The investigation of coherent structures in the wall region of a supersonic turbulent boundary layer based on DNS database

Through temporal mode direct numerical simulation, flow field database of a fully developed turbulent boundary layer on a flat plate with Mach number 4.5 and Reynolds number Reθ =1094 has been obtained. Commonly used detection meth- ods in experiments are applied to detecting coherent structures in the flow field, and it is found that coherent structures do exist in the wall region of a supersonic turbulent boundary layer. The detected results show that a low-speed streak is de- tected by using the Mu-level method, the rising parts of this streak are detected by using the second quadrant method, and the crossing regions from a low-speed streak to the high-speed one are detected by using the VITA method respectively. Notwithstanding that different regions are detected by different methods, they are all accompanied by quasi-stream-wise vortex structures.     

Simulation of coherent structures in nonlinear Schrödinger-type equations

This paper presents some numerical methods to simulate the evolution of coherent structures with small fluctuations, that appear as typical solutions of a class of nonintegrable nonlinear Schrödinger equations. The construction of the methods is particularly focused on two points: on one hand, the generation of the ground state profiles, to be used in the initial data of the simulations, combines a suitable spatial discretization with the resolution of a discrete variational problem. On the other hand, the approximation to leading parameters of these structures is controlled by the time integration. We compare different methods when simulating the evolution of initial ground state profiles and some initial data perturbed from them.     

Detection of coherent oceanic structures via transfer operators

Coherent nondispersive structures are known to play a crucial role in explaining transport in nonautonomous dynamical systems such as ocean flows. These structures are difficult to extract from model output as they are Lagrangian by nature and not revealed by the underlying Eulerian velocity fields. In the last few years heuristic concepts such as finite-time Lyapunov exponents have been used in an attempt to detect barriers to oceanic transport and thus identify regions that trap material such as nutrients and phytoplankton. In this Letter we pursue a novel, more direct approach to uncover coherent regions in the surface ocean using high-resolution model velocity data. Our method is based upon numerically constructing a transfer operator that controls the surface transport of particles over a short period. We apply our technique to the polar latitudes of the Southern Ocean.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

Finite-time rotation number: A fast indicator for chaotic dynamical structures

Lagrangian coherent structures are effective barriers, sticky regions, that separate chaotic phase space regions of different dynamical behavior. The usual way to detect such structures is by calculating finite-time Lyapunov exponents. We show that similar results can be obtained for time-periodic systems by calculating finite-time rotation numbers, which are faster to compute. We illustrate our claim by considering examples of continuous- and discrete-time dynamical systems of physical interest.     

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.     

Bailout embeddings and neutrally buoyant particles in three-dimensional flows

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dynamics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of impurities in tubular vortical structures, the detachment of particles from fluid trajectories near hyperbolic invariant lines, and the formation of nontrivial three-dimensional structures in the distribution of particles are predicted.     

Electroseismic waves excited by vertical magnetic dipole in borenole

Acoustic and electromagnetic fields are coupled in a fluid saturated porous medium due to seismoelectric effect. Seismoelectric well logging method has been proposed to detect deep target formation utilizing such effect. Because of uncoupling of SH waves with P-SV waves, a simple and forthright way to get shear waves information is possible, especially for soft or slow formation whose shear wave velocity is lower than the velocity of borehole fluid. We consider the wave fields excited by a vertical magnetic dipole (VMD) source. Two methods are used to simulate, one is the coupled method based on Pride model and the other is the uncoupled method. For two methods, the frequency wavenumber domain representations of the acoustic field and associated seismoelectric field are formulated. The full waveforms of acoustic waves and electromagnetic wave induced SH waves excited by VMD source in the time domain propagation in borehole are simulated and analyzed.     

Sticky Behavior of Fluid Particles in the Compressible Kraichnan Model

We consider the compressible Kraichnan model of turbulent advection with small molecular diffusivity and velocity field regularized at short scales to mimic the effects of viscosity. As noted in ref 5, removing those two regularizations in two opposite orders for intermediate values of compressibility gives Lagrangian flows with quite different properties. Removing the viscous regularization before diffusivity leads to the explosive separation of trajectories of fluid particles whereas turning the regularizations off in the opposite order results in coalescence of Lagrangian trajectories. In the present paper we re-examine the situation first addressed in ref 6 in which the Prandtl number is varied when the regularizations are removed. We show that an appropriate fine-tuning leads to a sticky behavior of trajectories which hit each other on and off spending a positive amount of time together. We examine the effect of such a trajectory behavior on the passive transport showing that it induces anomalous scaling of the stationary 2-point structure function of an advected tracer and influences the rate of condensation of tracer energy in the zero wavenumber mode.     

