Based on measurements of nonlinear second-sound resonances in a high-quality resonator, we have observed a steady-state wave energy cascade in He II involving a flux of energy through the spectral range towards high frequencies. We show that the energy balance in the wave system is nonlocal in K space and that the frequency scales of energy pumping and dissipation are widely separated. The wave amplitude distribution follows a power law over a wide range of frequencies. Numerical computations yield results in agreement with the experimental observations. We suggest that second-sound cascades of this kind may be useful for model studies of acoustic turbulence.

/pdf/formation-of-a-direct-kolmogorov-like-cascade-of-second-2gf2dctr7w.pdf

Formation of a direct Kolmogorov-like cascade of second-sound waves in He II.

Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics

Introduction. The recent decade has seen an active development of the technology of space applications of superfluid helium. Among the achievements one should note the launching of the two space observatories-telescopes Herschel and Planck, which took place in 2009. For the Herschel observatory, 2300 liters of liquid helium at a temperature of 1.65 K, placed in the cryostat before the launch, determine the lifetime of the entire structure (expected life is about 4 years) and ensure the efficiency and stability of both the guidance systems and the scientific instrumental base [1]. At the same time, creation of the Laboratory of Low-Temperature Investigations within the framework of the Russian Segment of the International Space Station assumes the extension of the base of basic research. Therefore, for a number of years, we have seen the development of the project of experiment investigations of boiling of superfluid helium under zero gravity. To ensure the preservation of helium in the cryostat volume, it is proposed that a porous shell coaxial with a cylindrical heater be used [2]. For corresponding experiments under laboratory conditions, it is planned to use a bench of the Department of Low Temperatures of the National Research University "Moscow Power Institute;" which bench has been created to investigate processes in superfluid helium in heat supply, including the case of constrained conditions. The corresponding mathematical model of an experimental cell is presented below. Furthermore, it is of separate interest to investigate the dynamics of a vapor film and flow of a quantum liquid in small-diameter channels under a thermal load of 10 4 W/m 2 . Formulation of the Problem and Mathematical Description. The heater in the form of a thin wire of prescribed radius R w is arranged inside a coaxial shell with internal radius R 0 and thickness L; the wire is manufactured from a material with known structural characteristics (porosity m and characteristic dimension d). The experimental cell is closed, on the ends, by optically transparent plugs and is fully submerged in the liquid volume to a depth h. Helium-II fills the internal space and the porous-shell channels. Above the free surface of the liquid, a constant pressure P b is maintained, to which there corresponds the liquid temperature T b as far as the saturation line is concerned. Once the thermal load q w has been applied, a vapor film of radius R 1 is formed on the heater surface, which expels the liquid through the channels in the porous body (Fig. 1). The objective of the work is to calculate the process of heat and mass transfer in the experimental cell with the aim of determining a combination of parameters at which a steady state can be reached. The system of equations is formulated under the assumption that the heat- and mass-transfer processes in helium-II are quasisteady. The liquid is assumed incompressible; the dependence of the processes on the local temperature is not considered.

Suppression of oscillations of the vapor–liquid phase boundary in boiling of superfluid helium inside a porous body

We review studies of the generation and propagation of nonlinear and shock sound waves in He II (the superfluid phase of 4He), both under the saturated vapor pressure (SVP) and at elevated pressures The evolution in shape of second and first sound waves excited by a pulsed heater has been investigated for increasing power W of the heat pulse It has been found that, by increasing the pressure P from SVP up to 25 atm, the temperature T_lambda, at which the nonlinearity coefficient alpha of second sound reverses its sign, is decreased from 188 to 158 K Thus at all pressures there exists a wide temperature range below T_lambda where alpha is negative, so that the temperature discontinuity(shock front) should be formed at the center of a propagating bipolar pulse of second sound Numerical estimates show that, with rising pressure, the amplitude ratio of linear first and second sound waves generated by the heater at small W should increase significantly This effect has allowed us to observe at P=133 atm a linear wave of heatingrarefaction in first sound, and its transformation to a shock wave of cooling (compression) Measurements made at high W for pressures above and below the critical pressure in He II, Pcr=22 atm, suggest that the main reason for initiation of the first sound compression wave is strong thermal expansion of a layer of He I (the normal phase) created at the heater-He II interface when W exceeds a critical value Experiments with nonlinear second sound waves in a high-quality resonator show that, when the driving amplitude of the second sound is sufficiently high, multiple harmonics of second sound waves are generated over a wide range of frequencies due to nonlinearity At sufficiently high frequencies the nonlinear transfer of the wave energy to sequentially higher wave numbers is terminated by the viscous damping of the waves

/pdf/nonlinear-and-shock-waves-in-superfluid-he-ii-363k0jri8d.pdf

Nonlinear and shock waves in superfluid He II

The problem of evolution of strong heat pulses in superfluid helium interacting with quantum vortices induced by these pulses is investigated numerically on the basis of equations of hydrodynamics of superfluid turbulence. The “discontinuity decay” method (Godunov method) is used for the calculations. In order to study nonlinear effects, the initial equations are expanded to the second order in the amplitudes of pulses. The influence of the main flow parameters—heat flux and rest time—on temperature evolution is reported. The numerical investigations are carried out at the bath temperature of 1.4 K. The obtained results are compared with experimental data.

Unsteady Heat Transfer in HeII in Cylindrical and Spherical Geometries

The problem of evolution of strong heat pulses in He II interacting with quantum vortices induced by these pulses is investigated numerically on the basis of equations of hydrodynamics of superfluid turbulence. In order to study nonlinear effects, the initial equations are expanded to the second order in the amplitudes of pulses. The one-dimensional case in the absence of mass transport (second sound) is considered. The initiation of vortices was simulated by the generation term in the Vinen equation. The results on the dynamics of pulses in various temperature ranges are presented. It is shown that the Feynman–Vinen theory is applicable in the phase-transition region.

Mutual influence of quantum vortices and heat pulses in superfluid helium

Dynamics of intense heat pulses propagating in He II and interacting with quantum vortices induced by these pulses has been investigated using numerical methods based on equations of superfluid turbulence hydrodynamics Investigation has been carried out for the plane geometry up to the second order in amplitude of pulses The initial generation of vortex filaments has been simulated by the generating term in the Vinen equation The results on pulse evolution for various heat fluxes are presented for different temperatures It has been shown that the Feynman–Vinen theory is applicable in the phase-transition region The results obtained have been compared to experimental data

Interaction of Intense Heat Pulses and Vortices in He II

We present the results of a simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. The evolution of vortex lines is calculated on the basis of the Biot—Savart law. The dissipative effects arising from the interaction with the normal component or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, i.e., we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-dissipation relation, which implies that thermodynamic equilibrium should be reached. We describe numerical methods for integration of the stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of a calculation of some characteristics of a vortex tangle such as the total length, the length distribution of the loops, and the energy spectrum.

pdf/simulation-of-a-stochastic-vortex-tangle-270zoj8ps1.pdf

Simulation of a stochastic vortex tangle

We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. 
Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the interaction with the normal component, or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, e.i. we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-disspation relation, which implies that thermodynamic equilibrium should be reached. In the paper we describe the numerical methods for integration of stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of calculation of some characteristics of a vortex tangle such as the total length, distribution of loops in the space of their length, and the energy spectrum.

Numerical simulation of stochastic vortex tangles

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Mutual influence of quantum vortices and heat pulses in superfluid helium

Interaction of Intense Heat Pulses and Vortices in He II

Simulation of a stochastic vortex tangle

Numerical simulation of stochastic vortex tangles