Finite-time Lyapunov Exponent Fields Research Articles

Lagrangian coherent structures and mass transport in T-junctions

The mechanisms of air water two-phase flow and phase distribution in T-junctions are studied using Lagrangian methods such as the Lagrangian Coherent Structure (LCS) and the particle tracking method. First, the air water two-phase flow field in the T-junctions is numerically simulated. In particular, characteristics such as phase distribution, pressure distribution, and streamline diagrams in mixing and separating regions are captured. Then, the ridges in finite-time Lyapunov exponent fields are extracted as LCSs. The mass transport process is discussed through contrasting the phase distribution and the LCSs. In the mixing region, the air water interfaces almost coincide with the attracting LCSs. At the same time, the attracting LCSs can demonstrate the evolution process of the vortices, which is crucial for the mixing of phases. In the separating region, employing the particle tracking method reveals that particles are entrained by the most attractive LCSs, while repelling LCSs demarcate regions with distinct flow directions, thereby playing a pivotal role in phase separation. In summary, we investigated mass transport in air water two-phase flow in T-junctions from the perspective of LCSs.

Applications of Finite-Time Lyapunov Exponent in detecting Lagrangian Coherent Structures for coastal ocean processes: a review

Addressing the threats of climate change, pollution, and overfishing to marine ecosystems necessitates a deeper understanding of coastal and oceanic fluid dynamics. Within this context, Lagrangian Coherent Structures (LCS) emerge as essential tools for elucidating the complexities of marine fluid dynamics. Methods used to detect LCS include geometric, probabilistic, cluster-based and braid-based approaches. Advancements have been made to employ Finite-time Lyapunov Exponents (FTLE) to detect LCS due to its high efficacy, reliability and simplicity. It has been proven that the FTLE approach has provided invaluable insights into complex oceanic phenomena like shear, confluence, eddy formations, and oceanic fronts, which also enhanced the understanding of tidal-/wind-driven processes. Additionally, FTLE-based LCS were crucial in identifying barriers to contaminant dispersion and assessing pollutant distribution, aiding environmental protection and marine pollution management. FTLE-based LCS has also contributed significantly to understanding ecological interactions and biodiversity in response to environmental issues. This review identifies pressing challenges and future directions of FTLE-based LCS. Among these are the influences of external factors such as river discharges, ice formations, and human activities on ocean currents, which complicate the analysis of ocean fluid dynamics. While 2D FTLE methods have proven effective, their limitations in capturing the full scope of oceanic phenomena, especially in 3D environments, are evident. The advent of 3D LCS analysis has marked progress, yet computational demands and data quality requirements pose significant hurdles. Moreover, LCS extracted from FTLE fields involves establishing an empirical threshold that introduces considerable variability due to human judgement. Future efforts should focus on enhancing computational techniques for 3D analyses, integrating FTLE and LCS into broader environmental models, and leveraging machine learning to standardize LCS detection.

Reynolds number effect of a vortex ring impinging on a concave hemi-cylindrical shell

Experimental investigations were conducted on a single vortex ring impinging on a concave hemi-cylindrical shell with Dm/De = 2 at different Reynolds numbers. Vortex rings with five different Reynolds numbers were generated for experimental studies, i.e., Re = 750, 1500, 3000, 5000, and 7000. The planar laser-induced fluorescence visualizations and two-dimensional particle image velocimetry measurements were used in the experiment. The vorticity field based on the Eulerian framework and the finite-time Lyapunov exponent (FTLE) field based on the Lagrangian framework were used to identify the dynamic processes of vortex rings, respectively. The results show that as the vortex rings impinge on concave surfaces from Re = 750 to Re = 7000, the extension of the main vortex ring in the straight-edged direction is larger than that in the concave direction, and the instability of the vortex ring is promoted. While the Reynolds number is increasing, the vortex ring deformation becomes larger, and the overall vortex ring cross section becomes smaller, leading to a larger attenuation of the vortex ring rotation. Calculations performed by the FTLE field were used to derive the Lagrangian coherent structure to analyze the boundaries of the vortex ring motion process, clearly observe the shape of the secondary vortex connecting segments, and verify the speculation by the vortex ring trajectory identification results. Finally, a dynamic model of vortex rings impinging a concave surface was proposed, and the inference of the experimental process was explained by the model.

