Turbulence of Capillary Waves on the Surface of Quantum Liquids

The techniques developed earlier for study of turbulence on the surface of liquid hydrogen was used for generation of nonlinear waves on the charged surface of liquid ⁴He. This permitted us to observe for the first time capillary turbulence on the surface of liquid ⁴He in normal and superfluid state, and to expand in a few times the relative width of the inertial interval, where the Kolmogorov-Zakharov spectrum of turbulence was observed.     

Switching Phenomena between Laminar and Turbulent Flows of Superfluid 4He Generated by a Vibrating Wire

We have investigated the turbulence transition of the superfluid ⁴He flow generated by a vibrating wire. For a 1.2-kHz vibrating wire, we observed intermittent switchings between laminar and turbulent flows. The switching rate decreases with increasing temperature above 100 mK, until no occurrence of the switchings at 350 mK. For a 2.4-kHz vibrating wire, we find that the switching rate is much lower than that of the 1.2-kHz vibrating wire even at low temperatures. This result indicates that a mechanism causing the switchings is influenced by the temperature and the oscillation frequency of the superfluid flow.     

New insight into the functional dependence rules in turbulence modelling

This paper is intended to revisit the Euclidean invariance of turbulence models, in particular of the algebraic Reynolds stress models (ARSM). The approach is motivated by the existing different interpretations of the Euclidean invariance of an equation. We show that these interpretations are not suitable to rule out functional dependencies in turbulence. We use the concept of Euclidean invariance with respect to a constitutive or flow rule class of a closure relation to analyze the Euclidean invariance properties of the ARSM. It turns out that the existing ARSM are Euclidean invariant with respect to two different classes, that are basically determined by the equilibrium assumption made in an inertial and a non-inertial reference frame, respectively. The first one is more restrictive and does not include the relative environment dependence of the Reynolds stress tensor in the implicit ARSM. The second class endeavors to involve this environment dependence. After this first step, the issue how to formulate a unified rationale for a consistent reduction procedure based on extended thermodynamics to rule out functional dependencies of the ARSM relations for Reynolds-averaged Navier-Stokes equations (RANS) or large eddy simulations (LES) is left for future work.     

Close Approach of a Spherical Particle and a Quantised Vortex in Helium II

To interpret the results of recent experiments which used the Particle Image Velocimetry (PIV) method it is necessary to understand the interaction of the particles with the quantised vortices. We present numerical calculations of the close approach of a small spherical particle to a vortex line. The collision time scale compares well with approximate analytical results.     

Self-Organization of Vortex Line Length Distribution in Dilute Quantum Turbulence

There has been an exponential growth of interest in scale-free structure of quantum turbulence in recent years. Recent studies revealed that the vortex length distribution (VLD), meaning the size distribution of the vortices, in decaying quantum turbulence at zero temperature obeys a power law. This power law is very important because it means that there is a kind of self-similarity in quantum turbulence during the decay. Unfortunately, however, there has been no practical study that answers the important question; why can the quantum turbulence acquire power law VLD? In this paper, we first propose that the nature of quantized vortices allows us to describe the decay of quantum turbulence with a simple model without loosing physical validity. This simple model well reproduces the observed power law and suggests that the emergence of power law VLD is a consequence of two mechanisms; Richardson cascade and dynamical scaling law of vortex dynamics.     

Vortex Pinning to a Solid Sphere in Helium II

We report here the results of a computer simulation of quantized vortex pinning in He II at 0 K in the simple situation where a single sphere and a rectilinear vortex are considered. Our simulation shows that a vortex nearby a sphere is captured due to a velocity field produced by the sphere, exciting Kelvin waves. The dependence of the “pinning” on temperature is investigated as well. Finally, the possibility of pinning in PIV experiments, which visualize superfluid turbulence, is discussed.     

