scholarly journals On the non-local geometry of turbulence

2008 ◽  
Vol 603 ◽  
pp. 101-135 ◽  
Author(s):  
IVÁN BERMEJO-MORENO ◽  
D. I. PULLIN
Keyword(s):  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Joint Probability ◽  
Curvelet Transform ◽  
Feature Space ◽  
Passive Scalar ◽  
Local Geometry ◽  
Multi Scale ◽  
Finite Set ◽  
Non Local

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

The bottleneck effect and the Kolmogorov constant in isotropic turbulence

2010 ◽  
Vol 657 ◽  
pp. 171-188 ◽  
Author(s):  
D. A. DONZIS ◽  
K. R. SREENIVASAN
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Numerical Data ◽  
Order Structure ◽  
Bottleneck Effect ◽  
Usual Procedure ◽  
Independent Constant ◽  
Non Local ◽  
Kolmogorov Constant

A large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 40963 and the Taylor–Reynolds number Rλ ≈ 1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, CK. The difficulties in estimating CK at any finite Reynolds number, introduced by intermittency and the bottleneck, are assessed. The data conclusively show that the bottleneck effect decreases with the Reynolds number. On this basis, an alternative to the usual procedure for determining CK is suggested; this proposal does not depend on the particular choices of fitting ranges or power-law behaviour in the inertial range. Within the resolution of the numerical data, CK thus determined is a Reynolds-number-independent constant of ≈1.58 in the three-dimensional spectrum. A simple model including non-local transfer is proposed to reproduce the observed scaling features of the bottleneck.

Multiresolution Non-Local Mean Filter for Infrared Dim and Small Target Background Suppression

2011 ◽  
Vol 135-136 ◽  
pp. 637-642
Author(s):  
Jia Li ◽  
Juan Chang ◽  
Han Lin Qin
Keyword(s):  
Infrared Image ◽  
Curvelet Transform ◽  
Background Suppression ◽  
Small Target ◽  
Least Mean Square ◽  
Multi Scale ◽  
Local Means ◽  
Mean Filter ◽  
Non Local ◽  
Local Gradient

Structured clouds and ground building background suppression are difficult problems for dim and small target detection technique. In this paper, the dim and small target background suppression method based on combined curvelet transform with modified non-local means filter was presented to solve the problem. And local gradient statistics is introduced to boost ability of method which suppresses false by background structure. The innovation was that the curvelet transform was adopted to decompose the input infrared image, which extracts multi-scale and directional detail features of the image. Moreover non-local means filter improved by local gradient characteristic was introduced to suppress background details and enhance target information for suppression background. Compared with two-dimensional least mean square (TDLMS) and modified partial differential equation (MPDE) methods, through visual quality and value index, several groups of experimental results demonstrate that the presented method can suppress complicated background in dim and small target image effectively.

scholarly journals Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

2010 ◽  
Vol 654 ◽  
pp. 233-270 ◽  
Author(s):  
YUE YANG ◽  
D. I. PULLIN ◽  
IVÁN BERMEJO-MORENO
Keyword(s):  
Velocity Field ◽  
Isotropic Turbulence ◽  
Geometric Analysis ◽  
Turbulent Velocity ◽  
Geometrical Parameters ◽  
Advection Equation ◽  
Local Geometry ◽  
Multi Scale ◽  
Surface Field ◽  
Turbulent Velocity Field

We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 10243 at different times, from t = 0 to t = Te, where Te is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.

Statistical characteristics of wall turbulence with a passive scalar

1988 ◽  
Vol 196 ◽  
pp. 157-185 ◽  
Author(s):  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Hermite Polynomials ◽  
Three Dimensional ◽  
Joint Probability ◽  
Passive Scalar ◽  
Present Theory ◽  
Wall Turbulence ◽  
Statistical Characteristics ◽  
Turbulent Shear ◽  
Scalar Fluxes ◽  
Turbulent Momentum

Various types of moments of velocity and scalar fluctuations of the first to the fourth order have been measured and analysed. First, an orthogonal series expansion for the three-dimensional joint probability density function (p.d.f.) is developed using the cumulants and Hermite polynomials. This p.d.f. is found to provide satisfactory predictions for the statistical characteristics, including triple products, of turbulent momentum and scalar transfer. Next, the conditional sampling and averaging technique is employed to investigate the statistical characteristics of coherent turbulent transfer processes of momentum and scalar. Conditional p.d.f.s are developed for various moments of velocity and scalar up to the third order. It is shown that the present p.d.f.s can predict the detailed role of coherent motions in the dynamics of wall turbulent shear flows and in the relevant process of scalar transport by turbulence. In particular, the importance of coherent motions in the turbulent diffusion process of Reynolds-stress components and scalar fluxes is demonstrated for the first time by the present theory.

scholarly journals Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

2009 ◽  
Vol 620 ◽  
pp. 121-166 ◽  
Author(s):  
IVÁN BERMEJO-MORENO ◽  
D. I. PULLIN ◽  
KIYOSI HORIUTI
Keyword(s):  
Composite Structures ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Continuous Distribution ◽  
Scalar Fields ◽  
Grid Resolution ◽  
Local Analysis ◽  
Multi Scale ◽  
Small Scales ◽  
Non Local

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 2563, 5123 and 10243 grid points, with kmax approximately 1, 2 and 4, respectively, the same initial conditions and Reλ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 2563 grid resolution case (kmax ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [Aij]+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 10243 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [Aij]+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.

