We study turbulence in self-gravitating superfluids by performing direct numerical simulations of the 3D Gross-Pitaevskii-Poisson (GPP) equation, which is also a model for dark matter haloes around galaxies. In the absence of self-gravity, the spectrally truncated Gross-Pitaevskii (GP) equation shows the emergence of Kolmogorov's $5/3$ scaling in the incompressible kinetic energy spectrum. Introducing self-gravity, we observe the formation of different structures, from sheet-like to spherically collapsed structures, which introduce a minimum in the kinetic energy spectrum that corresponds to the sizes of these structures. The system shows early convergence towards statistically stationary states, which we show by the onset of thermalisation in the compressible kinetic energy spectrum, where $E_{\rm kin}^c \propto k^2$. We also show that the formation of such large-scale structures suggests that the particles (bosons) move from small to large scales through an inverse cascade, supporting a mechanism for the formation of large-scale structures, such as dark matter haloes, around our galaxy Milky Way.
Externally driven interstellar turbulence plays an important role in shaping the density structure in molecular clouds. Here we study the dynamical role of internally driven turbulence in a self-gravitating molecular cloud core. Depending on the initial conditions and evolutionary stages, we find that a self-gravitating core in the presence of gravity-driven turbulence can undergo constant, decelerated, and accelerated infall, and thus has various radial velocity profiles. In the gravity-dominated central region, a higher level of turbulence results in a lower infall velocity, a higher density…
Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous, (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (Galtier and Banerjee, Phys. Rev. Lett., 107, 134501, 2011; Banerjee and Galtier, Phys. Rev. E, 87, 013019, 2013), the current exact relation shows t…
There exist inherent mechanisms of spontaneous breaking of local mirror symmetry (parity) in fluid turbulence. A good example is Kerr's mechanism based on the inviscid vortex interactions. Such interactions can result in the appearance of the local adjacent regions with strong oppositely signed helicity, while the global (net) helicity still remains zero due to the global mirror symmetry. It is shown, using results of direct numerical simulations and laboratory measurements, that the spontaneous breaking of local mirror symmetry can dominate turbulent dynamics in the superfluid helium II and i…
We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada (GOY) shell model. We examine the dependence of the multiscaling exponents on the normal-fluid fraction and the mutual-friction coefficients. Our extensive study of the 3D-HVBK shell model shows that the multiscaling behavior of the velocity structure functions in superfluid turbulence is …
In a two-dimensional (2D) classical fluid, a large-scale flow structure emerges out of turbulence, which is known as the inverse energy cascade where energy flows from small to large length scales. An interesting question is whether this phenomenon can occur in a superfluid, which is inviscid and irrotational by nature. Atomic Bose-Einstein condensates (BECs) of highly oblate geometry provide an experimental venue for studying 2D superfluid turbulence, but their full investigation has been hindered due to a lack of the circulation sign information of individual quantum vortices in a turbulent …
New methods of flow visualization near absolute zero have opened the way to directly compare quantum turbulence (in superfluid helium) to classical turbulence (in ordinary fluids such as air or water) and explore analogies and differences. We present results of numerical simulations in which we examine the statistics of the superfluid acceleration in thermal counterflow. We find that, unlike the velocity, the acceleration obeys scaling laws similar to classical turbulence, in agreement with a recent quantum turbulence experiment of La Mantia et al.
Nonthermal fixed points of far-from-equilibrium dynamics of a dilute degenerate Bose gas are analysed in two and three spatial dimensions. For such systems, universal power-law distributions, previously found within a nonperturbative quantum-field theoretic approach, are shown to be related to vortical dynamics and superfluid turbulence. The results imply an interpretation of the momentum scaling at the nonthermal fixed points in terms of independent vortex excitations of the superfluid. Long-wavelength acoustic excitations on the top of these are found to follow a non-thermal power law. The r…
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 w…
We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schrödinger-Helmholtz equations have a simultaneous inverse cascade …
We study two dimensional superfluid turbulence by employing an effective description valid in the limit where the density of superfluid vortices is parametrically small. At sufficiently low temperatures the effective description yields an inverse cascade with Kolmogorov energy spectrum $E(k) \sim k^{-5/3}$. Denoting the number of vortices as a function of time by $N(t)$, we find that the vortex annihilation rate scales like $\dot N \sim N^{5/3}$ in states with an inverse cascade and $\dot N \sim N^2$ for laminar flow.
