Coherent Structures Research Articles

Epileptic network identification: insights from Dynamic Mode Decomposition of sEEG data.

For medically-refractory epilepsy patients, stereoelectroencephalography (sEEG) is a surgical method using intracranial recordings to identify brain networks participating in early seizure organization and propagation (i.e., the epileptogenic zone, EZ). If identified, surgical EZ treatment via resection, ablation or neuromodulation can lead to seizure-freedom. To date, quantification of sEEG data, including its visualization and interpretation, remains a clinical and computational challenge. Given elusiveness of physical laws or governing equations modelling complex brain dynamics, data science offers unique insight into identifying unknown patterns within high dimensional sEEG data. We apply here an unsupervised data-driven algorithm, Dynamic Mode Decomposition (DMD), to sEEG recordings from five focal epilepsy patients (three with temporal lobe, and two with cingulate epilepsy), who underwent subsequent resective or ablative surgery and became seizure free. DMD obtains a linear approximation of nonlinear data dynamics, generating coherent structures ("modes") defining important signal features, used to extract frequencies, growth rates and spatial structures. DMD was adapted to produce Dynamic Modal Maps (DMMs) across frequency sub-bands, capturing onset and evolution of epileptiform dynamics in sEEG data. Additionally, we developed a static estimate of EZ-localized electrode contacts, termed the Higher-Frequency Mode-based Norm Index (MNI). DMM and MNI maps for representative patient seizures were validated against clinical sEEG results and seizure-free outcomes following surgery. DMD was most informative at higher frequencies, i.e. gamma (including high-gamma) and beta range, successfully identifying EZ contacts. Combined interpretation of DMM/MNI plots best identified spatiotemporal evolution of mode-specific network changes, with strong concordance to sEEG results and outcomes across all five patients. The method identified network attenuation in other contacts not implicated in the EZ. This is the first application of DMD to sEEG data analysis, supporting integration of neuroengineering, mathematical and machine learning methods into traditional workflows for sEEG review and epilepsy surgical decision-making.

Characterizing the dynamics of multi-scale global high impact weather events

The quantitative characterization and prediction of localized severe weather events that emerge as coherences generated by the highly non-linear interacting multivariate dynamics of global weather systems poses a significant challenge whose solution is increasingly important in the face of climate change where weather extremes are on the rise. As weather measurement systems (multiband satellite, radar, etc) continue to dramatically improve, increasingly complex time-dependent multivariate 3D datasets offer the potential to inform such problems but pose an increasingly daunting computational challenge. Here we describe the application to global weather systems of a novel computational method called the Entropy Field Decomposition (EFD) capable of efficiently characterizing coherent spatiotemporal structures in non-linear multivariate interacting physical systems. Using the EFD derived system configurations, we demonstrate the application of a second novel computational method called Space-Time Information Trajectories (STITs) that reveal how spatiotemporal coherences are dynamically connected. The method is demonstrated on the specific phenomenon known as atmospheric rivers (ARs) which are a prime example of a highly coherent, in both space and time, severe weather phenomenon whose generation and persistence are influenced by weather dynamics on a wide range of spatial and temporal scales. The EFD reveals how the interacting wind vector field and humidity scalar field couple to produce ARs, while the resulting STITS reveal the linkage between ARs and large-scale planetary circulations. The focus on ARs is also motivated by their devastating social and economic effects that have made them the subject of increasing scientific investigation to which the EFD may offer new insights. The application of EFD and STITs to the broader range of severe weather events is discussed.

Investigating hydrodynamics and turbulent effects in rivers for different flow conditions using spatial complexity metrics

