Extraction Of Vortices Research Articles

Multiresolution classification of turbulence features in image data through machine learning

During large-scale simulations, intermediate data products such as image databases have become popular due to their low relative storage cost and fast in-situ analysis. Serving as a form of data reduction, these image databases have become more acceptable to perform data analysis on. We present an image-space detection and classification system for extracting vortices at multiple scales through wavelet-based filtering. A custom image-space descriptor is used to encode a large variety of vortex-types and a machine learning system is trained for fast classification of vortex regions. By combining a radial-based histogram descriptor, a bag of visual words feature descriptor, and a support vector machine, our results show that we are able to detect and classify vortex features at various sizes at multiple scales. Once trained, our framework enables the fast extraction of vortices on new, unknown image datasets for flow analysis.

Vortex statistics in two-dimensional turbulence based on IB-LBM

In this paper, the two-dimensional (2D) turbulence perturbed by arrays of cylinders placed both horizontally and vertically is investigated by Immersed Boundary Lattice Boltzmann Method (IB-LBM). The energy spectrum reveals the coexistence of the inverse and direct cascades in 2D grid turbulence. By observing at the distribution of fluxes in space, the energy and enstrophy fluxes have explained the physical mechanism of the double cascades where the two Kolmogorov laws for structure functions are simultaneously observed. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show that the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The time-evolving vortex number density distribution constructs a theoretical framework involving a three-part: [Formula: see text]; [Formula: see text]; [Formula: see text], which is satisfied with the prediction well. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow by studying the energy ratio of all vortices to the entire flow field. What is more, it is an interesting phenomenon is that there is only a range where [Formula: see text] in the energy spectrum for the coherent structure field which is obtained by using Liutex as the extraction of vortices. The probability density function (PDF) of the fluctuations of longitudinal velocity shows that an indication of small intermittency in the direct cascade and the absence of intermittency in the inverse cascade range. On the other hand, the scaling exponents [Formula: see text] of the structure function for the inverse cascade are consistent with Kr67 model, which shows the absence of intermittency. While the measured intermittency parameters are [Formula: see text] and [Formula: see text], which explains that there is a very weak intermittent correction in the direct cascade, and ESS has verified the existence of intermittency in our 2D turbulence.

Hyper-Objective Vortices.

Almost all properties of vector fields, including magnitude, direction, λ2 and vorticity change under arbitrary movements of the observer. This is undesirable since measurements of physical properties should ideally not depend on the way the (virtual) measurement device moves. There are some properties that are invariant under certain types of reference frame transformations: Galilean invariance (invariance under equal-speed translation) and objectivity (invariance under any smooth rotation and translation of the reference frame). In this paper, we introduce even harder conditions than objectivity: we demand invariance under any smooth similarity transformation (rotation, translation and uniform scale) as well as invariance under any smooth affine transformation of the reference frame. We show that these new hyper-objective measures allow the extraction of vortices that change their volume or deform. Further, we present a generic approach that transforms almost any vortex measure into a hyper-objective one. We apply our methods to vortex extraction in 2D and 3D vector fields, and analyze the numerical robustness, extraction time and the minimization residuals for the Galilean invariant, objective, and the two new hyper-objective approaches.

A multi-grid framework for the extraction of large-scale vortices in Large-Eddy Simulation

The analysis of large-scale vortices from highly refined unsteady simulations becomes challenging as the mesh resolution increases. Beyond the large amount of data that needs to be processed, classical vortex visualization techniques based on invariants of the velocity gradient tensor fail in extracting the large-scale vortices as the velocity gradient tensor magnitude is greater for small turbulent eddies than for energy-containing vortices. This problem is even more important in highly-resolved simulations with a broad range of eddies. The methodology presented here is a geometric multi-grid high-order filtering (MGHOF) framework for on-line analysis of high-fidelity simulations. This approach relies on high-order implicit filters and enables the extraction of large-scale features from Large-Eddy Simulations (LES) on massive and distributed unstructured grids at a reduced cost. The MGHOF framework is first described and validated, then the methodology is applied to a 3D turbulent plane jet and to the LES of a 3D low-Mach number turbine blade with various mesh sizes, ranging from a few million to a few billion tetrahedra. In the latter case, the MGHOF enables to perform the dynamic mode decomposition of the velocity and temperature fields for the finer grid resolution.