We present the first direct-numerical-simulation study of the statistical properties of two-dimensional 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 …
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 $β=1/2$ …
We show by direct numerical simulations that the turbulence generated by steadily heating a long cylinder immersed in helium~II is strongly inhomogeneous and consists of a dense turbulent layer of quantized vortices localized around the cylinder. We analyse the properties of this superfluid turbulence in terms of radial distribution of the vortex line density and the anisotropy and we compare these properties to the better known properties of homogeneous counterflow turbulence in channels.
Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by S. Banerjee and S. Galtier (Phys. Rev. E,93, 033120, 2016) and S. Banerjee and S. Galtier (J. Phys. A, Math. and Theor.,50, 015501, 2017), an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kine…
There is a fundamental connection between temperature-quenched 2D superfluids and 2D quantum turbulence: the mechanism responsible for the decay of the vorticity after the quench is the enstrophy cascade of 2D turbulence. The range of the cascade is shown to increase with time after the quench as $t^{1/2}$, being equal to the dynamic scaling length characterizing the quench. These results may apply to other phase-ordering transitions involving the decay of topological objects.
Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, wherea…
Interacting systems driven far from equilibrium tend to evolve to steady states exhibiting large-scale structure and order. In two-dimensional turbulent flow the seemingly random swirling motion of a fluid can evolve towards persistent large-scale vortices. Lars Onsager proposed a model based on statistical mechanics of quantized vortices to explain such behavior. Here we report the first experimental confirmation of Onsager's model of turbulence. We drag a grid barrier through an oblate superfluid Bose--Einstein condensate to generate non-equilibrium distributions of vortices. We observe an i…
The local induction approximation (LIA) of the Biot-Savart law is often used for numerical and analytical investigations of vortex dynamics in the theory of superfluid turbulence. In this paper, using numerical simulation, some features of the LIA is considered. The temporal evolution of vortex loop spectrum is studied numerically.
Superfluid helium consists of two inter-penetrating fluids, a viscous normal fluid and an inviscid superfluid, coupled by a mutual friction. We develop a two-fluid shell model to study superfluid turbulence. We investigate the energy spectra and the balance of fluxes between the two fluids as a function of temperature in continuously forced turbulence, and, in the absence of forcing, the decay of turbulence. We furthermore investigate deviations from the $k^{-5/3}$ spectrum caused by the mutual friction force. We compare our results with experiments and existing calculations. We find that, at …
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a non-zero 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…
Kelvin waves propagating on quantum vortices play a crucial role in the phenomenology of energy dissipation of superfluid turbulence. Previous theoretical studies have consistently focused on the zero-temperature limit of the statistical physics of Kelvin-wave turbulence. In this letter, we go beyond this athermal limit by introducing a small but finite temperature in the form of non-zero mutual friction dissipative force; A situation regularly encountered in actual experiments of superfluid turbulence. In this case we show that there exists a new typical length-scale separating a quasi-inerti…
The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~ 1640. The result is corroborated by high-resolution simulations of Landau-Tisza's two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the Kármán-Howarth equation (including a viscous term) is not valid \emph{a priori} in a superfluid, it …
Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by mapping the dynamics of certain quantum theories onto the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov -5/3 scaling law, as it does for turbulent flows in normal fluid…
Superfluid turbulence is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the relative value of the friction force acting on a vortex with respect to the non-dissipative forces. The inverse parameter 1/q plays the same role as the Reynolds number Re=UR/νin classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence, described by a Kolmogorov cascade, occurs when Re >> 1 in classical hydrodynamics. In superfluids, the developed turbulence occurs at q << 1. Another …
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/νin classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is t…
We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate (BEC) that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation, we find that the remaining vortices self-organise into two macroscopic coherent `Onsager vortex' clusters that are stable indefinitely. We demonstrate that this occurs due to a novel physical mechanism --- the evaporative heating of the vortices --- that results in a negative temperature phase transition in the vortex degrees of freedom. At the end o…
The local induction approximation (LIA) of the Biot-Savart law is often used for numerical and analytical investigations of vortex dynamics (in particular in the theory of superfluid turbulence). In this paper, using renormalization group (RG) methods, some features of the LIA is considered. The exact statistical solution of the LIA equation is presented. The problem of "marginal" terms, appearing at the Wilson's approach to the RG-procedure, is concerned.