Holographic flow visualization as a tool for studying three-dimensional coherent structures and instabilities

Holography is capable of three-dimensional (3D) representation of spatial objects such as fluid interfaces and particle ensembles. Based on this, we adapt it into a 3D flow visualization tool called Holographic Flow Visualization (HFV). This technique provides a novel means of studying spatially and temporally evolving complex fluid flow structures marked by a disperse phase or interfaces of different fluids. This paper demonstrates that HFV is a straightforward technique, especially when the In-line Recording Off-axis Viewing (IROV) configuration is used. The technique can be applied either as a stand-alone experimental tool for studying scalar-based coherent structures, flow instabilities, interactions of different fluids driven by fluid dynamics, interfacial phenomena, or as a precursor to volumetric 3D velocity vector field measurement of complex transient flow dynamics. Experimental results in several complex fluid flows and flames demonstrate the effectiveness of HFV. Different methods are used to mark flow structures undergoing different instabilities: 1) a vortex ring grown out of a drop of polymer suspension falling in water, 2) cascade of a bag-shaped drop of milk in water, and 3) internal flow structures of a jet diffusion flame.     

Magnetic field correlations in random flow with strong steady shear

We analyze the magnetic kinematic dynamo in a conducting fluid where a stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, and their growth rates and scaling behavior are established. General assertions are illustrated by the explicit solution of a model where the velocity field is short-correlated in time.     

Spatial and temporal bilateral filter for infrared small target enhancement

This paper presents a spatial and temporal bilateral filter (BF) to detect target trajectories, by extracting spatial target information using a spatial BF and temporal target information using a temporal BF. Background prediction when it is covered by targets is the key to small target detection. In order to apply the BF to a small target detection field for this purpose, this paper presents a novel spatial and temporal BF with an adaptive standard deviation to predict spatial background and temporal background profiles, based on analysis of the blocks surrounding a spatial and temporal filter window. In order to discriminate between the edge or object regions with a flat background and the target region spatially and temporally, spatial and temporal variances of the blocks surrounding the filter window are calculated in a spatial infrared (IR) image and temporal profile. The spatial and temporal variances adjust standard deviations of the spatial and temporal BF. Through this procedure, spatial background and temporal background profiles are predicted, and then small targets can be detected by subtracting the predicted spatial background (and temporal background profile) from the original IR image (and original temporal profile) and multiplying spatial and temporal target information. To compare existing target detection methods and the proposed method, signal-to-clutter ratio gain (SCRG) and background suppression factor (BSF) are employed for spatial performance comparison and receiver operating characteristics (ROC) is used for detection-performance comparison of the target trajectory. Experimental results show that the proposed method has a superior target detection rate and a lower false-alarm rate.     

Symmetry Breaking Induced Geometric Surfaces with Topological Curves in Quantum and Classical Dynamics of the SU(2) Coupled Oscillators

In the three‐dimensional (3D) transversely symmetric oscillator, there are plentiful degeneracies and gaps in the quantum energy spectrum as a function of the ratio of the transverse to longitudinal frequency. It is theoretically verified that while the SU(2) interaction destroys the original degeneracies, numerous new degeneracies and gaps emerge around the original degeneracies to form a similar fine energy spectrum. The classical trajectories at the emergent degeneracies are analyzed to be localized on the 3D parametric surfaces which are constituted by the topologically invariant curves in the transverse tomography. The quantum coherent states are exploited to develop the wave functions that correspond to the 3D geometric surfaces in classical dynamics. Furthermore, the wave structures of the stationary coherent states at small quantum numbers are explored and found to display peculiar patterns with symmetries related to classical trajectories.     

Electronic Aharonov-Bohm effect induced by quantum vibrations

Mechanical displacements of a nanoelectromechanical system shift the electron trajectories and hence perturb phase coherent charge transport through the device. We show theoretically that in the presence of a magnetic field such quantum-coherent displacements may give rise to an Aharonov-Bohm-type of effect. In particular, we demonstrate that quantum vibrations of a suspended carbon nanotube result in a positive nanotube magnetoresistance, which decreases slowly with the increase of temperature. This effect may enable one to detect quantum displacement fluctuations of a nanomechanical device.     

A novel approach to the simulation of nitroxide spin label EPR spectra from a single truncated dynamical trajectory

A simple effective method for calculation of EPR spectra from a single truncated dynamical trajectory of spin probe orientations is reported. It is shown that an accurate simulation can be achieved from the small initial fraction of a dynamical trajectory until the point when the autocorrelation function of re-orientational motion of spin label has relaxed. This substantially reduces the amount of time for spectra simulation compared to previous approaches, which require multiple full length trajectories (normally of several microseconds) to achieve the desired resolution of EPR spectra. Our method is applicable to trajectories generated from both Brownian dynamics and molecular dynamics (MD) calculations. Simulations of EPR spectra from Brownian dynamical trajectories under a variety of motional conditions including bi-modal dynamics with different hopping rates between the modes are compared to those performed by conventional method. Since the relatively short timescales of spin label motions are realistically accessible by modern MD computational methods, our approach, for the first time, opens the prospect of the simulation of EPR spectra entirely from MD trajectories of real proteins structures.     

