Bifurcations analysis of turbulent energy cascade

This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.     

Dispersion und Absorption transversaler Schallwellen im Magnetfeld

The propagation velocity and absorption of transverse ultrasonic waves have bsen measured in a polycristalline metallic probe as functions of a magnetic field parallel to the direction of propagation. In agreement with the macroscopic theory, these measurements showed, that the propagation velocity was increased by the magnetic field for frequencies below a transition frequency characteristic for the medium. In case of high frequencies the magnetic field causes an absorption. In the dispersion region characterized by the transition frequency, the magnetohydrodynamic Reynolds number is of order one and the magnetically induced changes in propagation velocity and absorption are strongly frequency dependent.     

A numerical simulation of the transition to turbulence in a two-dimensional flow

A numerical simulation of the transition to turbulence is performed using a finite element method. The unsteady Navier-Stokes equations are discretized using a standard Galerkin approximation and a loading strategy for increasing the Reynolds number. The numerical results are then analysed at different Reynolds numbers showing a transition from a steady-state solution to a weakly chaotic one. Phase space diagrams are presented showing the presence of strange attractors. The dimension and Lyapunov's exponents of these attractors are computed and compared with existing results in the literature.     

Magnetic-field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.     

Laser Doppler velocimetry analysis of transitional pipe flow

The objective of this study has been to experimentally analyze the correlation structure of the strong temporal intermittency which characterizes pipe flow close to the transition to turbulence. In doing so transitional pipe flow has been analyzed by Laser Doppler velocimetry and the Reynolds number dependence of the covariance function has been studied. The range which has been analyzed covers the transition to turbulence and moderately developed turbulence (Reynolds number from 1 500 to 5 000). The correlation structure which has been evidenced is generally in agreement with the deterministic, dynamical, interpretation of temporal intermittency which explains the intermittent behavior as a result of a saddle node bifurcation. However, the analysis has evidenced fluctuations even before the onset of turbulence. The structure of these fluctuations is perfectly autoregressive which leads us to conclude that the transition to turbulence can be viewed as a transition from linear randomness to (non-linear) homogeneity. Received 29 March 1999 and Received in final form 6 September 1999     

Magnetic helicity tensor for an anisotropic turbulence

The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the alpha effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.     

SPRITE MRI of bubbly flow in a horizontal pipe

Bubble flow is characterised by numerous phase interfaces and turbulence, leading to fast magnetic resonance signal decay and artefacts in spin-warp imaging. In this paper, the SPRITE MRI pulse sequence, with its potential for very short encoding times, is demonstrated as an ideal technique for studying such dynamic systems. It has been used to acquire liquid velocity and relative intensity maps of two-phase gas–liquid dispersed bubble flow in a horizontal pipe at a liquid Reynolds number of 14,500. The fluids were air and water and a turbulence grid was used to generate a dispersed bubble flow pattern. The SPRITE technique shows promise for future research in gas–liquid flow.     

Flow separation behind a rib in a channel with laminar flow

Visualization data and results of combined measurements of flow quantities in flow with separation past a rib at nominally laminar regime of channel flow are reported. In the separation region, the flow is found to be essentially three-dimensional and unsteady, exhibiting a distinct cellular structure and flow zones with transverse motion. It is shown that the rib-induced flow separation gives rise to low-frequency fluctuations of flow velocity and initiates the turbulence transition in the channel flow. The critical Reynolds number at which flow instability starts developing in the channel is estimated. It is shown that at Reynolds numbers higher than the critical Reynolds number the linear integral scale of flow velocity fluctuations in the channel is defined by the duct size.     

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采用FLUENT软件分别对外加均匀横向磁场的等截面三维充分发展液态金属管流的层流模型和低雷诺数湍流Lam/Bremhost(LB)模型进行了数值模拟,分析了外加磁场对普通方管LB模型速度分布和压降的影响。比较在相同哈特曼数下,层流和湍流模型方管截面上速度分布和管道中MHD压降。其中,对电流的计算采用磁感应方程来求得。数值模拟结果证明了用低雷诺数LB湍流模型解决方管磁流体流动的可行性。通过层流模型和湍流模型的对比可知,层流模型有较短的入口长度,但管内流体的压降却很大;而湍流模型管内速度更加平均化,管内压降较小,但管内入口长度较长。     

High magnetic shear gain in a liquid sodium stable Couette flow experiment: a prelude to an α-Ω dynamo

The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(?) that is ?8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm?120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)(2)～10(-3).     

Energy transfers in dynamos with small magnetic Prandtl numbers

We perform numerical simulation of dynamo with magnetic Prandtl number Pm = 0.2 on 1024³ grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with Pm = 20 and decaying dynamo.     