Turbulenz – ein problemhistorischer Abriss

Turbulence in Perspective In the beginning of the 20th century, the riddles of turbulent flow became articulated as “the turbulence problem”. It comprised two parts: the onset of turbulence, which was conceived as an instability of laminar flow; and fully developed turbulence, for which both empirical (mixing length) and statistical theories of turbulence were developed. Up until the present time turbulence research has been inter-and transdisciplinary, attracting scientists and engineers from a variety of specialties and with diverse scientific and technological orientations. For this reason, turbulence research is also an interesting case for the sociological study of knowledge production in technoscience. The article traces the history of the turbulence problem in the first half of the 20th century, when the major pathways for its attack were first outlined and explored. The ups and downs of the turbulence problem in different local and cultural settings provide a unique opportunity to study a technoscience in the making, beyond sweeping assumptions about science-technology relations. Present fluid dynamicists rate the turbulence problem still as unsolved, but this evaluation should not prevent historians of science and technology from tackling it by their own means: it safeguards the historical analysis against the pitfall of whig history.

Diese Studie entstand im Rahmen eines Projekts zur Geschichte der Str?mungsforschung, das von der Deutschen Forschungsgemeinschaft als Teilprojekt der Forschergruppe 393 gef?rdert wurde. Ich danke auch den Kollegen am Deutschen Museum, wo ich ein für dieses Forschungsthema an der Schnittstelle von Wissenschafts- und Technikgeschichte bestens geeignetes Milieu gefunden habe.     

Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link

A multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM)-carrying beams is studied. We numerically analyze the effects of atmospheric turbulence on the system and find that turbulence induces attenuation and crosstalk among channels. Based on a model in which the constituent channels are binary symmetric and crosstalk is a Gaussian noise source, we find optimal sets of OAM states at each turbulence condition studied and determine the aggregate capacity of the multichannel system at those conditions. OAM-multiplexed FSO systems that operate in the weak turbulence regime are found to offer good performance. We verify that the aggregate capacity decreases as the turbulence increases. A per-channel bit-error rate evaluation is presented to show the uneven effects of crosstalk on the constituent channels.     

Numerical study of light scattering by a boundary-layer flow

Temperature inhomogeneities in free, isotropic turbulence have the effect of scattering light in near-forward angles. We investigate numerically modifications of free turbulence by a rigid wall and its effect on the propagation of light through turbulence. The wall is a 5 cm optical window placed at the leading edge of an instrument towed with speeds of 0.1 and 1 m/s in free turbulence. The turbulent flow field presents inhomogeneities of an embedded passive scalar (Pr = 7, temperature in water), which are modified by the boundary layer developing on the window. We find that the developing laminar boundary layer has a negligible effect on light scattering for the investigated geometry when considered in terms of the volume-scattering function (differential cross section). This indicates that the boundary layer is not an obstacle for optical measurements of turbulence.     

Numerical Studies of Quantum Turbulence

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 equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed to revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose–Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates, e.g., two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, some of which have not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally, we discuss open problems.     

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

No Heading We have measured responses of vibrating wire resonators in superfluid ⁴He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.PACS numbers: 67.40 Vs, 67.40 Pm     

Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 lidar

Laser speckle can influence lidar measurements from a diffuse hard target. Atmospheric optical turbulence will also affect the lidar return signal. We present a numerical simulation that models the propagation of a lidar beam and accounts for both reflective speckle and atmospheric turbulence effects. Our simulation is based on implementing a Huygens-Fresnel approximation to laser propagation. A series of phase screens, with the appropriate atmospheric statistical characteristics, are used to simulate the effect of atmospheric turbulence. A single random phase screen is used to simulate scattering of the entire beam from a rough surface. We compare the output of our numerical model with separate CO(2) lidar measurements of atmospheric turbulence and reflective speckle. We also compare the output of our model with separate analytical predictions for atmospheric turbulence and reflective speckle. Good agreement was found between the model and the experimental data. Good agreement was also found with analytical predictions. Finally, we present results of a simulation of the combined effects on a finite-aperture lidar system that are qualitatively consistent with previous experimental observations of increasing rms noise with increasing turbulence level.     