Control effect on the divergent and convergent riblets in particle-laden turbulent boundary layer

Particle image velocimetry was employed to investigate the impact of convergent–divergent riblets on turbulent boundary layers in both clear water and liquid–solid two-phase flow fields containing 155 μm polystyrene particles. The turbulence statistics such as turbulence intensity and Reynolds stress were investigated. The spatial topology of spanwise vortex head and the development and evolution process of hairpin vortices were explored from Euler and Lagrange perspectives, respectively. Additionally, the particle distribution, concentration, and dispersion within the turbulent boundary layer were statistically analyzed. The results indicated that the boundary layer thickness, friction resistance, integrated turbulence intensity, and Reynolds stress were significantly lower on divergent riblet walls compared to convergent riblet walls. Notably, divergent riblets with a yaw angle of 30° exhibited the best drag reduction effect in both single-phase and two-phase flow fields. The addition of particles resulted in an increase in boundary layer thickness but effectively reduced turbulent fluctuations in the logarithmic region, enhancing drag reduction. This extended the drag reduction range of divergent riblets to a yaw angle of 45°, increasing the maximum drag reduction rate to 26.18%. Through spatial multi-scale local average structure function and finite-time Lyapunov exponent field analysis, it was found that the 30° divergent riblet wall significantly inhibited the development of vortex structures and reduced momentum exchange within the boundary layer. Conversely, the 30° convergent riblet wall had the opposite effect, while the particle phase inhibited the development of all wall turbulent structures. Analysis of particle concentration variations within different regions of the turbulent boundary layer revealed that as the normal height of the boundary layer increased, particle concentration gradually increased, and particle dispersion decreased accordingly. The analysis further showed that particle dispersion was mainly influenced by flow structures, whereas concentration was significantly affected by turbulence intensity. These findings elucidate the effect of the flow field on the particle phase and provide insights into the interaction mechanism between the flow field and particles.

Spatial super-resolution of finite-time Lyapunov exponent fields with generative adversarial networks

In this article, two generative adversarial networks that enhance the spatial resolution of two- and three-dimensional finite-time Lyapunov fields by a factor of 4 in each dimension are presented. Using these models, high-resolution distributions can be approximated based on low-resolution input, the latter of which is associated with a computational cost and storage reduced by factors of about 42 and 43, respectively. Evaluating various test cases, the performance and generalizability of this approach are assessed. Shortcomings are only observed in the case of high-frequency spatial fluctuations where no sufficient statistical information is available in the low-resolution space. The major flow structures, however, are adequately rendered, giving rise to Lagrangian analyses of complex flow configurations that may otherwise remain elusive due to an excessive computational cost.

Deep Hierarchical Super Resolution for Scientific Data.

We present a novel technique for hierarchical super resolution (SR) with neural networks (NNs), which upscales volumetric data represented with an octree data structure to a high-resolution uniform grid with minimal seam artifacts on octree node boundaries. Our method uses existing state-of-the-art SR models and adds flexibility to upscale input data with varying levels of detail across the domain, instead of only uniform grid data that are supported in previous approaches. The key is to use a hierarchy of SR NNs, each trained to perform 2× SR between two levels of detail, with a hierarchical SR algorithm that minimizes seam artifacts by starting from the coarsest level of detail and working up. We show that our hierarchical approach outperforms baseline interpolation and hierarchical upscaling methods, and demonstrate the usefulness of our proposed approach across three use cases including data reduction using hierarchical downsampling+SR instead of uniform downsampling+SR, computation savings for hierarchical finite-time Lyapunov exponent field calculation, and super-resolving low-resolution simulation results for a high-resolution approximation visualization.

Understanding surgical smoke in laparoscopy through Lagrangian Coherent Structures.

