Quantum turbulence at finite temperature: The two-fluids cascade

Physical Review Fluids, 2021

We report hot-wire measurements performed in two very different, co-and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co-and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.

New Journal of Physics, 2021

Velocity measurements in turbulent superfluid helium between co-rotating propellers are reported. The parameters are chosen such that the flow is fully turbulent, and its dissipative scales are partly resolved by the velocity sensors. This allows for the first experimental comparison of spectra in quantum versus classical turbulence where dissipative scales are resolved. In some specific conditions, differences are observed, with an excess of energy at small scales in the quantum case compared to the classical one. This difference is consistent with the prediction of a pileup of superfluid kinetic energy at the bottom of the inertial cascade of turbulence due to a specific dissipation mechanism.

Physical Review B, 2021

Miniature heaters are immersed in flows of quantum fluid and the efficiency of heat transfer is monitored versus velocity, superfluid fraction and time. The fluid is 4 He helium with a superfluid fraction varied from 71% down to 0% and an imposed velocity up to 3 m/s, while the characteristic sizes of heaters range from 1.3 µm up to a few hundreds of microns. At low heat fluxes, no velocity dependence is observed, in agreement with expectations. In contrast, some velocity dependence emerges at larger heat flux, as reported previously, and three nontrivial properties of heat transfer are identified. First, at the largest superfluid fraction (71%), a new heat transfer regime appears at non-null velocities and it is typically 10% less conductive than at zero velocity. Second, the velocity dependence of the mean heat transfer is compatible with the square-root dependence observed in classical fluids. Surprisingly, the prefactor to this dependence is maximum for an intermediate superfluid fraction or temperature (around 2 K). Third, the heat transfer time series exhibit highly conductive short-lived events. These cooling glitches have a velocity-dependent characteristic time, which manifest itself as a broad and energetic peak in the spectrum of heat transfer time series, in the kHz range. After showing that the velocity dependence can be attributed to the breaking of superfluidity within a thin shell surrounding heaters, an analytical model of forced heat transfer in a quantum flow is developed to account for the properties reported above. We argue that large scale flow patterns must form around the heater, having a size proportional to the heat flux (here two decades larger than the heater diameter) and resulting in a turbulent wake. The observed spectral peaking of heat transfer is quantitatively consistent with the formation of a Von Kármán vortex street in the wake of a bluff body nearly two decades larger than the heater but its precise temperature and velocity dependence remains unexplained. An alternative interpretation for the spectral peaking is discussed, in connection with existing predictions of a bottleneck in the superfluid velocity spectra and energy equipartition.

Acta Applicandae Mathematicae, 2014

In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations presented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained confirm the non-classical signature of quantum turbulence already observed in past numerical studies.

Physical Review Fluids, 2018

The large scale turbulent statistics of mechanically driven superfluid 4 He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures T ∈ [1.3, 2.1] K. The numerics employ selfconsistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 K and 2 K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low T and close to T λ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

Physical Review B, 2014

The energy spectrum of the 3D velocity field, induced by collapsing vortex filaments is studied. One of the aims of this work is to clarify the appearance of the Kolmogorov type energy spectrum E(k) ∝ k −5/3 , observed in many numerical works on discrete vortex tubes (quantized vortex filaments in quantum fluids). Usually, explaining classical turbulent properties of quantum turbulence, the model of vortex bundles, is used. This model is necessary to mimic the vortex stretching, which is responsible for the energy transfer in classical turbulence. In our consideration we do not appeal to the possible "bundle arrangement" but explore alternative idea that the turbulent spectra appear from singular solution, which describe the collapsing line at moments of reconnection. One more aim is related to an important and intensively discussed topic-a role of hydrodynamic collapse in the formation of turbulent spectra. We demonstrated that the specific vortex filament configuration generated the spectrum E(k) close to the Kolmogorov dependence and discussed the reason for this as well as the reason for deviation. We also discuss the obtained results from point of view of the both classical and quantum turbulence.

Low Temperature Physics, 2019

The hydrodynamic problems of superfluid fluid containing chaotic tangles of quantized vortex filaments are discussed. The construction of such hydrodynamics crucially depends on the statistics of vortex tangles, and two important cases are presented. The first corresponds to a tangle that consists of entirely chaotic vortex filaments. This case is implemented in counterflowing helium, and is referred to as Vinen turbulence. In the construction of macroscopic dynamics, the system of equations is closed by the Vinen equation for the density of vortex filaments. The second, referred to as the Hall-Vinen-Bekarevich-Khalatnikov case, corresponds to a situation where the system contains bundles of polarized vortex filaments. In this instance, the system is closed by the Feynman equation that relates density of vortex filaments with the vorticity of superfluid velocity. Problems related to the application of both approaches are discussed.

Physical Review B, 2015

We present the first direct-numerical-simulation study of the statistical properties of twodimensional superfluid turbulence in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normal-fluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli. Our study leads to specific suggestions for experiments.

Physics of Fluids

We use pseudospectral direct numerical simulations to solve the three-dimensional (3D) Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model of superfluid helium. We then explore the statistical properties of inertial particles, in both coflow and counterflow superfluid turbulence (ST) in the 3D HVBK system; particle motion is governed by a generalization of the Maxey–Riley–Gatignol equations. We first characterize the anisotropy of counterflow ST by showing that there exist large vortical columns. The light particles show confined motion as they are attracted toward these columns, and they form large clusters; by contrast, heavy particles are expelled from these vortical regions. We characterize the statistics of such inertial particles in 3D HVBK ST: (1) The mean angle [Formula: see text] between particle positions, separated by the time lag τ, exhibits two different scaling regions in (a) dissipation and (b) inertial ranges, for different values of the parameters in our model; in parti...

Proceedings of the National Academy of Sciences, 2014

Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales.

The European Physical Journal Plus, 2020

We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is governed by a modified Navier–Stokes equation. The superfluid vortex lines and normal fluid components are fully coupled in a self-consistent manner by the friction force, which induces local disturbances in the normal fluid in the vicinity of vortex lines. The main focus of this work is the numerical scheme for distributing the friction force to the mesh points where the normal fluid is defined (stemming from recent advances in the study of the interaction between a classical viscous fluid and small active particles) and for evaluating the velocity of the normal fluid on the Lagrangian discretisation points along the vortex lines. In particular, we show that if this numerical scheme is not careful enough, spurious results may occur. The new scheme whic...

Physical Review B, 2016

In mechanically driven superfluid turbulence the mean velocities of the normal-and superfluid components are known to coincide: Un = Us. Numerous laboratory, numerical and analytical studies showed that under these conditions the mutual friction between the normal-and superfluid velocity components couples also their fluctuations: u ′ n (r, t) ≈ u ′ s (r, t) almost at all scales. In this paper we show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity Uns ≡ Un -Us = 0. We suggest a simple analytic model for the cross correlation function u ′ n (r, t) • u ′ s (r ′ , t) and its dependence on Uns. We demonstrate that u ′ n (r, t) and u ′ s (r, t) are decoupled almost in the entire range of separations |rr ′ | between the energy containing scale and intervortex distance.