Finite-time Lyapunov Exponent Fields Research Articles

Chaotic advection in a recirculating flow: Effect of a fluid-flexible-solid interaction.

The present work is on laminar recirculating flow-induced deformation as well as motion of a neutrally buoyant flexible elliptical solid, resulting in Lagrangian chaos in a two-dimensional lid-driven cavity flow. Using a fully Eulerian and monolithic approach-based single-solver for the fluid flow and flexible-solid deformation, a chaotic advection study is presented for various aspect ratios β ( =0.5-1.0) and a constant volume fraction Φ=10% of an elliptical solid at a constant Ericksen number Er=0.05 and Reynolds number Re=100. Our initial analysis reveals maximum chaotic advection at β=0.5 for which a comprehensive nonlinear dynamical analysis is presented. The Poincaré map revealed elliptic islands and chaotic sea in the fluid flow. Three large elliptic islands, apart from certain smaller islands, were identified near the solid. Periodic point analysis revealed the lowest order hyperbolic/elliptic periodic points to be three. Adaptive material tracking gave a physical picture of a deforming material blob revealing its exponential stretch along with steep folds and demonstrated unstable/stable manifolds corresponding to lowest order hyperbolic points. Furthermore, adaptive material tracking demonstrates heteroclinic connections and tangles in the system that confirm the existence of chaos. For the transient as compared to the periodic flow, adaptive material tracking demonstrates a larger exponential increase of the blob's interfacial area. The finite-time Lyapunov exponent field revealed attracting/repelling Lagrangian coherent structures and entrapped fluid zones. Our work demonstrates an immersed deformable solid-based onset of chaotic advection, for the first time in the literature, which is relevant to a wide range of applications.

Lagrangian Coherent Structures and hypoxia in the Baltic Sea

The spatial and temporal variations of Lagrangian Coherent Structures (LCSs) in the Baltic Sea are extracted from finite-time Lyapunov exponent (FTLE) fields. A validated 3-D hydrodynamic model of the Baltic Sea coupled with a water quality model is applied for the years 2000–2009. The novelty of the work is on the variation of LCSs with the sea depth, the state of hypoxia and the possible relationship with the blooming patterns in the Baltic. The study reveals a variety of LCSs with a typical core diameter of 10–40 km and a duration of 2–7 days that are formed offshore in all the basins of the Baltic Sea. They occur throughout the year even during winter times when the sea at the northern basins is partially covered with ice. The LCSs are more abundant in the southern basins where extensive algae blooms occur. The dominant structures are large vortex dipoles and anti-rotating vortex pairs that are not limited to the surface water layer but spread to a depth of 143.5 m. Likely mechanisms for the formation and the spread of LCSs are Kelvin-Helmholtz type instabilities, Proudman-Taylor column and Ekman Spiral. In the vicinity of the shorelines, the LCSs are smaller in diameter scaling with the mean Rossby radius to around 5 km. In the southern basins of the Baltic Sea; the dissolved oxygen (DO) content is permanently below 2 mg/l at depths below 80 m. DO contents vary seasonally with high values during winter and early spring times as opposed to lower values during summer and autumn periods. During late summers, the decline in DO content appears related to the extensive algae blooming consuming oxygen through the decomposition process. The LCSs map the patterns of Algae blooms detected by satellites. The duration of Algae blooming agrees with the persisting time of LCSs as well as the spatial surface water extents. The major 2003 inflow (MBI) increased the seabed DO content only in the lower part of the Arkona Basin that lasted just for about 3 weeks. The inputs of DO from the rivers and the 2003 MBI were not sufficient to counteract the seabed hypoxia in the Baltic Proper for the years 2000–2009.

Lagrangian Coherent Structure Analysis on the Vegetated Compound Channel with Numerical Simulation

Natural channels often consist of a mainstream near their thalwegs and shallow vegetated areas near shores. The compounded and partially vegetated cross-sections play a significantly role in determining the hydrodynamic characteristics of a channel. By employing the Lagrangian Coherent Structure (LCS) analysis, the present work unravels the effect of vegetation and geometry on the hydrodynamic interactions between mainstreams with the various depths and vegetated shallow areas. The LCS method is the concept of dynamical system analyses, which is determined by the finite-time Lyapunov exponents (FTLE) field of fluid particles. It enables to overcome the limitations of using the particle tracking method in cost and time for simulations. Since the LCSs represent material surfaces or asymptotic lines which particles approach, but do not pass through, they match well with the trajectories of particles or materials obtained by solving particle motion equations. Therefore, the temporal and spatial developments of the interfacial layers could be investigated by using the FTLE. As the difference of depth becomes appreciable, the values of FTLE are relatively larger farther from the vegetated area. It implies that the interfacial layer becomes wider with the larger size of vortex produced by the differences of velocities between the mainstreams and the vegetated areas. In other words, as depth differences become large, materials and momentum can be spread from the vegetated area to or collected from a wider area of the mainstream.