In laparoscopic surgery, one of the main byproducts is the gaseous particles, called surgical smoke, which is found hazardous for both the patient and the operating room staff due to their chemical composition, and this implies a need for its effective elimination. The dynamics of surgical smoke are monitored by the underlying flow inside the abdomen and the hidden Lagrangian Coherent Structures (LCSs) present therein. In this article, for an insufflated abdomen domain, we analyse the velocity field, obtained from a computational fluid dynamics model, first, by calculating the flow rates for the outlets and then by identifying the patterns which are responsible for the transportation, mixing and accumulation of the material particles in the flow. From the finite time Lyapunov exponent (FTLE) field calculated for different cross-sections of the domain, we show that these material curves are dependent on the angle, positions and number of the outlets, and the inlet. The ridges of the backward FTLE field reveal the regions of vortex formation, and the maximum accumulation, details which can inform the effective placement of the instruments for efficient removal of the surgical smoke.

Investigation of Lagrangian Areas of Minimal Stretching (LAMS) in a turbulent boundary layer

In this paper the three-dimensional finite-time Lyapunov exponent (FTLE) field of a direct numerical simulation of a flat-plate turbulent boundary layer is analysed in several wall-parallel sections. The data consider a case at a low subsonic Mach number with a moderate positive pressure gradient in the streamwise direction. In contrast to other studies mainly focusing on the maxima of the FTLE field, particular emphasis is placed on the regions of minimal stretching between the vortices and shear layers of the three-dimensional turbulent flow field. These visually appear as contiguous islands or ‘valleys’ between the ‘ridges’ of the FTLE maxima, both at forward and backward integration of the flow field in time. To clearly distinguish the structures investigated from their more common counterparts (e.g. Lagrangian coherent structures, LCS), the acronym LAMS (Lagrangian areas of minimal stretching) is proposed to denote the associated cohesive fluid regions. Consistent with intuition, the largest LAMS occur near the boundary-layer edge, where large regions of homogeneous laminar external flow coexist with upwelling turbulent structures. Compensating for turbulent regions pushing upward, they sink from there down toward the wall, becoming smaller and longer. This process is associated with an increased relative velocity of the LAMS compared with the mean flow, which is observed over the whole boundary layer in the range $y^+ \gtrsim 10$ . Furthermore, it is observed that the Q4 (sweep) events contained in the LAMS clearly dominate over Q2 (ejection) events above $y^+ \approx 10$ . Thereby, local maxima occur at $y^+ \approx 20$ and near the boundary-layer edge. Below $y^+ \approx 10$ , the relationship reverses. Sweeping LAMS from above $y^+ \approx 10$ and ejecting LAMS from below meet in the layer where the maximal vortical activity occurs. The latter is caused by mostly streamwise oriented vortices with maximal vortex stretching in the streamwise direction. Overall, LAMS are associated with cohesive fluid regions between the surrounding vortices and shear layers that both drop down from the boundary-layer edge toward the wall in the outer region of the boundary layer and lift from the wall in the near-wall region.

Extraction of Lagrangian Coherent Structures in the framework of the Lagrangian–Eulerian Stabilized Collocation Method (LESCM)

In recent years, the investigations on Lagrangian Coherent Structures (LCS) in complex flows have attracted increasing attention due to their ability to accurately describe flow field details. In this study, we propose a novel and accurate numerical technique based on the Lagrangian–Eulerian Stabilized Collocation Method (LESCM) for computing the Finite Time Lyapunov Exponents (FTLEs), which is essential for extracting LCSs in viscous incompressible flows. LESCM, previously employed for simulating fluid–structure interaction problems, was developed based on the Material Point Method (MPM). The hybrid Lagrangian–Eulerian​ description in LESCM enables explicit tracking of fluid flow trajectories throughout the simulation and direct evaluation of the FTLE field. Furthermore. The errors in FTLEs caused by the Particle Shifting Technique (PST) are completely avoided due to the Eulerian characteristic of LESCM as the deformation gradient is calculated based on fixed Eulerian nodes rather than fluid particles with unphysical shifting. Consequently, the novel technique based on LESCM surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex LCSs in flow fields. Additionally, By harnessing the remarkable efficiency of LESCM, MATLAB can now handle up to 16 million particles with ease, eliminating the need for parallel computation techniques. Several numerical examples, such as 2D Taylor-Green​ vortices, flow passing a circular cylinder and a 3-dimensional shear driven cavity problem, have been tested to demonstrate the effectiveness of this novel approach under various conditions.

