Coherent structure formation in turbulent thermal superfluids

By means of numerical calculations, we show that in turbulent thermal superfluids the normal fluid induces coherent bundles of quantized line vortices in the superfluid. These filamentary structures are formed in between the normal fluid vortices, acquiring eventually comparable circulation. They are self-stretched and evolve according to self-regulating dynamics. Their spectrum mimics the normal fluid spectrum with the mutual friction force exciting the large scales and damping the small scales. Strongly interacting triads of them merge sporadically into stronger, braided vortex filaments, inducing strong fluctuations in the system's energetics. A theoretical account of the system's statistical mechanics is proposed.     

Superfluid vortex front at T→0: decoupling from the reference frame

Steady-state turbulent motion is created in superfluid (3)He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of (3)He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.     

Quantum turbulence in a propagating superfluid vortex front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.     

A numerical investigation of vortex-coupled superfluidity

We have performed numerical simulations of quantized vortex lines in a model of normal fluid turbulence. The results are used to discuss the idea, put forward to explain some recent experiments, that in isothermal turbulent helium flow the high density of vortex lines locks the two fluid components together.     

Mutual friction in the laminar flow of superfluid helium II through capillary tubes

The Hall-Vinen-Bekarevich-Khalatnikov theory is applied to the laminar flow of superfluid helium through capillary tubes. Velocity profiles obtained for the superfluid are interpreted in terms of the motion of vortex rings. The thermodynamic potential gradient as a function of the average superfluid and normal fluid velocities compares favourably with recent experimental results. It is concluded that the vortex rings originate at the wall and disappear at the tube axis.     

Turbulence in boundary flow of superfluid 4He triggered by free vortex rings

The transition to turbulence in the boundary flow of superfluid 4He is investigated using a vortex-free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.     

Fluctuations and stability of superfluid turbulence at mK temperatures

Turbulent flow of superfluid 4He at mK temperatures around an oscillating microsphere is known to be unstable at low driving forces, switching intermittently between turbulent and laminar phases. The lifetimes of the turbulent phases are exponentially distributed, and the mean lifetimes grow exponentially with the square of the driving force. These experimental results are attributed to statistical fluctuations of the density L of the vortex line length. As a result, a normal probability distribution of L2 is found having a standard deviation of 2.9 x 10(14) m(-4) and a spectral bandwidth Deltaomega approximately 13 s(-1).     

Energy spectra of quantum turbulence in He II and 3He-B: A unified view

Quantum turbulence in superfluid He II and in ³He-B that can be regarded as nearly isothermal, isotropic, and homogeneous is discussed within the two-fluid model. A general form of the 3D energy spectrum is proposed: at large length scales, where normal and superfluid eddies are locked together by the mutual friction force, the energy spectrum is essentially classical and includes an inertial range of a Kolmogorov K62 form. With increasing wavenumber k, the normal fluid part of the spectrum terminates due to finite viscosity, while the superfluid part of the spectral energy density changes towards k ⁻³ and then back into Kolmogorov-like k ^−5/3 again. Agreement with computer simulations and experiments is claimed if account is taken of the turbulent box size and of the energy decay rate. The text was submitted by the author in English.     

Translational oscillations of a microsphere in superfluid helium

The translational motion of a microsphere (radius 100 μm) in liquid helium is investigated. The sphere is levitating inside a superconducting capacitor and oscillates about its equilibrium position. The velocity amplitude and the resonance frequency are measured as a function of driving force and temperature (0.35 K up to 2.2 K). By increasing the driving force we first find a linear regime (laminar flow) which changes abruptly into a nonlinear one (turbulent flow). For temperatures below 0.7 K the linear drag is given by ballistic roton and phonon scattering whereas for temperatures above 1.1 K the hydrodynamic force on the sphere is described by Stoke's solution. In the turbulent regime, above a temperature independent threshold velocity, we find the drag force to be given by turbulence in the superfluid component plus an essentially laminar drag by the normal component.     

On the dynamics of superfluid vorticity in non-dissipative processes

We investigate the consequences of the possible existence of superfluid vorticity on the Landau two-fluid equations. Assuming a conservation law for superfluid circulation, we show that in non-dissipative situations, the superfluid vorticity is swept along by the normal fluid.     