Lagrangian analysis of bio-inspired vortex ring formation

Pulsatile jet propulsion is a highly energy-efficient swimming mode used by various species of aquatic animals that continues to inspire engineers of underwater vehicles. Here, we present a bio-inspired jet propulsor that combines the flexible hull of a jellyfish with the compression motion of a scallop to create individual vortex rings for thrust generation. Similar to the biological jetters, our propulsor generates a nonlinear time-varying exit velocity profile and has a finite volume capacity. The formation process of the vortices generated by this jet profile is analysed using time-resolved velocity field measurements. The transient development of the vortex properties is characterised based on the evolution of ridges in the finite-time Lyapunov exponent field and on local extrema in the pressure field derived from the velocity data. Special attention is directed toward the vortex merging observed in the trailing shear layer. During vortex merging, the Lagrangian vortex boundaries first contract in the streamwise direction before expanding in the normal direction to keep the non-dimensional energy at its minimum value, in agreement with the Kelvin–Benjamin variational principle. The circulation, diameter and translational velocity of the vortex increase due to merging. The vortex merging takes place because the velocity of the trailing vortex is higher than the velocity of the main vortex ring prior to merging. The comparison of the temporal evolution of the Lagrangian vortex boundaries and the pressure-based vortex delimiters confirms that features in the pressure field serve as accurate and robust observables for the vortex formation process.

A Lagrangian Approach Towards Quantitative Analysis of Flow-mediated Infection Transmission in Indoor Spaces with Application to SARS-COV-2

The ongoing SARS-CoV-2 (Covid-19) pandemic has ushered an unforeseen level of global health and economic burden. As a respiratory infection, Covid-19 is known to have a dominant airborne transmission modality, wherein fluid flow plays a central role. The quantification of complex non-intuitive dynamics and transport of pathogen laden respiratory particles in indoor flows have been of specific interest. Here we present a Lagrangian computational approach towards the quantification of human-to-human exposure quantifiers and identification of pathways by which flow organises transmission. We develop a Lagrangian viral exposure index in a parametric form, accounting for key parameters such as building and layout, ventilation, occupancy, biological variables. We also employ a Lagrangian computation of the Finite Time Lyapunov Exponent field to identify hidden patterns of transport. A systematic parametric study comprising a set of 120 simulations, yielding a total of 1320 different exposure index computations are presented. Results from these simulations enable: (a) understanding the otherwise hidden ways in which air flow organises the long-range transport of such particles and (b) translating the micro-particle transport data into a quantifier for understanding infection exposure risks.

Fluid Flow Characteristics of Healthy and Calcified Aortic Valves Using Three-Dimensional Lagrangian Coherent Structures Analysis

Aortic valve calcification is an important cardiovascular disorder that deteriorates the accurate functioning of the valve leaflets. The increasing stiffness due to the calcification prevents the complete closure of the valve and therefore leads to significant hemodynamic alterations. Computational fluid dynamics (CFD) modeling enables the investigation of the entire flow domain by processing medical images from aortic valve patients. In this study, we computationally modeled and simulated a 3D aortic valve using patient-specific dimensions of the aortic root and aortic sinus. Leaflet stiffness is deteriorated in aortic valve disease due to calcification. In order to investigate the influence of leaflet calcification on flow dynamics, three different leaflet-stiffness values were considered for healthy, mildly calcified, and severely calcified leaflets. Time-dependent CFD results were used for applying the Lagrangian coherent structures (LCS) technique by performing finite-time Lyapunov exponent (FTLE) computations along with Lagrangian particle residence time (PRT) analysis to identify unique vortex structures at the front and backside of the leaflets. Obtained results indicated that the peak flow velocity at the valve orifice increased with the calcification rate. For the healthy aortic valve, a low-pressure field was observed at the leaflet tips. This low-pressure field gradually expanded through the entire aortic sinus as the calcification level increased. FTLE field plots of the healthy and calcified valves showed a variety of differences in terms of flow structures. When the number of fluid particles in the healthy valve model was taken as reference, 1.59 and 1.74 times more particles accumulated in the mildly and severely calcified valves, respectively, indicating that the calcified valves were not sufficiently opened to allow normal mass flow rates.