Characterization of a synthetic jet vortex ring flowing through honeycomb

The investigation of synthetic jet vortex rings flowing through a honeycomb is measured by two-dimensional particle-image velocimetry. The vortex is established using free synthetic jets generated by a piston–cylinder apparatus upstream of the honeycomb. On that basis, turbulence is obtained at circulation Reynolds numbers of ReΓ = 3437, 5155, 6874, and 8592, and Reynolds numbers of the synthetic jets of Resj = 561, 841, 1121, and 1402. The effects of the diameter Reynolds number (ReM = 41–449) and the length-to-cell ratio of the honeycomb (Φ = 4.2–12.5) on the characterization of flow are discussed in detail. A combinatorial similarity parameter that can characterize the effect of passive control on flow fields using a honeycomb is proposed and validated. The combinatorial similarity parameter, ReM/Φ, is determined through dimensional analysis and according to the change in momentum flux loss; its predictive capability is verified quantitatively based on the change in loss of kinetic energy and vortex-ring circulation. The evolutions of phase-averaged vorticity fields and finite-time Lyapunov exponents fields are nearly consistent using the close combinatorial similarity parameters. Furthermore, as indicated by the results, ReM/Φ responds to the combined effect of the relative magnitude of flow inertial and viscous forces, and the shape resistance of the honeycomb geometry to the flow-field–honeycomb interactions. Understanding the characterization of a vortex ring flowing through honeycomb is important for the accuracy of the prediction of turbulence models and the selection of the honeycomb size.

Neural Monte Carlo rendering of finite-time Lyapunov exponent fields

The finite-time Lyapunov exponent (FTLE) is widely used for understanding the Lagrangian behavior of unsteady flow fields. The FTLE field contains many important fine-level structures (e.g., Lagrangian coherent structures). These structures are often thin in depth, requiring Monte Carlo rendering for unbiased visualization. However, Monte Carlo rendering requires hundreds of billions of samples for a high-resolution FTLE visualization, which may cost up to hundreds of hours for rendering a single frame on a multi-core CPU. In this paper, we propose a neural representation of the flow map and FTLE field to reduce the cost of expensive FTLE computation. We demonstrate that a simple multi-layer perceptron (MLP)-based network can accelerate the FTLE computation by up to hundreds of times, and speed up the rendering by tens of times, while producing satisfactory rendering results. We also study the impact of the network size, the amount of training, and the predicted property, which may serve as guidance for selecting appropriate network structures.

Lagrangian mixing of pulsatile flows in constricted tubes

Several Lagrangian methods were used to analyze the mixing processes in an experimental model of a constricted artery under a pulsatile flow. Upstream Reynolds number Re was changed between 1187 and 1999, while the pulsatile period T was fixed at 0.96 s. Velocity fields were acquired using Digital Particle Image Velocimetry for a region of interest (ROI) located downstream of the constriction. The flow is composed of a central jet and a recirculation region near the wall where the vortex forms and sheds. To study the mixing processes, finite-time Lyapunov exponents (FTLE) fields and concentration maps were computed. Two Lagrangian coherent structures (LCS) responsible for mixing fluid were found from FTLE ridges. A first LCS delimits the trailing edge of the vortex, separating the flow that enters the ROI between successive periods. A second LCS delimits the leading edge of the vortex. This LCS concentrates the highest particle agglomeration, as verified by the concentration maps. Moreover, from particle residence time maps, the probability of a fluid particle leaving the ROI before one cycle was measured. As Re increases, the probability of leaving the ROI increases from 0.6 to 0.95. Final position maps rf were introduced to evaluate the flow mixing between different subregions of the ROI. These maps allowed us to compute an exchange index between subregions, EI¯, which shows the main region responsible for the mixing increase with Re. Finally, by integrating the results of the different Lagrangian methods, a comprehensive description of the mixing and transport of the flow was provided.