In non-uniform river flows, hydrodynamic features, such as gradients of velocity in flow directions, are of particular importance for explaining the abundance of aquatic habitats. Hydraulic complexity metrics referred to as M1, M2, and M3 play an important role when it comes to the analysis of habitat metrics on a 3D spatial level. Parameter M1 is proportional to the drag force experienced by an organism, parameter M2 represents how much more energy an organism must expend if it moves from the lower velocity to the higher velocity location, and parameters M3 illustrates the circulation in flow. The specific aim of the present study is to apply those parameters to characterize, under different flow conditions, the cross-sectional distribution of kinetic energy and coherent structures which are both relevant for many aquatic organisms. To this aim, laboratory data as well as field observations along Tiber River, in central Italy, were considered and the hydraulic complexity metrics were investigated in dimensionless form. On the laboratory-scale, the dimensionless parameters M1*, M2* and M3* identify the velocity gradient related to the high/low cross-sectional velocity and the high/low vorticity areas in selected cross-sections along the flume. Then, the evaluation of the parameter M2* in the horizontal plane allows to verify the relation between the localization of the high/low kinetic energy areas in the longitudinal direction. For the field-scale, the parameters were investigated, under high, moderate and low flow conditions, in a gauged site in the Tiber River. The results indicate that an aquatic organism should spend more energy where M3*, which is related to flow circulation, assumes high values. Furthermore, significant values of M1* and M2* are observed, which are linked to gradients in the cross-sectional distribution of velocity. These values are predominantly found at the river centerline for M1* and at the banks for M2*. In terms of echo-hydraulics, the results based on both laboratory and field data indicate that they are complementary, showing that for the larger magnitudes of M1 and M3, which are related to the kinetic energy and flow circulation, respectively, an aquatic organism should spend more energy in these zones. Overall, the results based on both laboratory and field studies suggest that parameters M1 and M2 are inversely linked, i.e., M1 decreased with increasing M2, while, there is no relationship between parameters M3 and M1. The findings of the present research would be of particular interest in quantifying biologically important flow patterns occurring at different spatial scales within different streams and under different flow conditions.

Direct numerical simulation of 45° oblique flow past surface-mounted square cylinder

Comprehensive coherent structures around a surface-mounted low aspect ratio square cylinder in uniform flow with an oblique angle of $45^{\circ }$ were investigated for cylinder-width-based Reynolds numbers of 3000 and 10 000 by direct numerical simulation based on a topology-confined mesh refinement framework. High-resolution simulations and the critical-point concept were scrutinized to reveal for the first time the reasonable and compatible topologies of flow separation and complete near-wall structures, due to their extensive impact on various engineering applications. Large-scale horseshoe vortices are observed at two notable foci in the viscous sublayer. Within this layer, a wall-parallel jet is formed by downflow intruding into the bottom surface at the half-saddle point, then deflecting in the upstream direction and finally penetrating the bottom surface until the half-saddle point. A pair of conical vortices on the cylinder's top surface switch themselves on two sides of the square cylinder, where the switching frequency is identical with that of the sway of the side shear layer. The undulation of the Kelvin–Helmholtz instability is identified in the instantaneous development of a conical vortex and side shear layer, where the scaling of the ratio of the Kelvin–Helmholtz and von Kármán frequencies follows the power-law relation obtained by Lander et al. (J. Fluid Mech., vol. 849, 2018, pp. 1096–1119). Large-scale arch-shaped vortex is often detected in the intermediate wake region of a square cylinder, involving two interconnected portions, such as the leg portion separated from leeward surfaces and head portion rolled up from the top surface. The leg portion of the arch-shaped vortex was rooted by two foci near the bottom-surface plane.

Drag reduction of lift-type Vertical axis wind turbine with slit modified Gurney flap

This study examines aerodynamic performance enhancement of Vertical Axis Wind Turbine (VAWT) blades with Gurney flap (GF) modified by slits. A quasi-3D computational fluid dynamics solution based on Reynolds-averaged Navier-Stokes model is employed to evaluate the effectiveness of slit GF blades, in particular the lift-to-drag ratio. The computational domain includes three pairs of GFs and slits combination along the blade span-wise direction to allow quasi-3D flow development while applying translational periodic boundary condition on the two end-wall boundaries. The inlet velocity is 9 m/s for a VAWT configuration with Tip Speed Ratios (TSRs) of 1.44, 2.64, and 3.3, respectively and each of these TSRs represents low, medium, and high regimes of TSRs. Simulation results have shown a significant 8% drag reduction for blades with slit GFs at medium range of TSRs, albeit with a 2% decrease in lift compared to blades with clean GFs. This improves the lift-to-drag ratio and enhances moment production. The power generation also shows increases of 1.5%, 6.5%, and 11.3% at low, medium, and high TSR regimes, respectively, for the analysed slit GF blades. The drag reduction is primarily attributed to the generation of small-scale vortices by the slit, dissipating large coherent flow structures more rapidly in the near wake-field.

