Lagrangian Coherent Structure Analysis of Terminal Winds Detected by Lidar. Part I: Turbulence Structures

2011 ◽  
Vol 50 (2) ◽  
pp. 325-338 ◽  
Author(s):  
Wenbo Tang ◽  
Pak Wai Chan ◽  
George Haller
Keyword(s):  
Coherent Structures ◽  
Finite Domain ◽  
Lidar Data ◽  
Commercial Aviation ◽  
Turbulence Structures ◽  
Finite Time Lyapunov Exponent ◽  
Turbulent Airflow ◽  
Vertical Slice ◽  
Convergence And Divergence ◽  
Hong Kong International Airport

Abstract The accurate real-time detection of turbulent airflow patterns near airports is important for safety and comfort in commercial aviation. In this paper, a method is developed to identify Lagrangian coherent structures (LCS) from horizontal lidar scans at Hong Kong International Airport (HKIA) in China. LCS are distinguished frame-independent material structures that create localized attraction, repulsion, or high shear of nearby trajectories in the flow. As such, they are the fundamental structures behind airflow patterns such as updrafts, downdrafts, and wind shear. Based on a recently developed finite-domain–finite-time Lyapunov exponent (FDFTLE) algorithm from Tang et al. and on new Lagrangian diagnostics presented in this paper that are pertinent to the extracted FDFTLE ridges, the authors differentiate LCS extracted from lidar data. It is found that these LCS derived from horizontal lidar scans compare well to convergence and divergence suggested by vertical slice scans. At HKIA, horizontal scans are predominant: they cover much bigger azimuthal ranges as compared with only two azimuthal angles from the vertical scans. LCS extracted from horizontal scans are thus advantageous in providing organizing turbulence structures over the entire observational domain as compared with a single line along the vertical scan direction. In Part II of this study, the authors will analyze the evolution of LCS and their impacts on landing aircraft based on recorded flight data.

scholarly journals Lagrangian Coherent Structure Analysis of Terminal Winds: Three-Dimensionality, Intramodel Variations, and Flight Analyses

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Brent Knutson ◽  
Wenbo Tang ◽  
Pak Wai Chan
Keyword(s):  
Coherent Structures ◽  
Three Dimensional ◽  
Light Detection And Ranging ◽  
Flow Structures ◽  
Lidar Data ◽  
Two Dimensional ◽  
Lagrangian Coherent Structure ◽  
Flight Data ◽  
Velocity Information ◽  
Hong Kong International Airport

We present a study of three-dimensional Lagrangian coherent structures (LCS) near the Hong Kong International Airport and relate to previous developments of two-dimensional (2D) LCS analyses. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR) data. Addition of the velocity information perpendicular to the LIDAR scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. We find that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory), their Lagrangian signatures over the entire domain are quite different—a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations.

Lagrangian Coherent Structure Analysis of Terminal Winds Detected by Lidar. Part II: Structure Evolution and Comparison with Flight Data

2011 ◽  
Vol 50 (10) ◽  
pp. 2167-2183 ◽  
Author(s):  
Wenbo Tang ◽  
Pak Wai Chan ◽  
George Haller
Keyword(s):  
Coherent Structures ◽  
Coherent Structure ◽  
Wind Shear ◽  
Light Detection And Ranging ◽  
Structure Evolution ◽  
Flow Structures ◽  
Lidar Data ◽  
Lagrangian Coherent Structure ◽  
Flight Data ◽  
Hong Kong International Airport

AbstractUsing observational data from coherent Doppler light detection and ranging (lidar) systems situated at the Hong Kong International Airport (HKIA), the authors extract Lagrangian coherent structures (LCS) intersecting the flight path of landing aircraft. They study the time evolution of LCS and compare them with onboard wind shear and altitude data collected during airplane approaches. Their results show good correlation between LCS extracted from the lidar data and updrafts and downdrafts experienced by landing aircraft. Overall, LCS analysis shows promise as a robust real-time tool to detect unsteady flow structures that impact airplane traffic.