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

Abstract. Backward drift simulations can aid the interpretation of in situ monitoring data. In some cases, however, trajectories are very sensitive to even small changes in the tracer release position. A corresponding spread of backward simulations implies attraction in the forward passage of time and, hence, uncertainty about the probed water body's origin. 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 (LCSs). Results closely resemble those obtained considering two-particle relative dispersion. It is argued that simulated FTLE fields might be used in support of the interpretation of monitoring data, indicating when simulations of backward trajectories are unreliable because of their high sensitivity to tracer seeding positions.

Vortex dynamics and transport phenomena in stenotic aortic models using Echo-PIV

Atherosclerosis is the most fatal cardiovascular disease. As disease progresses, stenoses grow inside the arteries blocking their lumen and altering blood flow. Analysing flow dynamics can provide a deeper insight on the stenosis evolution. In this work we combined Eulerian and Lagrangian descriptors to analyze blood flow dynamics and fluid transport in stenotic aortic models with morphology, mechanical and optical properties close to those of real arteries. To this end, vorticity, particle residence time (PRT), particle's final position (FP) and finite time Lyapunov's exponents (FTLE) were computed from the experimental fluid velocity fields acquired using ultrasonic particle imaging velocimetry (Echo-PIV). For the experiments, CT-images were used to create morphological realistic models of the descending aorta with 0%, 35% and 50% occlusion degree with same mechanical properties as real arteries. Each model was connected to a circuit with a pulsatile programmable pump which mimics physiological flow and pressure conditions. The pulsatile frequency was set to ≈0.9 Hz (55 bpm) and the upstream peak Reynolds number (Re) was changed from 1100 to 2000. Flow in the post-stenotic region was composed of two main structures: a high velocity jet over the stenosis throat and a recirculation region behind the stenosis where vortex form and shed. We characterized vortex kinematics showing that vortex propagation velocity increases with Re. Moreover, from the FTLE field we identified Lagrangian coherent structures (i.e. material barriers) that dictate transport behind the stenosis. The size and strength of those barriers increased with Re and the occlusion degree. Finally, from the PRT and FP maps, we showed that independently of Re, the same amount of fluid remains on the stenosis over more than a pulsatile period.

Motion-shape-based deep learning approach for divergence behavior detection in high-density crowd

We propose a novel method of abnormal crowd behavior detection in surveillance videos. Mainly, our work focuses on detecting crowd divergence behavior that can lead to serious disasters like a stampede. We introduce a notion of physically capturing motion in the form of images and classify crowd behavior using a convolution neural network (CNN) trained on motion-shape images (MSIs). First, the optical flow (OPF) is computed, and finite-time Lyapunov exponent (FTLE) field is obtained by integrating OPF. Lagrangian coherent structure (LCS) in the FTLE field represents crowd-dominant motion. A ridge extraction scheme is proposed for the conversion of LCS-to-grayscale MSIs. Lastly, a supervised training approach is utilized with CNN to predict normal or divergence behavior for any unknown image. We test our method on six real-world low- as well as high-density crowd datasets and compare performance with state-of-the-art methods. Experimental results show that our method is not only robust for any type of scene but also outperform existing state-of-the-art methods in terms of accuracy. We also propose a divergence localization method that not only identifies divergence starting (source) points but also comes with a new feature of generating a ‘localization mask’ around the diverging crowd showing the size of divergence. Finally, we also introduce two new datasets containing videos of crowd normal and divergence behaviors at the high density.