Observations of quantum turbulence in pure superfluid 4He in a rotating container are reported. New techniques of large-scale forcing (rotational oscillations of the cubic container) and detecting (monitoring ion transport along the axis of rotation) turbulence were implemented. Near the axial walls, with increasing forcing the vortex tangle grows without an observable threshold. This tangle gradually develops into bulk turbulence at a characteristic amplitude of forcing that depends on forcing frequency and rotation rate. At higher amplitudes, the total vortex line length increases rapidly. R…
The intermittency of turbulent superfluid helium is explored systematically in a steady wake flow from 1.28 K up to T>2.18K using a local anemometer. This temperature range spans relative densities of superfluid from 96% down to 0%, allowing to test numerical predictions of enhancement or depletion of intermittency at intermediate superfluid fractions. Using the so-called extended self-similarity method, scaling exponents of structure functions have been calculated. No evidence of temperature dependence is found on these scaling exponents in the upper part of the inertial cascade, where turbul…
In Fermi superfluids, like superfluid 3He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction the internal dynamics of the superfluid component becomes more important compared to the damping and coupling effects from the normal component. This causes profound changes in superfluid dynamics: the temperature-depe…
We consider the intermittent behavior of superfluid turbulence in $^4$He. Due to the similarity in the nonlinear structure of the two-fluid model of superfluidity and the Euler and Navier-Stokes equations one expects the scaling exponents of the structure functions to be the same as in classical turbulence for temperatures close to the superfluid transition $T_λ$ and also for $T\ll T_λ$. This is not the case when mutual friction becomes important. Using shell model simulations, we propose that for an intermediate regime of temperatures, such that the density of normal and superfluid components…
Inpired by recent measurements of the velocity and acceleration statistics of Lagrangian tracer particles embedded in a turbulent quantum liquid we propose a new superstatistical model for the dynamics of tracer particles in quantum turbulence. Our model consists of random sequences S/N/S/... where the particle spends some time in the superfluid (S) and some time in the normal fluid (N). This model leads to a superposition of power law distributions generated in the superfluid and Gaussian distributions in the normal liquid, in excellent agreement with experimental measurements. We include mem…
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…
Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.
We describe a new technique, using thin lines of triplet-state He2 molecular tracers created by femtosecond-laser field-ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid 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 fr…
We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose--Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross--Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equili…
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in …
We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a model with differential approximation for the energy fluxes in the k-space carried by the collective hydrodynamic motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves. The model predicts energy spectra of the hydrodynamic and the Kelvin waves components of the system, which experience a smooth crossover between different regimes of motion over a finite range of scales.
The results of experimental and theoretical studies of the parametric decay instability of capillary waves on the surface of superfluid helium He-II are reported. It is demonstrated that in a system of turbulent capillary waves low-frequency waves are generated along with the direct Kolmogorov-Zakharov cascade of capillary turbulence. The effects of low-frequency damping and the discreteness of the wave spectrum are discussed.
The energy spectrum of the superfluid turbulence without the normal fluid is studied numerically under the vortex filament model. Time evolution of the Taylor-Green vortex is calculated under the full nonlocal Biot-Savart law. It is shown that for k<2pi/l, the energy spectrum is very similar to the Kolmogorov's -5/3 law which is the most important statistical property of the conventional turbulence, where k is the wave number of the Fourier component of the velocity field and 1 the average intervortex spacing. The vortex length distribution becomes to obey a scaling property reflecting the sel…
The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence (NFT) have been a central challenge in quantum hydrodynamics, since it is expected to cause the unsolved T2 state of QT. We numerically studied the coupled dynamics of the two turbulences in thermal counterflow. NFT is driven by external forces to control its turbulent intensity, and the fast multipole method accelerates the calculation of QT. We show that NFT enhances QT via mutual friction. The vortex line density $L$ of the QT satisfies the statistical law $L^{1/2} \approx γV_{ns}$ with the counterflow velocity $V_{…
Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hyd…
Quantum mechanics places significant restrictions on the hydrodynamics of superfluid flows. Despite this it has been observed that turbulence in superfluids can, in a statistical sense, share many of the properties of its classical brethren; coherent bundles of superfluid vortices are often invoked as an important feature leading to this quasi-classical behavior. A recent experimental study [E. Rusaouen, B. Rousset, and P.-E. Roche, EPL, {\bf 118}, 1, 14005, (2017)] inferred the presence of these bundles through intermittency in the pressure field, however direct visualization of the quantized…