Efficient Sensor Location for HVAC Systems Using Lagrangian Coherent Structures

Study of thermo‐fluid flow has its significance in energy analysis of a building. Various thermo‐fluid analyses are performed in heating ventilation and air conditioning (HVAC) systems for energy efficient buildings by scientists and engineers to save energy consumption during the life of a building. In order to achieve energy conservation for different HVAC systems, determination of air flow pattern and flow physics are vital parameters. In case of fluid flow postprocessing techniques such as streamlines, vector plots and contours are often employed. These techniques help in understanding the nature of flow and its properties. Each of these postprocessing techniques mentioned are based on Eulerian methods and have certain inherent deficiencies pertaining to the amount of information they can convey about certain aspects of fluid flow. Lagrangian coherent structures (LCS) on the other hand use Lagrangian data for analysis purposes. LCS are generated using finite time Lyapunov exponent fields which in turn depict the rate of expansion or contraction of the trajectories around a certain point. LCS act as the transport barriers across which there is approximately zero mass flux. This property means that LCS can be applied to problems related to separation and reattachment in fluid flow and find virtual boundaries inside flows. In the current study, we focused on the application of LCS for efficient placement of sensors for HVAC systems. We computed LCS using velocity data extracted from the CFD simulations of a 2D room model. Thus, LCS can be used to identify the virtual boundaries in fluid flow. This helps in indication of regions where mixing of particles occurs and also where particles are stagnated. Inlet angles of 0, 15, 22, and 30 degrees are used and analysis shows that manifolds with 30 degree angles provide better ventilation. The outcome of this study can be used to improve the energy efficiency as well as predict the accurate location of HVAC sensor and control units.

Experimental investigation of the dynamic characteristics of the flow generated by a sliding dielectric barrier discharge in the flat plate boundary layer flow

The sliding dielectric barrier discharge (SL-DBD) has attracted attention due to its ability to suppress flow separation. This paper investigated the effect of SL-DBD on the flow field in the flat plate boundary layer by time-resolved particle image velocimetry. We obtained the finite-time Lyapunov exponent field and the Lagrangian coherent structures of the flow field through the velocity field. The results show the effect of SL-DBD has spatial differences, and SL-DBD will produce a “strong–weak–strong” spatial effect on the flow field. The directionality of the flow structure induced by SL-DBD is the main reason for the difference. SL-DBD will induce a large number of vortex structures in the local downstream area of the electrode. The vortex structure enhances the mixing and squeezing effects between the upper and lower flow fields. The upper flow field moves the lower flow field downward by about 0.1 mm through the squeezing effect. In addition, at the downstream region adjacent to the electrode, the oblique momentum injection of the SL-DBD is the dominant effect. At one electrode distance from the electrode, the SL-DBD induces a large number of vortex structures. However, when the distance from the electrode is twice the electrode spacing, the number of vortex structures decreases, and the structure becomes larger. The results show spatial differences in the perturbation of the flow field by SL-DBD, which cannot be ignored when SL-DBD is used to suppress flow separation.

Lagrangian analysis of the flow induced by a dielectric barrier discharge plasma actuator array under burst mode actuation

The dynamic properties of the flow induced by a dielectric barrier discharge (DBD) plasma actuator array are investigated from the Lagrangian perspective. First, numerical simulations based on a body force model are performed to obtain the flow field induced by unsteady plasma actuation in the burst mode. The numerical simulations capture the flow characteristics of plasma actuation well. Subsequently, the ridges of the finite-time Lyapunov exponent field are employed to identify the Lagrangian coherent structures (LCSs). Both the attracting and repelling LCSs organize the plasma-induced flow’s dynamic behaviors. The attracting LCSs visualize the plasma-induced vortices. The vortex formation, development, and merging processes in the unsteady plasma actuation are resolved well by the LCSs. The material transport in the plasma-induced flow is analyzed by tracing the fluid particle motions. Then, the influences of the actuation parameters, duty cycle, and burst frequency on the flow structures are explored via the attracting LCSs. The presented results enhance the understanding of plasma actuation flow physics and promote the optimal use of DBD plasma actuator arrays.