Experimental study on coherent structures by small particles suspended in high aspect-ratio (Γ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =$$\\end{document} 2.5) thermocapillary liquid bridges of high Prandtl number

In time-dependent traveling-wave convection, it has been confirmed that small particles of low Stokes number (St≪\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{St}\\ll$$\\end{document} 1) form three-dimensional closed structures known as the particle accumulation structures (PASs). We focus on coherent structures formed in high aspect-ratio thermocapillary liquid bridges (Γ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =$$\\end{document} 2.5), where oscillatory convection due to the so-called hydrothermal wave instability of mHTW=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{\ extrm{HTW}}=$$\\end{document} 1 stably emerges, and carry out experimental explorations into the volume ratio dependence of the emergence of coherent structures. Variation in the volume ratio induces the presence of coherent structures with different azimuthal wave numbers, that is, different spatial structures. Among the particles added to the liquid bridge, we perform spatio-temporal tracking of particles to quantify the correlation between the behavior of particles and the spatial structures of coherent structures with different rational wave numbers.

Aerodynamic noise analysis of the skirting board under an ultra-high-speed train based on bidimensional empirical mode decomposition

ABSTRACT The grille located in the lower part of the train often forms a grille-cavity structure in the equipment bay’s surface. The issue of flow-induced sound of this structure becomes more significant at high speeds. In this study, we focus on a skirting board with a grille, that is simplified as a grille-cavity structure. We use DDES in combination with modal decomposition, to analyze the fluidization mechanism of the structure. The results indicate that the shear oscillation at the opening of the cavity is more pronounced at ultra-high speed. Moreover, it has been shown that both POD and BEMD can accurately separate and identify coherent structures in the flow field. BEMD has higher accuracy. And the flow is primarily dominated by low-frequency acoustic oscillation. Finally, when we compare three grille configurations (V, ᴖ), we find that the grille’s presence mitigates the cavity’s aerodynamic noise, especially when using a -shaped grille.

Investigating coherent and semi-coherent interfacial structures and energetics in [formula omitted] interfaces: Theoretical insights into aluminum matrix composites bonding

Understanding the intricate interfacial structures and energetics between ceramics and aluminum is crucial for elucidating the mechanical properties of aluminum matrix composites (AMCs). However, previous theoretical simulations primarily focused on coherent interfaces, neglecting lattice constant variations on heterogeneous interfaces, which has led to discrepancies with experimentally observed semi-coherent interfaces. Here, using recently synthesized Al/Al3BC AMCs as a case study to systematically construct six semi-coherent interfacial models containing 383 to 588 atoms. These models are used to investigate the Al(11¯1)/Al3BC(0001) and Al(3¯11¯)/Al3BC(0001) structures and their associated energetics. Additionally, we examine 39 coherent interfaces for comparison. Work of adhesion and interfacial energy results reveal that the stable termination for semi-coherent interfaces is Al(B), which contrasts with AlC termination observed in coherent interfaces. Both Al(11¯1)/Al3BC(0001) and Al(3¯11¯)/Al3BC(0001) semi-coherent interfaces demonstrate higher stability but lower bonding strength compared to coherent interfaces. Bonding strength and stability of Al(B)-terminated semi-coherent interface in Al(3¯11¯)/Al3BC(0001) are lower than those in Al(11¯1)/Al3BC(0001). Electronic structure analysis indicates that AlC-terminated coherent interface exhibits greater charge transfer and stronger covalent metal bonds, while the Al(B)-terminated semi-coherent interface shows less charge transfer and more pronounced metallic bond characteristics. These computational insights provide valuable theoretical understanding of interfacial bonding mechanisms inherent in ceramic-reinforced AMCs.

