Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Nonlinear vortex dynamo in a rotating stratified moist atmosphere

We have found a new type of large-scale instability in a rotating stratified moist atmosphere with small-scale turbulence. The turbulence is excited by an external small-scale force with a low Reynolds number. We have constructed the theory based on the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motion have been derived in the third order of the perturbation theory. We have investigated the linear instability and stationary nonlinear regimes. Solutions in the form of localized vortex structures or kinks of a new type have been obtained.     

超声速混合层MHz级超高频流动可视化实验

研究发展了超高频基于纳米示踪的平面激光散射（nano-tracer planar laser scattering,NPLS）技术。基于多腔并联脉冲激光器技术、棱锥分光与短曝光相机集成技术以及高精度同步控制技术,实现了MHz级流场可视化和精细测量。采用超高频NPLS技术研究了对流Mach数Ma_c=0.17,0.26混合层流场,获得了时间序列的混合层高分辨率NPLS图像。采用阵列型涡流发生器开展流动控制研究,分析涡流发生器对混合层发展的影响特性。通过选取典型涡结构,分析了超声速混合层不同发展阶段的涡运动和发展演化规律。发现混合层中段的不稳定性发展阶段,涡结构以平移和旋转为主,伴随一定的拉伸;混合层后段以变形和破碎为主,有大量小尺度结构产生。并且小尺度结构会受到剪切、大尺度结构以及小激波的影响,发生明显的非定常运动。      

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k^–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.     

Large-eddy simulations and vortex structures of turbulent jets in crossflow

Using the method of large-eddy simulation, the 3-dimensional turbulent jets in crossflow with stream-wise and transverse arrangements of nozzle are simulated, emphasizing on the dynamical process of generation and evolution of vortex structures in these flows. The results show that the basic vortex structures in literatures, such as the counter-rotating vortex pair, leading-edge vortices, lee-side vortices, hanging vortices, kidney vortices and anti-kidney vortices, are not independent physical substances, but local structures of the basic vortex structure of turbulent jets in crossflow-the 3-D stretching vortex rings originating from the orifice of the nozzle, which is discovered in this study. Therefore, the most important large-scale structures of turbulent jets in crossflow are unified to the 3-D vortex rings which stretch and twist in stream-wise and swing in transverse directions. We also found that the shedding frequencies of vortex rings are much lower than the one corresponding to the appearance of leading-edge and lee-side vortices in the turbulent jets.     

A minimal flow unit for the study of turbulence with passive scalars

The concept of a minimal flow unit (MFU) for the study of the basic physics of turbulent flows is introduced. The MFU is an initial vorticity configuration that consists of a few simple well-defined large-scale vortex structures. The form and position of these structures are chosen so that their interaction produces turbulence capturing many of the essential characteristics of isotropic homogeneous turbulence produced from random-phase initial conditions or that produced by continual random-phase forcing. The advantage of using the MFU is that the evolution of the vortex structures can be followed more clearly and the relationship between the evolving vortex structures and the various ranges in the energy spectrum can be more clearly defined. The addition of passive scalar fields to the MFU permits an investigation of passive scalar mixing that is relevant to the study of combustion. With a particular choice of the MFU, one that produces a trend to a finite-time singularity in the vorticity field, it is demonstrated that passive scalar distributed in the original large-scale vortices will develop intense gradients in the region where the vorticity is tending toward a singularity. In viscous flow, the evolution of the MFU clearly shows how the volume of the regions where originally well-separated passive scalars come into contact increases with increasing Reynolds number.     

Evolution of the vortex structures and turbulent spots at the late-stage of transitional boundary layers

The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and dark spots structure observed by experiment research, has been confirmed by our computational results. The formation mechanisms of these structures have been explored. It is revealed that the new vortex structures, the ring-like vortex chain and induced disturbance velocities play a dominant role in the generation of turbulent spots.     

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.     

Vortex structure in BaFe2(As1 − x P x )2 single crystals

Single crystals of iron-containing Ba(FeAs)₂ superconductors doped with phosphorus have been studied. The vortex structure has been studied by means of the decoration method. Large domains of the triangular vortex structures have been observed in the phosphorus-doped single crystals of iron-containing superconductors. The effect of doping on pinning in iron-containing superconductors has been discussed.     

Explosive plasma-vortex optical radiation sources

The results of experimental study of explosive radiation sources based on pulsed injection of a cumulative plasma jet into atmospheric air are considered. The injection process is accompanied with intense vortex formation as well as the formation of a large-scale toroidal plasma vortex. High-power electromagnetic radiation in the optical range is generated due to shock-wave processes during deceleration of a plasma jet in air and plasma-chemical processes in the vortex. The temporal structure of a radiation pulse being generated contains components from the micro- and millisecond range. For a 20-g mass of the explosive charge, a peak radiation power of 300 kW/sr and an energy yield of 400–600 J/sr integrated over the emission spectrum are attained. The efficiency of conversion of the chemical energy of the explosive into radiation is 5.0–7.5%.     