Heat transfer enhancement by a pair of asymmetric flexible vortex generators and thermal performance prediction using machine learning algorithms

• Heat transfer enhancement system including two flexible vortex generators is analyzed by using an immersed boundary method. • Effects of the inclination angle, bending rigidity, and the gap distance on the thermal performance are analyzed in detail. • The thermal performance of the present heat transfer system is enhanced up to 122% as compared to baseline flow without flexible vortex generators. Heat transfer should be considered in the design process of various industrial fields such as electric-electronics, plants and refrigeration and air conditioning, etc. Many researchers have introduced vortex generators to promote mixing of fluids, thereby improving heat transfer performance. Convective heat transfer can be enhanced by using vortex generators where, however, the disadvantage of increased mechanical loss due to increased pressure drop is not avoidable. In order to compensate for the penalty, the present study utilizes the characteristics of self-sustained flapping motions of the flexible vortex generator to improve heat transfer without much increasing the pressure drop. The two flexible vortex generators (FVGs) fixed on the upper and lower channel walls, respectively, are introduced in the present study and they take the form of asymmetric configurations by adjusting the inclination angles. The heat transfer performance is observed to depend on the parametric conditions of FVGs such as the inclination angle, bending rigidity, and the gap distance between them. The present system including the asymmetric FVGs shows the improvement of thermal performance by 122% as compared to the baseline flow when the bending rigidity is 0.06, the initial inclination angle is 75°, and the gap distance is 2.4 times the length of FVGs. The attracting Lagrangian coherent structures (LCS) are visualized by calculating the finite-time Lyapunov exponent (FTLE) field to analyze the effects of the vortex structures near the heated channel walls on the fluid mixing. The net energy loss and average heat transfer are predicted by the three machine learning algorithms, i.e ., artificial neural network (ANN), support vector regression (SVR), and random forest (RF), where the inclination angle, bending rigidity, and gap distance of FVGs are selected as input data. The SVR and ANN algorithms show the best performance in predicting the mean energy loss and the heat transfer, respectively, with the R 2 value of above 0.99 and 0.95.

Lagrangian Identification of Coherent Structures and Mass Transport in a Buoyant Jet Diffusion Flame

ABSTRACT Using Lagrangian coherent structures (LCSs), the mass transport process of large-scale coherent structures in a buoyant jet diffusion flame is studied numerically to gain a key understanding of combustion instability. First, the reacting flow fields of the jet diffusion flame are numerically simulated for two cases, a stable case without considering the buoyancy effect and an unstable case that includes the buoyancy effect corresponding to combustion instability. In particular, large-scale Kelvin-Helmholtz instability (KHI) vortex structures outside the flame surface are captured in the unstable case. Then, the ridges in finite-time Lyapunov exponent (FTLE) fields that sketch the distinct regions in the reacting flow field are extracted as LCSs. The mass transport process is studied by comparing the distribution of LCSs with reaction fields. The flame surface is found to coincide with the attracting LCSs, which separate the fuel and air on opposite sides of the flame surface. In contrast, the reaction products, including species and reaction heat, are confined in the boundaries consisting of repelling LCSs on the inner and outer sides of the flame surface. Finally, the evolution of LCSs is tracked to analyze the generation of KHI vortices and species transport in the jet diffusion flame. With the aid of LCSs, it is found that there exist some saddle-type flow features separating the distinct flow structures into several regions, and the jet fuel and airflow enter into the separated regions from different open boundaries. Importantly, the attracting LCSs in the separated regions then bulge outwards, forming KHI vortices as the attracting LCSs further stretch and fold. Furthermore, the vortices continue moving upwards while species flow from repelling LCSs to attracting LCSs, leading to mixing. These results show that attracting and repelling LCSs can act as the flame surface and the mass and energy transport boundary of the reaction products, respectively. In summary, the work presented can provide a new method in combustion controlling to estimate the location of the flame surface and the transport boundaries of species from the velocity field, by using LCSs.