Embedded Coherent Structures from Magnetohydrodynamics to Sub-ion Scales in Turbulent Solar Wind at 0.17 au

We study intermittent coherent structures in solar wind turbulence from MHD to kinetic plasma scales using Parker Solar Probe data during its first perihelion (at 0.17 au) in the highly Alfvénic slow solar wind. We detect coherent structures using Morlet wavelets. For the first time, we apply a multiscale analysis in physical space. At MHD scales within the inertial range, times scales τ ∈ (1, 102) s, we find (i) current sheets including switchback boundaries and (ii) Alfvén vortices. Within these events are embedded structures at smaller scales: typically Alfvén vortices at ion scales, τ ∈ (0.08, 1) s, and compressible vortices at sub-ion scales, τ ∈ 8(10−3, 10−2) s. The number of coherent structures grows toward smaller scales: we observe ∼200 events during a 5 hr time interval at MHD scales, ∼103 at ion scales, and ∼104 at sub-ion scales. In general, there are multiple structures of ion and sub-ion scales embedded within one MHD structure. There are also examples of ion and sub-ion scale structures outside MHD structures. To quantify the relative importance of different types of structures, we do a statistical comparison of the observed structures with the expectations of models of the current sheets and vortices. The results show the dominance of Alfvén vortices at all scales in contrast to the widespread view of the dominance of current sheets. This means that Alfvén vortices are important building blocks of Alfvénic solar wind turbulence.

Persistence of large-scale coherent structures in a turbulent pipe flow through an improved lattice Boltzmann approach

We simulated a turbulent pipe flow within the lattice Boltzmann method using a multiple-relaxation-time collision operator with Maxwell–Boltzmann equilibrium distribution expanded, for the sake of a more accurate description, up to the sixth order in Hermite polynomials. The moderately turbulent flow (Reτ≈181.3) is able to reproduce up to the fourth statistical moment with great accuracy compared with other numerical schemes and with experimental data. A coherent structure identification was performed based on the most energetic streamwise turbulent mode, which revealed a surprising memory effect related to the large-scale forcing scheme that triggered the pipe's turbulent state. We observe that the existence of large-scale motions that are out of the pipe's stationary regime does not affect the flow's detailed single-point statistical features. Furthermore, the transitions between the coherent structures of different topological modes were analyzed as a stochastic process. We find that for finely resolved data, the transitions are effectively Markovian, but for larger decimation time lags, due to topological mode degeneracy, non-Markovian behavior emerges, in agreement with previous experimental studies.

The Relative Prevalence of Wave Packets and Coherent Structures in the Inertial and Kinetic Ranges of Turbulence as Seen by Solar Orbiter

The Solar Orbiter (SO) mission provides the opportunity to study the evolution of solar wind turbulence. We use SO observations of nine extended intervals of homogeneous turbulence to determine when turbulent magnetic field fluctuations may be characterized as: (i) wave packets and (ii) coherent structures (CSs). We perform the first systematic scale-by-scale decomposition of the magnetic field using two wavelets known to resolve wave packets and discontinuities, the Daubechies 10 (Db10) and Haar, respectively. The probability distribution functions (PDFs) of turbulent fluctuations on small scales exhibit stretched tails, becoming Gaussian at the outer scale of the cascade. Using quantile–quantile plots, we directly compare the wavelet fluctuations PDFs, revealing three distinct regimes of behavior. Deep within the inertial range (IR) both decompositions give essentially the same fluctuation PDFs. Deep within the kinetic range (KR) the PDFs are distinct as the Haar decompositions have larger variance and more extended tails. On intermediate scales, spanning the IR–KR break, the PDF is composed of two populations: a core of common functional form containing ∼97% of fluctuations, and tails that are more extended for the Haar decompositions than the Db10 decompositions. This establishes a crossover between wave-packet (core) and CS (tail) phenomenology in the IR and KR, respectively. The range of scales where the PDFs are two-component is narrow at 0.9 au (4–16 s) and broader (0.5–8 s) at 0.4 au. As CS and wave–wave interactions are both candidates to mediate the turbulent cascade, these results offer new insights into the distinct physics of the IR and KR.

