J. Salort, C. Baudet, B. Castaing, B. Chabaud, F. Daviaud, T. Didelot, P. Diribarne, B. Dubrulle, Y. Gagne, F. Gauthier, A. Girard, B. Hébral, B. Rousset, P. Thibault, P. -E. Roche
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 the superfluid transition differ from the ones of classical turbulence, above the transition.
To explain the observed decay of superfluid turbulence at very low temperature, it has been proposed that a cascade of Kelvin waves (analogous to the classical Kolmogorov cascade) transfers kinetic energy to length scales which are small enough that sound can be radiated away. We report results of numerical simulations of the interaction of quantized vortex filaments. We observe the development of the Kelvin-waves cascade, and compute the statistics of the curvature, the amplitude spectrum (which we compare with competing theories) and the fractal dimension.
We study intermittency of circulation moments in turbulent superfluid helium by using experimental grid turbulence and numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. More precisely, we compute the velocity circulation $Γ_r$ in loops of size $r$ laying in the inertial range. For both, experimental and numerical data, the circulation variance shows a clear Kolmogorov scaling $\langle Γ_r^2 \rangle \sim r^{8/3}$ in the inertial range, independently of the temperature. Scaling exponents of high-order moments are comparable, within error bars, to previously reported anomalous…
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 rece…
Dissipating of disorder quantum vortices in an annular two-dimensional Bose-Einstein condensate can form a macroscopic persistent flow of atoms. We propose a protocol to create persistent flow with high winding number based on a double concentric ring-shaped configuration. We find that a sudden geometric quench of the trap from single ring-shape into double concentric ring-shape will enhance the circulation flow in the outer ring-shaped region of the trap when the initial state of the condensate is with randomly distributed vortices of the same charge. The circulation flows that we created are…
The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, ${\rm Re}_s$, that ac…
When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a non-zero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the…
Heat is carried in superfluid He-4 by the motion of the normal fluid$^{1}$, a counterflowing superfluid component serving to eliminate any net mass flow. It has been known for many years that above a critical heat current the superfluid component in this counterflow becomes turbulent. This turbulence takes the form of a disorganized tangle of quantized vortex lines and is maintained by the relative motion of the two fluids$^{2-3}$. It has been suspected that the normal fluid may also become turbulent$^{4}$, but experimental verification is difficult without a technique for visualizing the flow…
In this paper, we report the first evidence of an enhancement of the heat transfer from a heated wire by an external turbulent flow of superfluid helium. We used a standard Pt-Rh hot-wire anemometer and overheat it up to 21 K in a pressurized liquid helium turbulent round jet at temperatures between 1.9 K and 2.12 K. The null-velocity response of the sensor can be satisfactorily modeled by the counter flow mechanism while the extra cooling produced by the forced convection is found to scale similarly as the corresponding extra cooling in classical fluids. We propose a preliminary analysis of t…
Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this system is through the application of a heat flux, so called thermal counterflow. Of particular interest is how turbulence in the superfluid responds to both a laminar and turbulent normal fluid in the presence of walls. We model superfluid vortex lines as reconnecting space curves with fixed circulation, and consider both laminar (Poiseuille) and turbulent norma…
The onset of turbulent flow around an oscillating sphere is known to occur at a critical velocity vc ~ sqrt(kappa omega) where kappa is the circulation quantum and omega is the oscillation frequency. However, in a small interval of driving force amplitudes F (or corresponding velocity amplitudes of few percent above vc) the turbulent flow is found to be unstable. The flow pattern switches intermittently between potential flow and turbulence. The lifetimes of the turbulent phases have an exponential distribution and the mean lifetimes tau grow very rapidly with increasing driving force, namely …
We study the necessary condition under which a resonantly driven exciton polariton superfluid flowing against an obstacle can generate turbulence. The value of the critical velocity is well estimated by the transition from elliptic to hyperbolic of an operator following ideas developed by Frisch, Pomeau, Rica for a superfluid flow around an obstacle, though the nature of equations governing the polariton superfluid is quite different. We find analytical estimates depending on the pump amplitude and on the pump energy detuning, quite consistent with our numerical computations.
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 …
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…
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 …
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…
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…
Filamentary regions of high vorticity irregularly form and disappear in the turbulent flows of classical fluids. We report an experimental comparative study of these so-called " coherent structures " in a classical versus quantum fluid, using liquid helium with a superfluid fraction varied from 0% up to 83%. The low pressure core of the vorticity filaments is detected by pressure probes located on the sidewall of a 78-cm-diameter Von Kármán cell driven up to record turbulent intensity (R $λ$ $\sim$ $\sqrt$ Re 10000). The statistics of occurrence, magnitude and relative distribution of the fila…
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…
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…
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…
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…
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.