Boundary β‐plumes and their vorticity budgets

Analytic solutions for the β‐plume near a solid boundary with Rayleigh drag are presented and their vorticity budgets calculated. It is shown that, when the boundary tilts into the westward plume of streamlines, the β‐plume decays exponentially with a characteristic e‐folding length‐scale that depends inversely as the cosine of the angle of the boundary. Most of the vorticity is extracted from the flow in a short range along the wall. By contrast, when the boundary tilts away from the westward plume of streamlines, the vorticity extraction is reduced by a factor that depends exponentially on the distance to the wall and the sine of the wall angle. Numerical solutions for horizontal viscous dissipation are also presented, and it is shown that they resemble the β‐plume with Rayleigh drag. However, the plume tail decays as an exponential modulated by a harmonic oscillation. The characteristic e‐folding decay scale is shorter than with Rayleigh drag by one to five times, depending on wall angle; the oscillation wavelength is about 3.4 times the e‐folding scale. These results suggest the relevant parameters and scalings controlling bathymetric interactions in more complex situations, such as the real ocean.

Extraction of coherent vortices from homogeneous turbulence using curvelets and total variation filtering methods

Most filtering methods for turbulent flow depend on wavelet and Fourier decompositions; however, this paper employs curvelets and total variation (TV) filtering methods. These two methods are investigated to extract the coherent and incoherent parts of a forced homogeneous isotropic turbulent field. The Lattice Boltzmann method with resolutions of 1283 and 2563 is used to simulate the turbulent fields, and the Q-identification method is applied to extract the elongated vortical structures. Most of the previous efforts apply filtering techniques to the velocity or vorticity fields; however, this paper applies the two filtering methods to the Q-field. 3D curvelet filtering is applied using a nonlinear thresholding technique. The 3D total variation method is applied using the split Bregman regularization method. The results indicate that the two filtering methods identify the coherent and incoherent parts smoothly. The results of the two filtering methods tend to identify coherent vortices and remove incoherent noise without any change in the physical structure of the turbulent fields. The results are compared with previous efforts using wavelet and Fourier decompositions.

Adaptive Extraction and Quantification of Geophysical Vortices

We consider the problem of extracting discrete two-dimensional vortices from a turbulent flow. In our approach we use a reference model describing the expected physics and geometry of an idealized vortex. The model allows us to derive a novel correlation between the size of the vortex and its strength, measured as the square of its strain minus the square of its vorticity. For vortex detection in real models we use the strength parameter to locate potential vortex cores, then measure the similarity of our ideal analytical vortex and the real vortex core for different strength thresholds. This approach provides a metric for how well a vortex core is modeled by an ideal vortex. Moreover, this provides insight into the problem of choosing the thresholds that identify a vortex. By selecting a target coefficient of determination (i.e., statistical confidence), we determine on a per-vortex basis what threshold of the strength parameter would be required to extract that vortex at the chosen confidence. We validate our approach on real data from a global ocean simulation and derive from it a map of expected vortex strengths over the global ocean.

TRACKING OF VORTICAL STRUCTURES IN THREE-DIMENSIONAL DECAYING HOMOGENEOUS ISOTROPIC TURBULENCE

Direct numerical simulation of three-dimensional decaying homogeneous isotropic turbulence with a resolution of 1283 is carried out using the Lattice Boltzmann Method (LBM). The aim of this paper is to investigate the statistical characteristics of the obtained turbulent flow field and the behavior of the vortical structures. Most of the LBM simulations of decaying turbulence were mainly focused on the statistical results of the velocity field, however the characteristics of the coherent vortices and their time evolution are ignored. In this paper, the statistical properties of the velocity field as well as the extraction and tracking processes of individual vortices are considered. Results show that the present simulation could recover important features of turbulence such as isotropy, skewness, energy spectrum and elongated vortical structures. A vortex ring is identified in the flow field which can be considered as a sign for the existence of vortex rings in homogeneous isotropic turbulence. Forward and reverse tracking of individual vortical structures shows that vortex rings can be generated from the interaction and the overlapping of vortex tubes.