Experimental study on the interaction between particles and coherent structures in dilute liquid–solid two-phase turbulent boundary layer

In order to reveal the modulation of particles on turbulent coherent structures and particle concentration variations induced by turbulence, particle image velocimetry experiments were performed in a dilute liquid–solid two-phase turbulent boundary layer. Large-scale coherent structures, including streaks and hairpin vortices, were extracted in the liquid–solid two-phase turbulent boundary layer by using multiple methods, such as proper orthogonal decomposition and finite-time Lyapunov exponent. The results showed that the addition of particles thickened the buffer layer of the average velocity profile, weakened the streamwise turbulence intensity at y+ > 10, strengthened the wall-normal turbulence in the near wall region (y+ < 52), and weakened the Reynolds stress in the logarithmic law region. A more thorough study of the turbulent structure revealed that the particles caused the mean spacing of the near-wall streak structure to increase, hairpin vortex migration to slow down, the uplift of hairpin vortex to be suppressed, and the overall size of the hairpin vortex packet to be compressed. This demonstrated that particles could modulate turbulence by inhibiting the development of hairpin vortices.

Similarity solutions of a class of unsteady laminar boundary layer

The study of laminar unsteady boundary layer flows is essential for understanding the transition from laminar to turbulent flow, as well as the origins of turbulence. However, finding solutions to this phenomenon poses significant challenges. In this study, we introduce a novel method that employs a similarity transformation to convert the two-dimensional unsteady laminar boundary layer equations into a single partial differential equation with constant coefficients. By applying this transformation, we successfully derive similarity solutions for flat plate boundary layer flow, expressed in terms of Kummer functions. For convergent boundary layer flow, we derive an approximate analytical solution that includes both shock wave and soliton wave solutions. The superposition of these solutions provides evidence for the existence of solitons or soliton-like coherent structures (SCS) within boundary layers. Additionally, this paper explores two- and three-dimensional laminar flows, as well as three-dimensional turbulent flow equations, revealing that they all incorporate third-order derivatives with respect to spatial coordinates. This finding suggests that all viscous fluid motions have the potential to exhibit solitons/like coherent structures (SCS).

Correlation-enhanced short-time analysis of coherent structures for acoustic bursts in subsonic jets

A correlation-enhanced event-driven decomposition (CEED) method is developed to analyze the coherent structure during the acoustic burst in subsonic jets. To sample the acoustic burst signal for the CEED, a conditional filter is proposed. The correlation between the acoustic burst signal and the signal from the flow field is introduced into the decomposition, to deal with the low signal-to-noise ratio issue between these two signals. Suitability for the subsonic jets is demonstrated for the CEED, based on validated large eddy simulation results. Then, the short-time evolution of the coherent structure is analyzed by the CEED. The results show that the sampled acoustic burst signal is intermittent. Its spectrum appears the same shape as that of the original signal. Thus, the acoustic burst is dominant in the sound radiation. The correlation is found to accelerate the convergence of the CEED. The leading mode of the CEED is shown able to represent the short-time evolution of the coherent structure clearly. During the acoustic burst, the leading mode appears as a train of puffs, and it presents three stages: (1) Two in-phase puffs enclose an anti-phase puff. These puffs move downstream with their size growing. (2) The anti-phase puff vanishes, while the two in-phase puffs merge into a large puff. The large puff forms a wavefront. (3) Three puffs form waves in sequence. Together, these waves compose a train of waves. The merging accelerates the puff into a supersonic state intermittently; therefore, the merging is responsible for the acoustic burst.

Role of very large-scale motions in shock wave/turbulent boundary layer interactions

The present study investigates the cause of low-frequency unsteadiness in shock wave/turbulent boundary layer (TBL) interactions. A supersonic turbulent flow over a compression ramp is studied using wall-resolved large eddy simulation (LES) with a freestream Mach number of 2.95 and a Reynolds number (based on δ0: the thickness of the incoming TBL) of 63 560. From the view of stability analysis, the effect of intrinsic instability on such low-frequency unsteadiness is excluded from the flow system by designing a ramp angle of 15°, and our attention is paid to the convective instability contributed by the incoming TBL. The LES results are analyzed by linear and nonlinear disambiguation optimization (LANDO), spectral proper orthogonal decomposition (SPOD), and resolvent analysis. The LANDO results reveal a streamwise scale-frequency relation of coherent structures in a very long (around 60δ0) TBL, which indicates that the dynamics of very large-scale motions (VLSMs) in the TBL are featured by a low frequency. The SPOD results reveal that the most energetic SPOD mode features a low frequency that is identical to the dominant low frequency of the wall-pressure spectrum. Additionally, coherent structures of the mode resemble the VLSMs in the incoming TBL. These consistencies imply that the dynamics of VLSMs contribute to the low-frequency unsteadiness of the present flow. A resolvent analysis then further suggests that the origins of low-frequency dynamics of the present flow are from the VLSMs, which can be optimally amplified by the forcing in the turbulent flow.