Kinetics and prey capture by a paddling jellyfish: three-dimensional simulation and Lagrangian coherent structure analysis

Abstract

Paddling motion of a free-swimming jellyfish and Lagrangian coherent structure analysis

Swimming and prey capture by prolate and oblate jellyfishes are numerically examined in two-dimensions using multi-relaxation-time lattice Boltzmann (MRT-LB) and immersed boundary (IB) methods. The near-field fluid structure interaction (FSI) and predator-prey interaction mechanisms are revealed via the simulated Eulerian flow characteristics, finite-time Lyapunov exponent (FTLE) field, and Lagrangian coherent structures (LCS). We implement appropriate periodic body force (Fb) distribution at nodal points of the elastic bell in radial direction to model the paddled swimming as well as complex feeding behavior. For a paddling jellyfish the evolved starting and stopping vortices, as move close to each other in near-wake, create the necessary vortex induced thrust that facilitate the forward body motion. The forced bell contraction in power stroke assists quicker propulsive swimming, whereas passive bell expansion in resting phase facilitates the continued vortex induced forward movement for larger duration, via the refilled fluid momentum. For feeding the detailed prey interception and precise capture areas for various jellyfish models are identified hereby via the computed prey tracks, forward and backward time FTLE fields, and LCS. Swimming performances are analyzed based on interactive thrust and drag forces, input power (energy rate required for bell contraction), output power (thrust multiplied by centroid velocity), and cost of transport (COT). At low Reynolds number (Re) the COT becomes higher for an oblate jellyfish than that of a prolate one; while with increased Re the oblate species appears more economical. However, for enhanced paddling force (Fb) or reduced flapping frequency of bell, the COT for an oblate jellyfish steadily decreases. Hereby impacts of the varied force duration, flapping amplitude, flapping frequency, and bell-elasticity on the swimming are analyzed in greater detail. Notably, the propulsion efficiency increased for higher flapping frequency. The present numerical model efficiently unfolds prey capture mechanisms that are adopted by prolate and oblate medusae and quantifies their success rate (clearance rate, CR) in prey capture. Unlike in past studies, the FTLE fields and LCS that are computed here by tracking the transient motion of a large number of suspended Lagrangian prey particles exhibit the realistic predator-prey interaction and precise prey capture surface, which are difficult to measure or analyze empirically.

Surface water exchanges in the Luzon Strait as inferred from Lagrangian coherent structures

This study presents a Lagrangian view of upper water exchanges across the Luzon Strait based on the finite-time Lyapunov exponents (FTLE) fields computed from the surface geostrophic current. The Lagrangian coherent structures (LCSs) extracted from the FTLE fields well identify the typical flow patterns and eddy activities around the Luzon Strait. In addition, they reveal the intricate transport paths and fluid domains, which are validated by the tracks of satellite-tracked surface drifters and cannot be visually recognized in the velocity maps. The FTLE fields indicate that there are mainly four types of transport patterns near the Luzon Strait; among them, the Kuroshio northward-flowing “leaping” pattern and the clockwise rotating “looping” pattern occur more frequently than the “leaking” pattern of the direct Kuroshio branch into the SCS and the “outflowing” pattern from the SCS to the Pacific. The eddy shedding events of the Kuroshio at the Luzon Strait are further analyzed, and the importance of considering LCSs in estimating transport by eddies is highlighted. The anticyclonic eddy (ACE) shedding cases reveal that ACEs mainly originate from the looping paths of Kuroshio and thus could effectively trap the Kuroshio water before eddy detachments. LCSs provide useful information to predict the positions of the upstream waters that finally enter the ACEs. In contrast, LCS snapshots indicate that during the formation of cyclonic eddies (CEs), most CEs are not connected with the pathways of Kuroshio water. Hence, the contribution of CEs to the surface water exchanges from the Pacific into the SCS is tiny.

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube* *Project supported by the National Natural Science Foundation of China (Grant Nos. 91441205 and 91941301) and China Postdoctoral Science Foundation (Grant No. 2018M642007).

In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation, a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangian coherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver section at the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transport during the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation number for the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by elliptic LCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSs encompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The other parts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the elliptic LCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. In addition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.