Formation of vortices in a laminar jet under the action of acoustic field

Results on visual investigation of a structure of a round minijet under the action of an acoustic field are presented. Characteristic features of the laminar jet structure in the acoustic field were revealed from the data of video and photo records of a flow picture. In the flow we observed characteristic large-scale vortex structures and violent turbulent mixing zones.We revealed formation of vortex structures in a laminar jet under acoustic field and an oscillating jet flow regime at the outlet from the pipe 1.35 mm in diameter.     

三维气固两相混合层湍流拟序结构的直接数值模拟

本文对三维气固两相混合层湍流拟序结构进行了直接数值模拟。气相流场应用拟谱方法对Ｎ－Ｓ方程组进行直接求解,通过模拟时间模式的混合层流动,分析流场失稳后涡的卷起、配对、合并及撕裂过程,研究三维混合层湍流拟序结构的演变特征;计算颗粒场时,采用Ｌａｇｒａｎｇｉａｎ方法,针对颗粒不同的Ｓｔｏｋｅｓ数,模拟了颗粒场的瞬态分布,并分析流场三维大涡结构对颗粒分布的影响。     

Statistics and structures of pressure and density in compressible isotropic turbulence

We study statistics and structures of pressure and density in the presence of large-scale shock waves in a forced compressible isotropic turbulence using high-resolution numerical simulation. The spectra for pressure and density exhibit a ?2 scaling over an operational definition of the inertial range. Both the numerical simulation and a heuristic PDF model reveal that the PDFs of pressure increment exhibit a ?2 power law region for the separation in the operational definition of inertial range, quantitatively similar to the PDF of pressure gradient, which also displays a ?2 power law region. Moreover, the statistical relation between density increment and pressure increment has been investigated through a shock-relation model. There is a positive correlation between the vorticity magnitude and pressure, which is different from the case of incompressible turbulence. We argue that this difference is due to large-scale shock waves, another type of intermittent structures in addition to vortex structures in incompressible turbulence.     

A clustering-based approach to vortex extraction

Since vortex is an important flow structure and has significant influence on numerous industrial applications, vortex extraction is always a research hotspot in flow visualization. This paper presents a novel vortex extraction method by employing a machine learning clustering algorithm to identify and locate vortical structures in complex flow fields. Specifically, the proposed approach firstly chooses an objective, physically based metric that describes the vortex-like behavior of intricate flow and then normalizes the metric for applying on different flow fields. After that, it performs the clustering on normalized metric to automatically determine vortex regions. Our method requires relatively few flow variables as inputs, making it suitable for vortex extraction in large-scale datasets. Moreover, this approach detects all vortices in the flow simultaneously, thereby showing great potential for automated vortex tracking. Extensive experimental results demonstrate the efficiency and accuracy of our proposed method in comparison with existing approaches.     

Random vortex-street model for a self-similar plane turbulent jet

We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large-scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large-scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact self-similar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.     

Transition micromagnetic structures in the Bloch and Néel asymmetric domain walls containing singular points

A three-dimensional computer simulation of transition structures separated from each other by regions of vortex asymmetric domain walls of the Bloch and Néel types in magnetically uniaxial permalloy films with in-plane anisotropy has been performed. The structures without localized magnetostatic poles on the surface of the film with one or two singular points have been investigated. It has been shown that the singular points and the vortex formations being elements of the domain walls can be considered as topological structures. A method has been proposed for visualizing the topology of magnetic configurations, which is based on the numerical determination of spatial distributions of topological charges of two types.     

高雷诺数气固湍流射流的直接数值模拟

本文对流动雷诺数 Re=5990的空间发展的气固两相湍流射流进行了直接数值模拟。其中对流场的求解采用具有四阶精度的紧致差分格式,对颗粒场的跟踪采用拉格朗日方法。结果表明,湍流拟序结构逐渐由对称模式发展到非对称模式;较小 Stokes 数的颗粒在流场中均匀分布,较大 Stokes 数的颗粒沿横向没有明显的扩散,而 Stokes 数为 1的量级的颗粒则大量聚集在大涡结构的外围。     

Topological defects in incommensurate magnetic and crystal structures and quasi-periodic solutions of the elliptic sine-Gordon equation

Vortex-type singular solutions with a topological charge of the elliptic sine-Gordon equation have been studied. One- and two-dimensional vortex lattices on a homogeneous and periodic background are constructed in the explicit form using the Bäcklund transformation. The interaction of vortices is investigated and finite energy configurations are found. On the basis of the obtained results new topological defects in incommensurate magnetic and crystal structures are predicted and described. The interaction of vortex magnetic structures with nonlinear spin waves is considered.     

New types of spatial structures in multisublattice antiferromagnets

A broad class of three-dimensional space structures in multisublattice antiferromagnets was found in the isotropic approximation (the principal chiral field model on the SU(2) group). According to the Andreev-Marchenko theory, this approximation is applicable to spin glasses and provides qualitative understanding of structures in real multisublattice antiferromagnets. Special substitutions were used to reduce the equations of the model to new equations with simple geometric interpretation. A differential geometry method was applied to obtain various structure types (some of which were determined by arbitrary functions), including localized and nonlocalized textures, structures with the degree of mapping equal to one, antiferromagnetic “targets” and three-dimensional sources, and two-and three-dimensional vortex and spiral structures. Possibilities for experimentally checking the presence of localized, vortex, and spiral structures in antiferromagnets were demonstrated.