Integrated positron emission particle tracking (PEPT) and X-ray computed tomography (CT) imaging of flow phenomena in twisted tape swirl flow

A combined positron emission particle tracking (PEPT) and X-ray computed tomography (CT) technique is presented, and its utility is demonstrated through investigation of flow in a pipe with twisted tape swirl insert with varying flow conditions (diameter-based Reynolds numbers 16,300–63,300). A description of this technique is given, as well as data handling practices used to relate geometric information captured by CT to fluid flow data gathered via PEPT. It is found that the CT component is readily capable of capturing the stainless steel insert geometry in this present system, but the use of combined plastic and metal materials leads to artifacts in imaging of the plastic surface. Nonetheless, CT data are related to PEPT flow measurements, and average velocity fields are calculated via a pseudo-framing and interpolation scheme and used to visualize and interrogate key flow phenomena within the system. Radial velocity profiles of the mean flow characteristics are seen to collapse to a nearly common form across all flow conditions considered. Helical vortices are seen propagating through the flow field, generated by bypass flow around the gap between the insert and pipe wall, with additional coherent secondary flow structures seen in the higher Reynolds number cases. These findings enhance the understanding of the mixing mechanisms in these swirl flows and encourage the continued development of PEPT-CT methodologies for 3D flow measurements in optically inaccessible systems.

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories.

We propose a framework of Lagrangian Coherent Structures (LCSs) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone, which eventually impinges on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward-facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analyzed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection, in turn, prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

Shedding-scheme transition of hemisphere near wake dependent on Reynolds number

The shedding-scheme transition of hemispherical wake is investigated with time-resolved tomographic particle image velocimetry. Experiments are carried out with Reynolds numbers based on the hemisphere radius R in the range of Rer=924–2315, crossing the critical value of Rer≈2000. The variation of the hemispherical wake across the critical Reynolds number is carefully studied, and a detailed mechanism of the shedding-scheme transition is explored. A singular-shedding pattern of hairpin vortices at a low Rer is replaced by a pairing-shedding pattern at a moderate Rer, and finally, a less ordered wake and an unstable shedding pattern are observed at Rer > 2000. The onset of the pairing-shedding pattern is due to a streamwise modulation caused by the varicose modes, which is related to the Kelvin–Helmholtz (K–H) instability. Consequently, the pseudo-periodicity induced by the K–H instability is observed in the wake. When Rer > 2000, the stronger sinuous modulation intensifies interactions among the hairpin vortices, leading to frequent absorption and annihilation of those coherent structures, which further makes the dominant frequency of main hairpin vortices halved downstream.

Turbulent boundary layer structures downstream of a square cylinder

Particle image velocimetry is used to investigate the coherent structures within a turbulent boundary layer (TBL) perturbed by a slender square cylinder. A moderate Reynolds number of Reτ=3691 is considered. The cylinder is immersed in different vertical regions of the TBL, from the viscous sublayer to the logarithmic layer, depending on the value of the cylinder–wall gap ratio within the range of G/D=0.0−2.0. Here, G is the distance between the wall and the lower surface of the cylinder, and D is the cross-section size of the square cylinder. The results reveal a substantial influence of the TBL statistics and structures. Utilizing velocity correlation and proper orthogonal decomposition (POD), we highlight the intriguing influence of large-/very large-scale turbulent structures induced by the cylinder. When the cylinder is positioned on or in close proximity to the wall, periodic shedding of vortices is not apparent. In the presence of a cylinder, the large-/very large-scale turbulent structures are reduced in size compared with those in the undisturbed TBL, owing to the interaction between the flow around the cylinder and the boundary layer turbulence. The lower modes of the POD in the disturbed TBL are similar to those of the undisturbed flow field. However, the large-/very large-scale turbulent structures are increasingly affected by the strengthening of the shedding vortices with increasing G/D when the cylinder is located in the logarithmic region. As a result, the Kármán vortex street becomes the dominant structure associated with the higher POD modes at sufficiently high cylinder–wall gap ratios.