence in superfluid $^3$He-B at ultralow temperatures. We simulate the evolution of moderately dense, three-dimensional, quasiclassical vortex tangles and the Andreev reflection of thermal quasiparticle excitations by these tangles. This numerical simulation enables us to generate the two-dimensional map of local Andreev reflections for excitations incident on one of the faces of a cubic computational domain, and to calculate the total coefficient of Andreev reflection as a function of the vortex lin…
The influence of He-3 nuclear magnetization relaxation on the second viscosity in quantum solutions subjected to an external oscillating magnetic field is studied. The cases of first-, second- and forth-sound waves are examined. The expressions for the second viscosity coefficients are derived and the conditions for the viscosity to be decreased are analyzed.
In classical turbulence the kinematic viscosity $ν$ is involved in two phenomena. The first is the energy dissipation and the second is the mechanical momentum flux toward the wall. In superfluid turbulence the mechanism of energy dissipation is different, and it is determined by an effective viscosity which was introduced by Vinen and is denoted as $ν'$. In this paper we show that in superfluid turbulence the transfer of mechanical momentum to the wall is caused by the presence of a quantum vortex tangle, giving rise to another effective "momentum" viscosity that we will denote as $ν_\text{m}…
The $p$-wave superfluid state is a promising spin-triplet and non $s$-wave pairing state in an ultracold Fermi gas. In this work we study the low-temperature shear viscosity of a one-component $p$-wave superfluid Fermi gas, by means of Kubo formalism. Our study is done in the strong-coupling limit where Fermi superfluid reduces into a system of composite bosons. Taking into account ${{p}_{x}}$-wave Cooper channel in the self-energy, the viscous relaxation rates are determined. The relaxation rates related to these interactions are calculated as a function of temperature. Their temperature depe…
We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature T limit the shear viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the chemical potential and the Fermi energy, mu=xi E_F. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature T_c. A naive extrapola…
We report on the extension of the experiments (P. M. Walmsley et al., Phys. Rev. Lett. 99, 265302 (2007)) on the decay of quasiclassical turbulence generated by an impulsive spin-down from angular velocity Omega to rest of superfluid 4He in a cubic container at temperatures 0.15 K - 1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Following the spin-down, the maximal density of vortices is observed after time t ~ 10 Omega^-1. By observing the propagation of ions along the axis of the initial rotation, the transient dynamics of the turbulence spreading fro…
We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by th…
In this work we study the influence of orbital viscosity on the dynamics of the order parameter texture in the superfluid B-phase of $^3$He near a moving bounda ry. Based on the redistribution of thermal quasiparticles within the texture, we develop a model which bestows a significant effective mass on the interface, an d gives a new mechanism for friction as the boundary moves. We have tested the model against existing data of a moving A-B interface whose motion was controlled using magnetic field. The model allows some predictions in experimental situations which involve texture rearrangemen…
Turbulence in a superfluid in the zero temperature limit consists of a dynamic tangle of quantized vortex filaments. Different types of turbulence are possible depending on the level of correlations in the orientation of vortex lines. We provide an overview of turbulence in superfluid $^4$He with a particular focus on recent experiments probing the decay of turbulence in the zero temperature regime below 0.5 K. We describe extensive measurements of the vortex line density during the free decay of different types of turbulence: ultraquantum and quasiclassical turbulence in both stationary and r…
We compute the coefficients of bulk viscosity for a non-relativistic superfluid corresponding to a fermionic system close to the unitarity limit. We consider the low temperature regime assuming that the transport properties of the system are dominated by phonons. To compute the coefficients of bulk viscosity we use kinetic theory in the relaxation time approximation and the low energy effective field theory of the corresponding system. We show that the three independent bulk viscosity coefficients, $ζ_1, ζ_2, ζ_3$, associated with irreversible flows vanish for phonons with a linear dispersion …
Reynolds similitude, a key concept in hydrodynamics, states that two phenomena of different length scales with a similar geometry are physically identical. Flow properties are universally determined in a unified way in terms of the Reynolds number ${\cal R}$ (dimensionless, ratio of inertial to viscous forces in incompressible fluids). For example, the drag coefficient $c_D$ of objects with similar shapes moving in fluids is expressed by a universal function of ${\cal R}$. Certain studies introduced similar dimensionless numbers, that is, the superfluid Reynolds number ${\cal R}_s$, to charact…
Based on our current understanding of statistics of quantum turbulence as well as on results of intensive ongoing analytical, numerical and experimental studies we overview here the following problems in the large-scale, space-homogeneous, steady-state turbulence of superfluid $^4$He and $^3$He: 1) Energy spectra of normal and superfluid velocity components; 2) Cross-correlation function of normal and superfluid velocities; 3) Energy dissipation by mutual friction and viscosity; 4) Energy exchange between normal and superfluid components; 5) High-order statistics and intermittency effects. The…
The dynamics of quantized vortices is studied in superfluid 3He-B after a rapid stop of rotation. We use Andreev reflection of thermal excitations to monitor vortex motion with quartz tuning fork oscillators in two different experimental setups at temperatures below 0.2Tc. Deviations from ideal cylindrical symmetry in the flow environment cause the early decay to become turbulent. This is identified from a rapid initial overshoot in the vortex density above the value before the spin-down and its subsequent decay with a t^(-3/2) time dependence. The high polarization of the vortices along the r…
Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\exp(-k/k_β)^β$ and $β= 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $β=1/2$ …
To model isotropic homogeneous quantum turbulence in superfluid helium, we have performed Direct Numerical Simulations (DNS) of two fluids (the normal fluid and the superfluid) coupled by mutual friction. We have found evidence of strong locking of superfluid and normal fluid along the turbulent cascade, from the large scale structures where only one fluid is forced down to the vorticity structures at small scales. We have determined the residual slip velocity between the two fluids, and, for each fluid, the relative balance of inertial, viscous and friction forces along the scales. Our calcul…
In low-temperature superfluid helium, viscosity is zero, and vorticity takes the form of discrete, vortex filaments of fixed circulation and atomic thickness. We present numerical evidence of three-dimensional inverse energy transfer from small length scales to large length scales in superfluid turbulence generated by a flow of vortex rings. We argue that the effect arises from the anisotropy of the flow, which favours vortex reconnections of vortex loops of the same polarity, and that it has been indirectly observed in the laboratory. The effect open questions about analogies with related pro…
There are two commonly discussed forms of quantum turbulence in superfluid $^4$He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, $L$, in the former case is often described by the equation $dL/dt=-χ_2 (κ/2π)L^2$, where $κ$ is the quantum of circulation, and $χ_2$ is a…