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 …
Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_{1},l_{2},l)$ and $B(l,l_{1},l_{2})$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_{1}$and $l_{2}$ collide and form the single loop of length $ l=l_{1}+l_{2}$. Quantity $% B(l,l_{1},l_{2})…
The coupled dynamics of the two-fluid model of superfluid $^4$He is numerically studied for quantum turbulence of the thermal counterflow in a square channel. We combine the vortex filament model of the superfluid and the Navier-Stokes equations of normal fluid. Simulations of the coupled dynamics show that the velocity profile of the normal fluid is deformed significantly by superfluid turbulence as the vortices become dense. This result is consistent with recently performed visualization experiments. We introduce a dimensionless parameter that characterizes the deformation of the velocity pr…
We study numerically the process of vortex nucleation at the wake of a moving object in superfluids using a generalized and non-local Gross-Pitaevskii model. The non-local potential is set to reproduce the roton minimum present in the excitation spectrum of superfluid helium. By applying numerically a Newton-Raphson method we determine the bifurcation diagram for different types of non-linearities and object sizes which allow for determining the corresponding critical velocities. In the case of a non-local potential, we observe that for small object sizes the critical velocity is simply determ…
An approximate method to compute mean velocity profiles in turbulent flows is developed. This approach is based on the equation connecting the Reynolds stress and mean velocity. By using the measured values of pressure drop and average (bulk) flow velocity, such characteristics of a turbulent flow as the mean velocity and Reynolds stress distributions were calculated and compared with the experimental measurements in different pipes and channels for various fluids and gases. These show good agreement for a wide range of Reynolds numbers.
We investigate and model pressure effects on the turbulent burning velocity over a wide range of pressures and turbulence intensities with the direct numerical simulation (DNS) of statistically planar turbulent premixed flames for lean hydrogen/air mixture. DNS results indicate that the stretch factor has an impact on the turbulent burning velocity and flame surface area at elevated pressures. In particular, the enhanced stretch factor at high pressures increases the ratio of turbulent and laminar burning velocities, diminishing the "bending" effect. Based on a good consistency between turbule…
The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow, obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations.
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…
The velocity-vorticity correlation integral (Chkhetiani invariant) is an invariant of a viscous Karman-Howarth equation. In the tree-dimensional space this invariant can naturally determine a turbulent diffusivity (viscosity). It is shown, using results of direct numerical simulations, that distributed chaos dominated by this integral can provide an adequate description of the turbulent Rayleigh-Bénard convection, stably stratified turbulence and Rayleigh-Taylor mixing at Prandtl number $Pr \sim 1$.
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.
We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate which depends on the flow properties. The same law is observed in two different flows indicating that it can be a generic property of turbulent flows.
A composite representation of the turbulent boundary-layer velocity profile is proposed, which combines a recently determined accurate interpolation of the universal law of the wall with a simple analytical expression of the smooth transition of velocity to a constant value in the outer stream. Several examples are given of application of this representation to DNS and experimental data from the literature, and a conjecture is offered for the asymptotic approach of the velocity to its constant inviscid value.
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…
On the grounds of both widely known experimental and numerical data of the strain-rate tensor statistical properties in the fully developed incompressible turbulent flow and the integral transformations deduced in the article, some important statistical properties of the flow, known as kinematical, are found to be dynamical (i.e. taking place purely in a turbulent flow). A new pseudo-Gauss distribution is introduced in the article and, as a consequence of these properties, a considerable feature distinguishing this distribution from the Gauss one is found to be the general feature of the turbu…
We investigate the thermal counterflow of the superfluid $^4$He by numerically simulating three-dimensional fully coupled dynamics of the two fluids, namely quantized vortices and a normal fluid. We analyze the velocity fluctuations of the laminar normal fluid arising from the mutual friction with the quantum turbulence of the superfluid component. The streamwise fluctuations exhibit higher intensity and longer-range autocorrelation, as compared to transverse ones. The anomalous fluctuations are consistent with visualization experiments [Mastracci et al., Phys. Rev. Fluids, Vol. 4, 083305 (201…
It is extremely uncommon to be able to predict the velocity profile of a turbulent flow. In two-dimensional flows, atmosphere dynamics, and plasma physics, large scale coherent jets are created through inverse energy transfers from small scales to the largest scales of the flow. We prove that in the limits of vanishing energy injection, vanishing friction, and small scale forcing, the velocity profile of a jet obeys an equation independent of the details of the forcing. We find another general relation for the maximal curvature of a jet and we give strong arguments to support the existence of …
A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over a wide range of Re yield 0.45 to be the universal Karman constant. A new spatial invariant characterizing outer dynamics is discovered and validated by reliable experimental data. The theory predicts the mean velocity profile (MVP) with 99% accuracy for high Re experimental data (up to 40 millions), and offers a quantitative explanation for recent observatio…
The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.
The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid Gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe a reduction of velocity fluctuations at all frequencies in the spectrum when the magnetic field is increased.
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed by n = 2 and 3 velocity gradients at a single point in turbulent homogeneous shear flows, and in the log-layer of a turbulent channel flow, and we characterize the departure of these tensors from the corresponding isotropic prediction. Specifically, we separate the even components of the tensors, invariant under reflexion with respect to all axes, from the …
Motivated by experiments performed in superfluid helium, we study numerically the motion of toroidal bundles of vortex filaments in an inviscid fluid. We find that the evolution of these large-scale vortex structures involves the generalised leapfrogging of the constituent vortex rings. Despite three dimensional perturbations in the form of Kelvin waves and vortex reconnections, toroidal vortex bundles retain their coherence over a relatively large distance (compared to their size), in agreement with experimental observations.
We model the dynamics of Jupiter's jets by averaging the dynamics of eddies, in a barotropic beta-plane model, and explicitly predicting the balance between Reynolds' stresses and dissipation, thus predicting the average velocity profile explicitly.In order to obtain this result, we adopt a non-equilibrium statistical mechanics approach. We consider a relevant limit for Jupiter troposphere, of a time scale separation between inertial dynamics on one hand, and stochastic forcing and dissipation on the other hand. We assume that the forcing acts on scales much smaller than the jet scale, and we …
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…
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…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cut off wavelength of the instability. The developed theory is used to analyse recent experi…