About bursty behaviour, coherent structures, wide scrape-off layer and large parallel flows in the edge of the Tore Supra tokamak

We present the measurements of plasma characteristics in the scrape-off layer (SOL) of the Tore Supra tokamak performed by means of reciprocating Langmuir probe. The probe is inserted into the machine from top. As the radial distance from last closed flux surface (LCFS) increases, ion saturation current exhibits stronger bursty character and its probability density function becomes increasingly skewed towards positive values. At the same time, burst duration and inter-burst time increase dramatically. We explain this phenomenon by radial propagation and dynamics of the ensemble of coherent turbulent structures of different size. The results of two-dimensional fluid modelling based of flux-driven interchange instability mechanism are in excellent agreement with experimental results. We obtained clear experimental evidence that most of the coherent structures are formed in poloidally localized region of the SOL around the outboard midplane. If the probe is magnetically connected to this region, the SOL is very wide and we detect bursty behaviour in the far SOL. On the other hand, if the probe is not magnetically connected to the outboard midplane region (magnetic field lines are intercepted by the outboard limiter), then the SOL is very thin and bursty behaviour is much less prominent. Detection of bursty behaviour in the far SOL is correlated with existence of wide SOL pointing on important role of bursty transport by means of coherent turbulent structures in establishing the width of the SOL in tokamaks. The measurements of parallel flow in the SOL shows that plasma particle radial flux coming from confinement region to the SOL is mostly poloidally localized around the outboard midplane. Our estimations show that more than 80% of plasma particle radial flux is coming from confinement region to the SOL in poloidally localized region — approximately ±15° — around the outboard midplane. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.     

Large eddy simulation of compressible turbulent channel flow with spanwise wall oscillation

The influences of the modification of turbulent coherent structures on temperature field and heat transfer in turbulent channel flow are studied using large eddy simulation (LES) of compressible turbulent channel flows with spanwise wall oscillation (SWO). The reliability of the LES on such problems is proved by the comparisons of the drag reduction data with those of other researches. The high consistency of coherent velocity structures and temperature structures is found based on the analyses of the turbulent flow field. When the coherent velocity structures are suppressed, the transportations of momentum and heat are reduced simultaneously, demonstrating the same trend. This shows that the turbulent coherent structures have the same effects on the transportations of momentum and heat. The averaged wall heat flux can be reduced with appropriate oscillating parameters. Supported by the Key Subjects of National Natural Science Foundation of China (Grant No. 10732090), the National Natural Science Foundation of China (Grant No. 50476004), and the 111 Project (Grant No. B08009)     

Set-based corral control in stochastic dynamical systems: making almost invariant sets more invariant

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.     

高雷诺数双螺旋涡尾迹演化特性分析

螺旋状尾迹涡是直升机悬停旋翼流场的主导特征之一,其时空演化特性对旋翼气动性能具有重要影响.为了揭示悬停状态下旋翼尾迹涡的演化特征,对两桨叶刚性旋翼在高雷诺数悬停状态下的双螺旋状尾迹涡开展数值研究,采用基于流场特征的网格自适应技术,结合低耗散迎风/中心混合格式以及延迟脱体涡模拟方法对Caradonna-Tung旋翼在桨尖马赫数为0.439、桨尖雷诺数为1.92×10~6的悬停流场进行了高分辨率计算.基于欧拉和拉格朗日两种描述方法对计算结果进行了分析,揭示了双螺旋尾涡系统的演化特性:后缘尾涡面在桨尖附近的反向卷起及其与下游桨尖涡的相互作用是影响涡系稳定性以及涡-涡相互作用的重要因素;涡龄小于720°时,在固连于桨叶上的旋转坐标系中观察,涡系具有时空稳定性,涡管中心处轴向涡量随涡龄按照幂函数规律衰减.在固连于漩涡中心的局部极坐标系中,周向速度分布以及涡核半径随涡龄的变化与理论涡模型相符合,环量随涡龄的变化显示了漩涡的生长、平衡及耗散等演化阶段;模态分析结果表明,除点涡模态外,来流与点涡的复合模态在漩涡演化过程中对流动特征的转变有重要影响;涡系轴截面速度场的拉格朗日拟序结构直观地显示了漩涡场的时空演化过程,揭示了漩涡配对和共旋穿越等流动特征,同时也展示了后缘尾涡面卷起现象在漩涡演化过程中的作用.     

Characterization of local structures with bond-order parameters and graphs of the nearest neighbors,a comparison

We compare two methods for the characterization of local order in samples undergoing crystal nucleation and growth. Particles with a crystal-like surrounding need to be identified to follow the nucleation process. Both methods are based on the knowledge of the particle positions in a small volume of the sample. (i) Local bond-order parameters are used to quantify the orientation of the nearest neighbors of a particle, while (ii) the graph method determines the topological arrangement of the nearest neighbors and the bonds between them. Both methods are used to detect crystal-like particles and crystal nuclei in a supercooled fluid surrounding and to determine the structure of small crystal nuclei. The properties of these nuclei are of great interest for a deeper understanding of crystal nucleation, and they can be studied in detail in colloidal model systems that allow to follow the evolution of the nuclei with single particle resolution.