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.
The fact that superfluid helium always leaks out of an open container is usually explained by the phenomenon of wetting. In the present paper it is demonstrated that this explanation is unconvincing. The fact can be readily explained from the viewpoint of the interpretation of superfluidity proposed earlier by the author according to which superfluidity is an equilibrium state of liquid helium where the symmetry is spontaneously broken because of an intrinsic superflow. Experiments on the thickness of moving helium films that have given rise to much controversy are discussed as well. Some expe…
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…
We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by the interaction with quantized vortices terminating at the free surface. We identify two types of particle trajectories and the associated vortex structures: vertical linear vortices pinned at the bottom of the container and half-ring vortices travelling along the free surface of the liquid.
We demonstrate the trapping of millimeter-scale superfluid Helium drops in high vacuum. The drops are sufficiently isolated that they remain trapped indefinitely, cool by evaporation to 330 mK, and exhibit mechanical damping that is limited by internal processes. The drops are also shown to host optical whispering gallery modes. The approach described here combines the advantages of multiple techniques, and should offer access to new experimental regimes of cold chemistry, superfluid physics, and optomechanics.
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…
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…
The Einstein's research ideas on the thermodynamical fluctuational nature of certain electrical phenomena [1] and the physical nature of the electric potentials difference U in an electric capacitor at the temperature of T [2] were proposed in 1906-1907. On the base of Einstein's research ideas, we explain the recent experimental results [3, 4] and propose the consistent theory on the physical nature of the electric effects in an electric capacitor at an action of the second sound standing wave in the superfluid Helium (4He) and in the rotational torsional mechanical resonator in Helium II. Th…
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…
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 report on the production and study of stable, highly charged droplets of superfluid helium. Using a novel experimental setup we produce neutral beams of liquid helium nanodroplets containing millions of atoms or more that can be ionized by electron impact, mass-per-charge selected, and ionized a second time before being analyzed. Droplets containing up to 55 net positive charges are identified and the appearance sizes of multiply charge droplets are determined as a function of charge state. We show that the droplets are stable on the millisecond time scale of the experiment and decay throug…
We numerically study the spatial spreading of quantized vortex lines in low temperature liquid helium. The vortex lines, initially concentrated in a small region, diffuse into the surrounding vortex-free helium, a situation which is typical of many experiments. We find that this spreading, which occurs in the absence of viscosity, emerges from the interactions between the vortex lines, and can be interpreted as a diffusion process with effective coefficient equal to approximately 0.5$κ$ where $κ$ is the quantum of circulation.
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 …
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 …
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…
A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.
Presented in this paper are measurements of an optomechanical device in which various acoustic modes of a sample of superfluid helium couple to a fiber-based optical cavity. In contrast with recent work on the paraxial acoustic mode confined by the cavity mirrors, we focus specifically on the acoustic modes associated with the helium surrounding the cavity. This paper provides a framework for understanding how the acoustic modes depend on device geometry. The acoustic modes are observed using the technique of optomechanically induced transparency/amplification. The optomechanical coupling to t…
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 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…
Metastable helium molecules generated in a discharge near a sharp tungsten tip operated in either pulsed mode or continuous field-emission mode in superfluid liquid $^{4}$He are imaged using a laser-induced-fluorescence technique. By pulsing the tip, a small cloud of He$_{2}^{*}$ molecules is produced. At 2.0 K, the molecules in the liquid follow the motion of the normal fluid. 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 genera…