Three-dimensional Reconstruction of Microscopic Image Based on Multi-ST Algorithm

2020 ◽  
Vol 64 (2) ◽  
pp. 20506-1-20506-7
Author(s):  
Min Zhu ◽  
Rongfu Zhang ◽  
Pei Ma ◽  
Xuedian Zhang ◽  
Qi Guo
Keyword(s):  
3D Reconstruction ◽  
Three Dimensional ◽  
Scale Model ◽  
Microscopic Image ◽  
Multi Scale ◽  
Gaussian Pyramid ◽  
Cost Aggregation ◽  
Dimensional Reconstruction ◽  
Image Pairs ◽  
Accurate Matching

Abstract Three-dimensional (3D) reconstruction is extensively used in microscopic applications. Reducing excessive error points and achieving accurate matching of weak texture regions have been the classical challenges for 3D microscopic vision. A Multi-ST algorithm was proposed to improve matching accuracy. The process is performed in two main stages: scaled microscopic images and regularized cost aggregation. First, microscopic image pairs with different scales were extracted according to the Gaussian pyramid criterion. Second, a novel cost aggregation approach based on the regularized multi-scale model was implemented into all scales to obtain the final cost. To evaluate the performances of the proposed Multi-ST algorithm and compare different algorithms, seven groups of images from the Middlebury dataset and four groups of experimental images obtained by a binocular microscopic system were analyzed. Disparity maps and reconstruction maps generated by the proposed approach contained more information and fewer outliers or artifacts. Furthermore, 3D reconstruction of the plug gauges using the Multi-ST algorithm showed that the error was less than 0.025 mm.

scholarly journals Non-Local and Multi-Scale Mechanisms for Image Inpainting

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3281
Author(s):  
Xu He ◽  
Yong Yin
Keyword(s):  
Markov Random Fields ◽  
Receptive Fields ◽  
Image Inpainting ◽  
Long Distance ◽  
Visual Appearance ◽  
Fine Grained ◽  
Multi Scale ◽  
Non Local ◽  
Relationship Of

Recently, deep learning-based techniques have shown great power in image inpainting especially dealing with squared holes. However, they fail to generate plausible results inside the missing regions for irregular and large holes as there is a lack of understanding between missing regions and existing counterparts. To overcome this limitation, we combine two non-local mechanisms including a contextual attention module (CAM) and an implicit diversified Markov random fields (ID-MRF) loss with a multi-scale architecture which uses several dense fusion blocks (DFB) based on the dense combination of dilated convolution to guide the generative network to restore discontinuous and continuous large masked areas. To prevent color discrepancies and grid-like artifacts, we apply the ID-MRF loss to improve the visual appearance by comparing similarities of long-distance feature patches. To further capture the long-term relationship of different regions in large missing regions, we introduce the CAM. Although CAM has the ability to create plausible results via reconstructing refined features, it depends on initial predicted results. Hence, we employ the DFB to obtain larger and more effective receptive fields, which benefits to predict more precise and fine-grained information for CAM. Extensive experiments on two widely-used datasets demonstrate that our proposed framework significantly outperforms the state-of-the-art approaches both in quantity and quality.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

scholarly journals Single image super resolution based on multi-scale structure and non-local smoothing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenyi Wang ◽  
Jun Hu ◽  
Xiaohong Liu ◽  
Jiying Zhao ◽  
Jianwen Chen
Keyword(s):  
Super Resolution ◽  
Principal Component ◽  
Feature Mapping ◽  
Multi Scale ◽  
Non Local ◽  
Image Super Resolution ◽  
Gaussian Blur ◽  
Single Image Super Resolution ◽  
Global And Local ◽  
Bicubic Interpolation

AbstractIn this paper, we propose a hybrid super-resolution method by combining global and local dictionary training in the sparse domain. In order to present and differentiate the feature mapping in different scales, a global dictionary set is trained in multiple structure scales, and a non-linear function is used to choose the appropriate dictionary to initially reconstruct the HR image. In addition, we introduce the Gaussian blur to the LR images to eliminate a widely used but inappropriate assumption that the low resolution (LR) images are generated by bicubic interpolation from high-resolution (HR) images. In order to deal with Gaussian blur, a local dictionary is generated and iteratively updated by K-means principal component analysis (K-PCA) and gradient decent (GD) to model the blur effect during the down-sampling. Compared with the state-of-the-art SR algorithms, the experimental results reveal that the proposed method can produce sharper boundaries and suppress undesired artifacts with the present of Gaussian blur. It implies that our method could be more effect in real applications and that the HR-LR mapping relation is more complicated than bicubic interpolation.

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