We present velocity spectra measured in three cryogenic liquid 4He steady flows: grid and wake flows in a pressurized wind tunnel capable of achieving mean velocities up to 5 m/s at temperatures above and below the superfluid transition, down to 1.7 K, and a "chunk" turbulence flow at 1.55 K, capable of sustaining mean superfluid velocities up to 1.3 m/s. Depending on the flows, the stagnation pressure probes used for anemometry are resolving from one to two decades of the inertial regime of the turbulent cascade. We do not find any evidence that the second order statistics of turbulence below…
This letter addresses the question which, after a decade-long discussion, still remains open: what is the nature of the ultraquantum regime of decay of quantum turbulence? The model developed in this work reproduces both the ultraquantum and the quasiclassical decay regimes and explains their hydrodynamical natures. In the case where turbulence is generated by forcing at some intermediate lengthscale, e.g. by the beam of vortex rings in the experiment of Walmsley and Golov [Phys. Rev. Lett. {\bf 100}, 245301 (2008)], we explained the mechanisms of generation of both ultraquantum and quasiclass…
We discuss a recent experiment in which the spectrum of the vortex line density fluctuations has been measured in superfluid turbulence. The observed frequency dependence of the spectrum, $f^{-5/3}$, disagrees with classical vorticity spectra if, following the literature, the vortex line density is interpreted as a measure of the vorticity or enstrophy. We argue that the disagrement is solved if the vortex line density field is decomposed into a polarised field (which carries most of the energy) and an isotropic field (which is responsible for the spectrum).
Superfluid flow around an oscillating microsphere is investigated at temperatures down to 25 mK. Stable laminar flow below a critical velocity and turbulence at large drives are found to be separated below 0.5 K by an intermediate range of driving forces where the flow is unstable, intermittently switching between laminar and turbulent phases. We have recorded time series of this switching phenomenon and have made a statistical analysis of the switching probability. The mean lifetime of the turbulent phases grows with increasing drive and becomes infinite at a critical value. Stability of the …
Cosmic structure formation is characterized by the complex interplay between gravity, turbulence, and magnetic fields. The processes by which gravitational energy is converted into turbulent and magnetic energies, however, remain poorly understood. Here, we show with high-resolution, adaptive-mesh simulations that MHD turbulence is efficiently driven by extracting energy from the gravitational potential during the collapse of a dense gas cloud. Compressible motions generated during the contraction are converted into solenoidal, turbulent motions, leading to a natural energy ratio of E_sol/E_to…
The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vort…
Intermittency is a hallmark of turbulence, which exists not only in turbulent flows of classical viscous fluids but also in flows of quantum fluids such as superfluid $^4$He. Despite the established similarity between turbulence in classical fluids and quasi-classical turbulence in superfluid $^4$He, it has been predicted that intermittency in superfluid $^4$He is temperature dependent and enhanced for certain temperatures, which strikingly contrasts the nearly flow-independent intermittency in classical turbulence. Experimental verification of this theoretical prediction is challenging since …
We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.
We suggest a "minimal model" for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier-Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to the temperature dependent parameter $q=α/(1+α')$, where $α$ and $α'$ denote the dimensionless parameters chara…
Superfluid Turbulence is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, inter penetrating turbulent fluids: the first is inviscid with quantised vorticity, 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 o ordinary turbulence. We present experimental, numerical and theoretical results which explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller sc…
We use pseudospectral direct numerical simulations (DNSs) 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 towards these columns and they f…
We have simulated the decay of thermal counterflow quantum turbulence from a statistically steady state at T=1.9[K], with the assumption that the normal fluid is at rest during the decay. The results are consistent with the predictions of the Vinen equation (in essence the vortex line density (VLD) decays as t^{-1}). For the statistically steady state, we determine the parameter c_2, which connects the curvature of the vortex lines and the mean separation of vortices. A formula connecting the parameter χ_2 of the Vinen equation with c_2 is shown to agree with the results of the simulations. Di…
In a two-dimensional (2D) turbulent fluid containing point-like vortices, Lars Onsager predicted that adding energy to the fluid can lead to the formation of persistent clusters of like-signed vortices, i.e., Onsager vortex (OV) clusters. In the evolution of 2D superfluid turbulence in a uniform disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV clusters with opposite signs can form without any energy input. This striking spontaneous order was explained as due to a vortex evaporative-heating mechanism, i.e., annihilations of vortex-antivortex pairs which remove the…
We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids, and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed in Ref. \cite{10LN} enjoys existence, uniqueness and regularity of the pre-factor. Furthermore, we present numerical results of the dynamical …