Analysis of ocean turbulence using adaptive CVE on altimetry maps

It has been often argued that oceanic turbulence is similar to 2D turbulence; they share many properties and more particularly they seem to be driven by the dynamics of coherent vortices over large scales. For this reason, the application of techniques based on the extraction of coherent vortices as the Coherent Vortex Extraction (CVE) seems a natural choice for the description of ocean data. In this paper we will discuss on the properties of oceanic turbulence under the perspective of the Microcanonical Multifractal Formalism (MMF), and specifically for the description of altimetry data. We will see that MMF gives a good description of the geometry and statistical properties of altimetry data. We will show that a direct application of CVE on altimetry data has a rather low performance in comparison to other systems, which we justify as a consequence of the inhomogeneous character of ocean turbulence. We also show that a MMF-based separation criterion improves the standard CVE and allows to mitigate these problems. The results are discussed in the perspective of a cascade-based description of ocean turbulence.

Extraction and tracking of multi-scaled vortices from a homogeneous isotropic turbulent field

Vortex structures of various scales are extracted from an isotropic homogeneous turbulent field, and they are tracked. By filtering the flow field using Fourier decomposition and removing the fragments of small volumes, three flow fields, namely the large, intermediate and fine, each containing vortices of similar scales are obtained. Also, an automatic vortex-tracking scheme that can handle the vortex division is presented. By comparing the vortex structures found in flow fields of various scales, it is shown that vortex structures are more actively stretching in the fine-scale flow field compared to the larger-scale flow fields. By tracking the vortex structures in flow fields of various scales, it is shown that vortex structures in the large-scale flow field have a tendency to stretch when vortex division into smaller pieces is taking place, though such a tendency cannot be found among the vortex structures of smaller-scale flow fields. The division process is found to be slower for the vortex structures of the smaller-scale flow fields.

Vortex characteristics in laminar cavity flow at very low Mach number

In the present paper, a laminar cavity is analysed at very low Mach numbers. The characteristics of core-vortices are proposed and commented. The experiments were performed in an open subsonic wind tunnel using particle image velocimetry (PIV). A rectangular cavity with a length-to-depth ratio of 4 was used (shallow and open type). Three different Reynolds numbers, based on cavity depth and free stream velocity, were examined (Re h =4,000, 9,000 and 13,000). The upstream boundary layer was investigated using classical hot-wire anemometry and was found to be laminar. For each Reynolds number, a total of 1,000 vectors fields were acquired. The results are given in terms of conventional quantities (mean flow velocity, turbulence characteristics, Reynolds shear stress) and also in terms of vortex characteristics (such as probability density function of vortex location, vortex size and vortex circulation). Some of these vortex characteristics are then proposed in a local averaged presentation. The extraction of vortices from instantaneous flow fields has been done through the use of a home-made algorithm based on continuous wavelet analysis.

Swirl Condition in Low-Pressure Vortices

A numerical method of extraction of the axis of tubular vortices in turbulent flows, which was previously proposed by Miura and Kida [J. Phys. Soc. Jpn. 66 (1997)], is improved by imposing a swirl condition. This condition guarantees the extraction of low-pressure vortices with swirling motion as well as the demarcation of the core regions around the central axis. The mean radius of vortex cores is found to be five to six times the Kolmogorov length in turbulence of micro-scale Reynolds number of 46.

Confirmation of the modified Bean model from simulations of superconducting vortices.

From a very simple description of vortices and pinning centers and without using any electrodynamical assumptions, we obtain nonlinear density profiles of vortices in type-II dirty superconductors that result from raising or lowering an external magnetic field. The results confirm a modified Bean model description of these systems, and in particular, follow the Kim empirical form that relates the current inside the material to the local magnetic field. We also obtain realistic magnetization hysteresis loops and examine the discrete evolution of the density profiles in our systems. This evolution is not continuous, but takes place by the occurrence of avalanches of vortices promoted by the addition or extraction of vortices from the edges of the system.