Vortex instability and the onset of superfluid turbulence

Quantized circulation, the absence of Galilean invariance due to a clamped normal component, and the vortex mutual friction are the major factors that make superfluid turbulence behave in a way different from that in classical fluids. The model is developed for the onset of superfluid turbulence that describes the initial avalanchelike multiplication of vortices into a turbulent vortex tangle.     

Polarization of superfluid turbulence

We show that normal-fluid eddies in turbulent helium II polarize the tangle of quantized vortex lines present in the flow, thus inducing superfluid vorticity patterns similar to the driving normal-fluid eddies. We also show that the polarization is effective over the entire inertial range. The results help explain the surprising analogies between classical and superfluid turbulence which have been observed recently.     

Decay of pure quantum turbulence in superfluid 3He-B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.     

Vortex lattices in a rotating Fermi superfluid in the BCS–BEC crossover with many Landau levels

We present an explicit analytical analysis of the ground state of vortex lattice structure, based on a minimization of the generalized Gross–Pitaevskii energy functional in a trapped rotating Fermi superfluid gas. By a Bogoliubov-like transformation we find that the coarse-grained average of the atomic density varies as inverted parabola in three dimensional cases; the Fermi superfluid in the BEC regime enters into the lowest Landau level at fast rotation, in which the vortices form an almost regular triangular lattice over a central region and the vortex lattice is expanded along the radial direction in the outer region; the fluid in the unitarity and BCS regimes occupies many low-lying Landau levels, in which a trapped gas with a triangular vortex lattice has a superfluid core surrounded by a normal gas. The calculation is qualitatively consistent with recent numerical and experimental data both in the vortex lattice structure and vortex numbers and in the density profiles versus the stirring frequency in the whole BCS–BEC crossover.     

A flow phase diagram for helium superfluids

The existence of the flow phase diagram predicted by Volovik [JETP Lett. 78, 553 (2003)] is discussed based on the available experimental data for He II and ³He-B. The effective temperature-dependent but scale-independent Reynolds number Re_eff≡1/q≡(1?α′)/α, where α and α′ are the mutual friction parameters, and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram permits the identification of the experimentally observed turbulent states I and II in counterflowing He II with the classical and quantum turbulent regimes suggested by Volovik.     

基于Lattice Boltzmann方法的圆柱绕流大涡模拟

Lattice Boltzmann(LB)方法是近年来出现的一种流体计算的新方法,在流体力学及相关领域取得了很大的成功。但LB方法在模拟湍流流动时常常引起计算的不稳定。本文基于一种结合大涡模型的LB方法对圆柱绕流问题进行的模拟,并与其他文献的实验结果和计算结果进行对比。计算表明:这种混合LB方法能获得比较满意的结果。     

Fractal dimension of superfluid turbulence

Superfluid turbulence consists of a disordered tangle of quantized vortex filaments which interact with each other and with the normal fluid. We develop a kinematic model of normal-fluid turbulence to study superfluid vortex tangles at finite temperatures and show by numerical simulation that the system of filaments has a fractal dimension larger than one. We find that the fractal dimension is directly related to the vortex-line density and is independent of temperature over a wide range.     

叶片尾缘内冷通道中最佳强化传热的针肋排列结构研究

本文应用湍流模型对涡轮叶片尾缘针肋通道的换热与流动进行了二维数值模拟研究。为了研究通道内针肋排列 方式对换热与流动的影响,对三种不同的针肋排列方式的通道进行了数值模拟计算。比较了顺排和叉排的区别,并提出了 一种沿流向叉排的针肋排列方式,且对各种排列的传热和阻力特性进行了综合分析和比较。     

空气横掠波纹管束流动与传热性能的数值模拟

本文应用层流模型和湍流模型的数值模拟方法,对空气外掠8排波纹管束时的流动与传热性能进行了研究,并将数值结果与实验结果进行了对比,结果表明:层流模型数值模拟结果较湍流更接近于实验值。同时,对两种模型的数值模拟结果拟合出了Nu-Re的关联式。