Passive scalar mixing induced by the formation of compressible vortex rings

This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process. Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing. The passive scalar mixing induced by the formation of a canonical compressible vortex ring (CVR) generated at the end of a shock tube is investigated by using numerical simulation. In addition, the method of finite-time Lyapunov exponent (FTLE) field are detected to identify the region of CVR, as well as to analyze the passive scalar mixing during the CVR formation. As the CVR rolls up, the ambient fluid outside the shock tube is entrained into the ring. The entrainment fraction (the mass of entrained fluid to the total mass of CVR) is found to strongly depend on two features of CVRs. One is the compressibility of CVRs, which is characterized by the Mach number of the incident shock denoted by Mach number (Ma). The other is pinch-off of CVRs, which happens at a certain timescale with narrow range of 2–4. As Ma increases, the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility. After CVRs pinch off, trailing vortices appear and show less effective at entrainment than the leading CVRs do. Moreover, the tendency of the rate of entrainment is examined. The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet.

In vitro characterization of Lagrangian fluid transport downstream of a dysfunctional bileaflet mechanical aortic valve

This experimental study aims to explore the Lagrangian nature of fluid transport downstream of a bileaflet mechanical aortic valve under different malfunction scenarios that might be encountered clinically. Time-resolved planar particle image velocimetry measurements are performed to extract instantaneous velocity fields downstream of the bileaflet mechanical valve implanted in an elastic aortic model. The results show an increase in particle residence time with the severity of malfunction. This is attributed to the expansion of the recirculation regions downstream of the valve. The time-evolution of Lagrangian coherent structures over one cardiac cycle (using finite-time Lyapunov exponent fields) shows the effect of valve dysfunction on the material transport and its barriers inside the aorta. The unbalanced flow through the dysfunctional leaflets leads to a significant redistribution of the LCS, thus the fluid transport along the ascending aorta. Moreover, a new technique for the evaluation of the highest accumulated shear stresses is applied along the Lagrangian trajectory of particles being released from the extracted Lagrangian coherent structures where the highest stretching occurs. Finally, the induced non-laminar flow behavior by the valve dysfunction is analyzed using the time-frequency spectra of velocity signals at selected points in the ascending aorta.

Separated Flow Response to Rapid Flap Deflection

The transient response of a massively separated flow over an airfoil to rapid flap actuation is presented. A NACA 0006 airfoil is oriented at a fixed incidence of 20 deg for a Reynolds number of . The experiments are performed in a water tunnel with a wing spanning the width of the test section to produce a nominally two-dimensional flowfield. The airfoil is bisected about the midchord position, resulting in a 50%-chord trailing-edge flap. The flap is rapidly deflected in a smoothed-ramp profile over a range of deflection speeds and amplitudes. The flap maneuver is completed in a fraction of a single convective time. Focus is given to a deflection amplitude of 2 deg to minimize geometric deviation from the nondeflected configuration. The desired response to such a flap motion is the evocation of vortical transients conducive to lift enhancement. Through this study, two distinct transient responses are observed that are directionally dependent on flap actuation. In motions resulting in an increase in airfoil camber, the lift is increased instantaneously to modest values before relaxation to a separated steady state. In effect, this mode expedites convergence to the steady-state value of the final airfoil configuration and is devoid of the “antilift” spike associated with the discrete actuation of conventional fluidic actuators. In motions resulting in a decrease in airfoil camber, the lift profile is characterized by an initial reduction before a surge in lift, culminating in a global peak and followed by relaxation. Both deflection modes prove disruptive to the leading-edge shear-layer dynamics through trailing-edge actuation and are cause for rollup of a leading-edge vortex. Ridges of the finite-time Lyapunov exponent field are used to determine that the net decrease in camber motion induces significant entrainment near the trailing edge, leading to a smaller recirculation region and reattachment of the flow above the suction surface trailing-edge region. The net increase in camber motion does not generate this entrainment, and therefore yields a significantly larger recirculation region.

Uncertainty in finite-time Lyapunov exponent computations

The Finite-Time Lyapunov Exponent (FTLE) is a well-established numerical tool for assessing stretching rates of initial parcels of fluid, which are advected according to a given time-varying velocity field (which is often available only as data). When viewed as a field over initial conditions, the FTLE's spatial structure is often used to infer the nonhomogeneous transport. Given the measurement and resolution errors inevitably present in the unsteady velocity data, the computed FTLE field should in reality be treated only as an approximation. A method which, for the first time, is able for attribute spatially-varying errors to the FTLE field is developed. The formulation is, however, confined to two-dimensional flows. Knowledge of the errors prevent reaching erroneous conclusions based only on the FTLE field. Moreover, it is established that increasing the spatial resolution does not improve the accuracy of the FTLE field in the presence of velocity uncertainties, and indeed has the opposite effect. Stochastic simulations are used to validate and exemplify these results, and demonstrate the computability of the error field.