Spin Turbulence and the −7/3 Power Law in a Trapped Spin-1 Spinor Bose-Einstein Condensate

We numerically study the spin turbulence in a two-dimensional trapped spin-1 spinor Bose-Einstein condensate, focusing on the energy spectrum. The spin turbulence in the trapped system is generated through the instability of the initial helical structure of the spin density vector. The spectrum of the spin-dependent interaction energy in the ferromagnetic case becomes to exhibit the ?7/3 power law as the spin turbulence develops, which was confirmed in a uniform system by the counterflow instability. Hence the spin turbulence with the ?7/3 energy spectrum is robust independently of how the turbulence is generated.     

Light propagation through anisotropic turbulence

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ?. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ?(2-α).     

弱光61单元自适应光学系统的控制优化

在自适应光学系统中,波前校正残误差主要由未完全补偿湍流所引起的误差和系统闭环噪声组成。基于一阶比例－积分控制器分析了弱光６１单元适应光学系统的控制特性。在此基础上风云地非Ｋｏｌｍｏｇｏｒｏｖ湍流情况,提出一种根据实际测量的大气湍流波前扰动功率谱来确定系统,针对非Ｋｏｌｍｏｇｏｒｏｖ湍流情况,提出一根据实际测量的大气湍流波前扰动功率谱来确定系统最优控制带宽的新方法。应用这种方法对弱光６１单元自适应光     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.     

Measurements of the four-point coherence function by the use of the coherence enhancement phenomenon

We present laboratory results for measurements of the four-point coherence function of a spherical wave in the region of coherence enhancement after backscattering through turbulence. Experimental results are compared with the theoretical predictions. We conclude that the shape of the four-point coherence function in our experiment depends on the value of the inner scale of turbulence.     

Possibility of Inverse Energy Cascade in Two-Dimensional Quantum Turbulence

We numerically study two-dimensional quantum turbulence by using the Gross-Pitaevskii model and the Vortex-Point model. Two-dimensional classical turbulence has long been investigated as an ideal system of geophysical phenomena. The amazing character of this turbulence is inverse energy cascade which carries energy toward low wavenumbers and excites large-scale motion. We expect these phenomena in two-dimensional quantum turbulence because in three-dimensional turbulence we know classical and quantum analogue. However, we have not yet confirmed inverse cascade in two-dimensional quantum turbulence. In this work, we show numerical results and discuss why inverse cascade does not occur in two-dimensional quantum turbulence by referring to the mechanism of two-dimensional classical turbulence.     

Stable and unbiased flow turbulence estimation from pulse echo ultrasound

A new method for stable and unbiased flow turbulence estimation has been developed for medical ultrasonic color flow imaging. Conventional turbulence estimates from a finite number of transmitted pulses could be biased, unreliable, and erroneous. We found that a conventional method cannot provide quantitative estimates of variance of flow velocity. We propose a new approach for flow turbulence estimation that is based on analysis of the flow velocity vectors. The new method estimates the variance of the flow velocity and provides reliable estimates for flow turbulence. Numerical examples, computer simulations, and experiments using a flow phantom demonstrate that the new method can estimate variance of flow velocity accurately and without bias. This work also reports a complete derivation in the time domain for both unbiased velocity and turbulence estimations. The results include two velocity estimation equations agreeing with the 1-D and 2-D autocorrelation methods derived from the frequency domain. The results indicate that the new method for flow turbulence is particularly useful when the 2-D autocorrelation method is used for color flow imaging. The new method also appears to be able to detect low turbulence; therefore, it may be useful for diagnosing abnormalities such as minor stenoses and valvular jets.     

Comparison of near-forward light scattering on oceanic turbulence and particles

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.