Lagrangian Detection of Wind Shear for Landing Aircraft

2013 ◽  
Vol 30 (12) ◽  
pp. 2808-2819 ◽  
Author(s):  
Hossein Amini Kafiabad ◽  
Pak Wai Chan ◽  
George Haller
Keyword(s):  
Lyapunov Exponent ◽  
Coherent Structures ◽  
Wind Shear ◽  
Particle Dynamics ◽  
Spring Season ◽  
Multiple Sources ◽  
Alert System ◽  
Finite Time Lyapunov Exponent ◽  
Ground Based Lidar ◽  
Hong Kong International Airport

Abstract Recent studies have shown that aerial disturbances affecting landing aircraft have a coherent signature in the Lagrangian aerial particle dynamics inferred from ground-based lidar scans. Specifically, attracting Lagrangian coherent structures (LCSs) mark the intersection of localized material upwelling within the cone of the lidar scan. This study tests the detection power of LCSs on historical landing data and corresponding pilot reports of disturbances from Hong Kong International Airport. The results show that a specific LCS indicator, the gradient of the finite-time Lyapunov exponent (FTLE) field along the landing path, is a highly efficient marker of turbulent upwellings. In particular, in the spring season, projected FTLE gradients closely approach the efficiency of the wind shear alert system currently in operation at the airport, even though the latter system relies on multiple sources of data beyond those used in this study. This shows significant potential for the operational use of FTLE gradients in the real-time detection of aerial disturbances over airports.

Transport and Mixing in Patient Specific Abdominal Aortic Aneurysms With Lagrangian Coherent Structures

2012 ◽  
Author(s):  
Amirhossein Arzani ◽  
Shawn C. Shadden
Keyword(s):  
Coherent Structures ◽  
Abdominal Aortic Aneurysms ◽  
Aortic Aneurysms ◽  
Lagrangian Coherent Structures ◽  
Patient Specific ◽  
Complex Flow ◽  
Flow Topology ◽  
Finite Time Lyapunov Exponent ◽  
Abdominal Aortic ◽  
High Gradients

Abdominal aortic aneurysms (AAA) are characterized by disturbed flow patterns, low and oscillatory wall shear stress with high gradients, increased particle residence time, and mild turbulence. Diameter is the most common metric for rupture prediction, although this metric can be unreliable. We hypothesize that understanding the flow topology and mixing inside AAA could provide useful insight into mechanisms of aneurysm growth. AAA morphology has high variability, as with AAA hemodynamics, and therefore we consider patient-specific analyses over several small to medium sized AAAs. Vortical patterns dominate AAA hemodynamics and traditional analyses based on the Eulerian fields (e.g. velocity) fail to convey the complex flow structures. The computation of finite-time Lyapunov exponent (FTLE) fields and underlying Lagrangian coherent structures (LCS) help reveal a Lagrangian template for quantifying the flow [1].

scholarly journals Shape Coherence and Finite-Time Curvature Evolution

2015 ◽  
Vol 25 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Tian Ma ◽  
Erik M. Bollt
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Coherent Structures ◽  
Finite Time ◽  
Large Curvature ◽  
Nonautonomous Dynamical Systems ◽  
Finite Time Lyapunov Exponent ◽  
Close Proximity ◽  
Definition Of ◽  
Curvature Growth

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-Time Lyapunov Exponent (FTLE) computation, often used to indicate hyperbolic material curves as Lagrangian Coherent Structures (LCS). We show that often the FTC troughs are in close proximity to the FTLE ridges, but in other scenarios, the FTC indicates entirely different regions.

scholarly journals Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging

2021 ◽  
Vol 18 (181) ◽  
pp. 20210523
Author(s):  
Nathaniel J. Linden ◽  
Dennis R. Tabuena ◽  
Nicholas A. Steinmetz ◽  
William J. Moody ◽  
Steven L. Brunton ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Calcium Imaging ◽  
Large Scale ◽  
Vector Fields ◽  
Brain Activity ◽  
Time Varying ◽  
Finite Time Lyapunov Exponent ◽  
Synthetic Datasets ◽  
The Brain ◽  
Analyse Time

Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits . These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

scholarly journals Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

2019 ◽  
Vol 488 (3) ◽  
pp. 3076-3088 ◽  
Author(s):  
Abraham C-L Chian ◽  
Suzana S A Silva ◽  
Erico L Rempel ◽  
Milan Gošić ◽  
Luis R Bellot Rubio ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Local Maximum ◽  
Lagrangian Coherent Structures ◽  
Quiet Sun ◽  
Finite Time Lyapunov Exponent ◽  
Magnetic Elements ◽  
Disc Centre ◽  
Transport Barriers ◽  
Intensity Images

ABSTRACT The quiet Sun exhibits a wealth of magnetic activities that are fundamental for our understanding of solar magnetism. The magnetic fields in the quiet Sun are observed to evolve coherently, interacting with each other to form prominent structures as they are advected by photospheric flows. The aim of this paper is to study supergranular turbulence by detecting Lagrangian coherent structures (LCS) based on the horizontal velocity fields derived from Hinode intensity images at disc centre of the quiet Sun on 2010 November 2. LCS act as transport barriers and are responsible for attracting/repelling the fluid elements and swirling motions in a finite time. Repelling/attracting LCS are found by computing the forward/backward finite-time Lyapunov exponent (FTLE), and vortices are found by the Lagrangian-averaged vorticity deviation method. We show that the Lagrangian centres and boundaries of supergranular cells are given by the local maximum of the forward and backward FTLE, respectively. The attracting LCS expose the location of the sinks of photospheric flows at supergranular junctions, whereas the repelling LCS interconnect the Lagrangian centres of neighbouring supergranular cells. Lagrangian transport barriers are found within a supergranular cell and from one cell to other cells, which play a key role in the dynamics of internetwork and network magnetic elements. Such barriers favour the formation of vortices in supergranular junctions. In particular, we show that the magnetic field distribution in the quiet Sun is determined by the combined action of attracting/repelling LCS and vortices.

scholarly journals Sensitive dependence of trajectories on tracer seeding positions – coherent structures in German Bight surface drift simulations

2020 ◽  
Author(s):  
Ulrich Callies
Keyword(s):  
Coherent Structures ◽  
German Bight ◽  
Sea Surface ◽  
In Situ Monitoring ◽  
Relative Dispersion ◽  
Finite Time Lyapunov Exponent ◽  
Sensitive Dependence ◽  
Behaviour Changes ◽  
Surface Drift

Abstract. Backward drift simulations can aid the interpretation of in situ monitoring data. Some trajectories, however, are sensitive to even small changes of the tracer release position. A corresponding spread of backward simulations implies convergence in the forward passage of time. Such uncertainty about the probed water body's origin complicates the interpretation of measurements. This study examines surface drift simulations in the German Bight (North Sea). Lines across which drift behaviour changes non-smoothly are obtained as ridges in the fields of the finite-time Lyapunov exponent (FTLE), a parameter used in dynamical systems theory to identify Lagrangian coherent structures (LCS). Results are shown to closely resemble those obtained considering a) two-particle relative dispersion and b) the average divergence of Eulerian velocities that tracers experience. Structures observed in simulated sea surface temperature and salinity further corroborate the FTLE results.

Pattern-recognized structures in bounded turbulent shear flows

1977 ◽  
Vol 83 (4) ◽  
pp. 673-693 ◽  
Author(s):  
James M. Wallace ◽  
Robert S. Brodkey ◽  
Helmut Eckelmann
Keyword(s):  
Reynolds Stress ◽  
Coherent Structures ◽  
Shear Flows ◽  
Local Maximum ◽  
Total Sample ◽  
Turbulent Shear ◽  
Turbulence Structures ◽  
Signal Pattern ◽  
Turbulent Shear Flows ◽  
High Reynolds

It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.

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