Topological analysis of particle transport in lung airways: Predicting particle source and destination

Particle transport in lung airways can induce respiratory disease and play a vital role in aerosol drug delivery. Herein, we present dynamical systems features that influence airflow and particle transport in the tracheobronchial trees. Computational fluid dynamics (CFD) was used to solve for unsteady airflow in a patient-specific model. Particle tracking simulations were performed for micron-size particles. The destination map that connects the particle final location to the initial location and injection time was constructed. Finite-time Lyapunov exponent (FTLE) fields were calculated to identify inertial Lagrangian coherent structures (ILCS), topological features that act as separatrices. Our results demonstrated that these topological features control the destination map at the trachea. The temporal evolution of ILCS influenced the sensitivity of particle transport fate to injection time, whereas the emergence of new ILCS with an increased integration time controlled transport to different generations of airways. Additionally, particles starting at the ILCS were shown to mostly deposit at the airway walls. Finally, an innovative source inversion strategy was introduced to integrate the Maxey–Riley equation backward in time and identify the origin of dispersed particles. Our study explores novel dynamical systems tools that improve our understanding of particle transport and deposition in the airways and could be used to guide future targeted drug delivery studies.

Evaluating the Effect of the Number of Wire of Flow Diverter Stents on the Nonstagnated Region Formation in an Aneurysm Sac Using Lagrangian Coherent Structure and Hyperbolic Time Analysis

Giant aneurysms at carotid arteries are typically treated with flow diverter (FD) stents in the clinic. Although the goal of an FD stent is to direct most of the blood flow into the main artery, not much is known regarding the effects of wire number an FD possesses on the hemodynamics inside the aneurysm. In this study, 48-, 72-, and 96-wire FD stents were separately implanted into the site of aneurysm of a 45-year-old woman to evaluate the effects of the FD's number of wires on fluid flow behavior in the aneurysm sac. Time evolution of both finite-time Lyapunov exponent (FTLE) and hyperbolic time fields in the aneurysm sac were calculated by using computational fluid dynamics along with Lagrangian coherent structure (LCS) methods. The computations reveal that a 48-wire FD stent allows a large amount of blood to enter inside the aneurysm sac revealing scattered nonstagnant flow zones formation. Besides, time-dependent results of LCS analysis show that most of the blood flow is diverted into the main artery when 72- and 96-wire number Surpass brand FD stents are separately implanted into the site of the aneurysm, yielding a small amount of blood flow to penetrate into the aneurysm sac. Furthermore, FTLE and hyperbolic time field plots are in good agreement with the patient's digital subtraction angiography image captured 3.5 minutes after 72-wire Surpass brand FD stent implantation.

Thermal fronts and attracting Lagrangian Coherent Structures in the north Bay of Bengal during December 2015–March 2016

We investigate two-dimensional advective stirring by satellite-derived ocean surface currents in the north Bay of Bengal during December 2015–March 2016 using the framework of Lagrangian Coherent Structures (LCS). The forward and backward finite-time Lyapunov exponent (fFTLE and bFTLE, respectively) fields indicate that freshwater parcels from the river run-off are subjected to intense stirring by the ocean surface currents, which contain both geostrophic and wind-forced Ekman currents. Large-scale thermal fronts present in the satellite-based sea surface temperature (SST) fields are then shown to closely resemble attracting LCS (aLCS) that govern horizontal advective stirring on subseasonal time scales. Statistical estimates of the angle between the thermal fronts (of all spatial scales present in the SST data) and the aLCS from the entire north Bay of Bengal show a preference to align with each other. Significantly, in the presence of sufficiently strong aLCS in their neighbourhood, thermal fronts are shown to have a strong preference to align with them. Finite-time advection of fluid particles over around a week to compute the bFTLE fields results in the strongest alignment between the thermal fronts and neighbouring aLCS. The robustness of our results are established by presenting analyses of (i) geostrophic currents from altimeter data, and (ii) a reanalysis-based fine-scale salinity field. Attracting LCS, identified as sufficiently strong ridges in the bFTLE fields, are argued to represent reasonable estimates of the location and orientation of fronts (thermal or salinity) formed by advective stirring over subseasonal time scales.