Intrinsic ambipolarity and rotation in stellarators

It is shown that collisional plasma transport is intrinsically ambipolar only in quasiaxisymmetric or quasihelically symmetric magnetic configurations. Only in such fields can the plasma rotate freely, and then only in the direction of quasisymmetry. In a non-quasi-symmetric magnetic field, the average radial electric field is determined by parallel viscosity, which in turn is usually governed by collisional processes. Locally, the radial electric field may be affected by turbulent Reynolds stress producing zonal flows, but on a radial average taken over several ion gyroradii, it is determined by parallel viscosity, at least if the turbulence is electrostatic and obeys the conventional gyrokinetic orderings. This differs from the situation in a tokamak, where there is no flow damping by parallel viscosity in the symmetry direction and the turbulent Reynolds stress may affect the global radial electric field.     

Digital Interferometric Measurement of Forced Convection Heat Transfer in a Miniature Rectangular Channel

Investigations have been performed on convective heat transfer in water flowing through mini-channels using the non intrusive technique of laser interferometry coupled with digital image processing. Optical glass channels, fabricated with metallic heating surfaces, were studied using a Mach-Zehnder interferometer configuration. Fringe patterns captured using a high-sensitivity CCD camera were analyzed digitally based on a calculation method developed for the liquid medium. Results of parametric studies were compared and contrasted with relevant theoretical solutions from the literature. Indication of the onset of turbulence at Reynolds numbers smaller than the conventional transition Reynolds number for large channels has also been noticed in the experimental investigation.     

Computational study of the laminar to turbulent transition over the SD7003 airfoil in ground effect

In this work, we present a numerical study of the laminar-turbulence transition flow around a symmetrical air-foil at a low Reynolds number in free flow and near the ground surface at different angles of attack. Finite volume method is employed to solve the unsteady Reynolds-averaged Navier–Stokes (RANS) equation. In this way, the Transition SST turbulence model is used for modeling the flow turbulence. Flow around the symmetrical airfoil SD7003 is numerically simulated in free stream and near the ground surface. Our numerical method can detect different aspects of flow such as adverse pressure gradient, laminar separation bubble and laminar to turbulent transition onset and the numerical results are in good agreement with the experimental data.     

Magnetic stabilization of nematic turbulence

Under an applied magnetic field, turbulence starts off in a nematic liquid at higher critical Reynolds numbers. Also, the internal scale of turbulence is enlarged.     

带引流条导电矩形管磁流体湍流大涡数值模拟

为研究引流条对磁流体湍流的影响，采用自主开发的低磁雷诺数流固耦合磁流体相干结构模型大涡模拟求解器，对均匀磁场作用下平行层内带引流条导电矩形管和标准导电矩形管中液态金属湍流进行了数值模拟研究。结果表明，外加垂直流动方向的均匀磁场与流动的导电流体相互作用产生与流动方向相反的洛伦兹力，能够抑制磁流体的湍流脉动，这种抑制作用随着哈特曼数增大而增强。在弱导电率条件下，当Re=16350、Ha=212 时，两种管道中的流动均转换为层流流动状态。管道内壁面摩擦系数随着哈特曼数的增大而增大。引流条能在其近壁局部区域增强横向速度，有效激发湍流，但在弱壁面导电率条件下，带引流条导电矩形管壁面摩擦系数较标准矩形管大。     

Effect of gravity on the development of homogeneous shear turbulence laden with finite-size particles

Fully resolved simulations of homogeneous shear turbulence (HST) laden with sedimenting spherical particles of finite size have been performed to clarify the effects of gravity on the development of particle-laden turbulent shear flows. We consider turbulence in a horizontal flow subjected to vertical or horizontal shear. Numerical results show that the development of HST laden with finite-size particles are significantly altered by gravity. The effects of gravity lead to a slower increase in the Taylor-microscale Reynolds number, whose value is found to be well correlated with the average particle Reynolds number. The gravity also causes a slower increase in the turbulence kinetic energy (TKE) through the enhancement of energy dissipation. The change in the Reynolds shear stress (RSS) due to particles also significantly contributes to the relative change in TKE. In vertically sheared cases, RSS has high values between counter-rotating trailing vortices behind the particles, which causes a transient relative increase in TKE. In horizontally sheared cases, on the other hand, RSS is reduced in the wakes of particles, which contributes to a significant relative reduction in TKE.     

Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.     

圆形射流中心线上小尺度湍流的统计特性及其受高频噪声的影响

本文采用热线风速仪测量了出口雷诺数为Re (≡ U_jd/ν) = 20100的圆形射流的中心线轴向速度,其中U_j为动量平均出口速度,d为喷嘴出口直径,ν为运动黏性系数.在有效去除热线测量数据中的高频噪声后,作者对射流中心线上小尺度湍流统计量的变化规律进行了系统的分析.研究发现,射流在经过一定距离的发展后,其小尺度统计量逐渐进入自相似状态,湍动能平均耗散率ε随下游距离的增加以指数形 关键词： 恒温热线 圆形湍射流 耗散率 小尺度     

Intermittency,Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.