Applying finite-time lyapunov exponent to study the tidal dispersion on oil spill trajectory in Burrard Inlet

This study used a combination of Finite-Time Lyapunov Exponent (FTLE) values, residual currents, and tidal excursion lengths to systematically investigate the effects of tidal dispersion on oil spill trajectories in Burrard Inlet, BC, Canada, which is a tidally dominated estuary. The FTLE analysis results showed that tidal type and tidal phase significantly influenced the FTLE fields because the flow structure and the location of saddle points varied as a function of the tidal type and tidal phase. Some transport barriers formed in the Inner Harbour, which blocked the water exchange between the western and eastern parts of the inlet. Moreover, tidal mixing in the wider regions of Burrard Inlet (i.e., the western Outer Harbour) was relatively weak than in the narrower areas (i.e., First Narrows and Second Narrows). The observations from the FTLE analysis agreed well with the residual currents and tidal excursion results. The drifter trajectories were consistent with the Lagrangian coherent structure lines extracted from the FTLE analysis. To verify the tidal dispersion impact on an oil spill trajectory in the inlet, the FTLE fields were compared with a real oil spill that occurred in Burrard Inlet in 2015 (the M/V Marathassa oil spill). The FTLE fields reasonably explained the spilled oil’s trajectories from the real event. In addition, a set of stochastic oil spill models were run in this study and found that the FTLE analysis was a reliable tool for oil spill tracking. Overall, the FTLE method would be a valuable addition to practical oil spill response planning.

Computation of Lagrangian coherent structures from experimental fluid trajectory measurements in a mechanically agitated vessel

• Lagrangian coherent structures are computed from 3D particle tracking measurements. • LCSs characterise the hidden complex topology of turbulent flow in a stirred vessel. • Results show that LCSs are related to mixer configuration and macroscale mixing. In mechanically agitated vessels, bulk flow circulation which plays a leading role in macroscale mixing is controlled by hidden Lagrangian coherent structures (LCSs). We use a numerical finite-time Lyapunov exponent (FTLE) approach, for the first time, to resolve such LCSs. Experimental 3D Lagrangian trajectories obtained from a unique positron emission particle tracking (PEPT) technique are used to drive the FTLE model. By computing forward and backward FTLE fields and extracting repelling and attracting FTLE ridges in various azimuthal planes of the flow, a highly complex flow topology is unravelled which varies significantly with azimuthal position. We demonstrate how LCSs organise and quantify the chaotic behaviour of fluid particle paths that underpin mixing through the exchange of fluid between zones of different kinematics. This new Lagrangian approach driven by unique PEPT data is able to unfold some of the complexities of turbulent flow that are beyond the capability of traditional methods.

On the Lagrangian dynamics of saliva particles during normal mouth breathing

The flow and saliva particulate transport dynamics during normal human breathing through the mouth are simulated numerically using an Eulerian large-eddy simulation (LES) approach for the flow coupled with a Lagrangian approach for the transport of saliva particles. The coupled Eulerian–Lagrangian (EL) simulation results reveal new striking insights into the rich dynamics of the Lagrangian coherent structures (LCS) that arise from saliva particles during normal breathing. Specifically, they uncover a new time-periodic mechanism via which particles are introduced into the flow as individual breathing pulses and accumulate to form a slowly propagating vortex front that persists long distances away from the source. The simulated LCS reveal a wealth of recurrent material motion through which the biosols propagate forward while their cloud expands laterally with a slowly evolving vortex front. Also, the finite-time Lyapunov exponent (FTLE) field of human breathing was calculated using the flow map from the LES velocity field. The ridges of the calculated FTLE field revealed distinct hyperbolic LCS, which closely resemble trajectories of saliva particles obtained from the coupled EL simulation. Finally, simulation results for normal breathing with a non-medical face mask show that the mask can effectively disrupt the formation of coherent particle surfaces and, thus, effectively limit saliva particle propagation.