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.

Impact of typhoon Lekima(2019)on material transport in Laizhou Bay using Lagrangian coherent structures

Typhoon has an impact on an estuary and coastal environment.However,the present research lacks the detailed description of material transport processes during typhoon passage,such as the transport channels and barriers in the course of material transport and material accumulation area,etc.Therefore,Lagrangian coherent structures(a method developed for describing the transport structure of fluids in recent years)was introduced to investigate and predict the floating material and debris transport process in the Laizhou Bay,Bohai Sea,during typhoon Lekima in 2019.Results show that the Lagrangian coherent structure could well explain the complex flow phenomena in the bay.During the typhoon,the general direction of floating material transport in the Laizhou Bay was anticlockwise.There was a channel for material transport in the northwest and south of the bay,and there are transportation obstacles in the northeast-southwest direction in the middle of the bay.Therefore,the typhoon might worsen the water quality.These results provide references for precise countermeasures to control the formulation of pollution in the Laizhou Bay.

Lagrangian coherent structures analysis of gas-liquid flow in a bubble column

The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water. In the numerical simulations, the standard k-c turbulence model is employed to de- scribe the turbulence phenomenon occurring in the continuous fluid. The Finite-Time Lyapunov Exponent （FTLE） and Lagrangian Coherent Structures （LCS） are applied to analyze the vortex structures in multiphase flow. Reasonable agreements are obtained between the numerical and experimental data. The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages. During the initial stage, the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically. During the periodical developing stage, the bub- ble hose starts to oscillate periodically, and the vortexes move along the bubble hose to the bottom of column alternately. Compared to the Euler-system-based identification criterion of a vortex, the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles. During the initial stage, the interfaces between the forward and backward flows are highlighted by the LCS. As for the periodical developing stage, the LCS curls near the vortex centers, providing a method of analyzing a flow field from a dynamical system perspec- tive.

Lagrangian coherent structures and their heat-transport mechanism in the turbulent Rayleigh-Bénard convection

In this paper,we investigate the Lagrangian coherent structures(LCSs)and their heat-transport mechanism in turbulent Rayleigh-Bénard(RB)convection.Direct numerical simulations(DNS)are performed in a closed square cell with Rayleigh numbers(Ra)ranging from 10^(6) to 10^(9) and Prandtl(Pr)number fixed at Pr=0.7.First,our results show the power-law relationship between Nusselt number(Nu)and Ra,Nu=0.99Ra^(0.30±0.02),confirming the results from previous studies.To gain insights into the material transport,LCSs are extracted using the finite-time Lyapunov exponent(FTLE)method.Interestingly,lobe structures are widely present,and we elucidate their role in transporting heat from the corner rolls to large-scale circulation.Next,the relationships between LCSs and thermal plumes are examined,and we identify two behaviors of thermal plumes:first,most plumes transport along the LCSs;second,few plumes are exposed to the bulk and subsequently mix with the turbulent background.Furthermore,we quantify the heat flux along the LCSs,which contributes to about 85%of the total flux regardless of Ra.This suggests that LCSs play a significant role in heat transport.Finally,the viscous(thermal)dissipation rate along the LCSs is quantified,which is larger than 80%(60%)of the total value,suggesting that LCSs are responsible for the large viscous and thermal dissipations.

Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition,they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution.The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube

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 Lagrangiancoherent 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 sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.

Lagrangian eddies in the Northwestern Pacifi c Ocean

The Lagrangian eddies in the western Pacifi c Ocean are identifi ed and analysed based on Maps of Sea Level Anomaly(MSLA)data from 1998 to 2018.By calculating the Lagrangian eddy advected by the AVISO velocity fi eld,we analyzed the variations in Lagrangian eddies and the average transport eff ects on diff erent time scales.By introducing the Niño coeffi cient,the lag response of the Lagrangian eddy to El Niño is found.These data are helpful to further explore the role of mesoscale eddies in ocean energy transfer.Through normalized chlorophyll data,we observed chlorophyll aggregation and hole eff ects caused by Lagrangian eddies.These fi ndings demonstrate the important role of Lagrangian eddies in material transport.The transportation volume of the Lagrangian eddy is calculated quantitatively,and several major transport routes have been identifi ed,which helps us to more accurately and objectively estimate the transport capacity of Lagrangian eddies in the western Pacifi c Ocean.

A Comprehensive Lagrangian Transport Study in A Long-Narrow Bay,Xiangshan Bay,China

Study on the transport and mixing in coastal waters is of great concern to the ocean resources exploitation and ecological system protection.Lagrangian methods are direct and effective of researching mass transport.Two Lagrangian tools were adopted and combined to describe water transport in a long-narrow bay,Xiangshan Bay,China.Based on the fields of tidal velocity simulated from the 3-D hydrodynamic model,Lagrangian Coherent Structures(LCSs)and synoptic Lagrangian maps(SLMs)were calculated in the study area.Through comparison of the results,the features and relation of the two tools were discussed.The results show that the LCSs act as the separatrix of the water regions with different transport characteristics and can identify the water areas with different transport time scales.The comprehensive application of the Lagrangian tools is helpful to obtain more insight into the water transport process.

Kinematic and mixing characteristics of vortex interaction induced by a vortex generator model:a numerical study

The underlying effect of vortex interaction characterized by the merging and non-merging on mixing enhancement is of fundamental significance to understand the flow dynamics of strut injectors in scramjets.Starting from a simplified configuration of a vortex generator,this study focuses on the influence of geometric parameters on vortex structures and fluid mixing through compressible Navier-Stokes(NS)simulations.By adjusting the induction of outer vortices,the inner co-rotating vortex pair exhibits two modes of interaction(merging/separation regime)reflected by closer/farther vortex centers.Defined by the zero variation rate of the inner vortex spacing,the critical state of equilibrium is determined.The critical condition is well predicted by a theoretical model based on the Biot-Savart law.Through the introduction of mixedness and mixing time,the intrinsic impact of interaction modes on fluid mixing is revealed.Compared with the vortex dynamics in the merging regime,the one in the separation regime is more effective for passive scalar mixing augmentation.With efficient material stretching characterized by the higher interface stretching factor and averaging finite-time Lyapunov exponent(FTLE),the mixing time is shortened by as much as 2.5 times in the separation regime.The implication of the present two interaction regimes in mixing enhancement physically reflected by the averaging FTLE has the potential to improve the combustion performance and shorten the combustor chamber.

Lagrangian methods for water transport processes in a long-narrow bay-Xiangshan Bay, China

A better understanding of water transport processes is highly desirable for the exploitation of the ocean resources and the protection of the ocean ecological system. In this paper, the Lagrangian methods are used to study the water transport processes in Xiangshan Bay in China, a typical semi-closed and narrow-shaped bay with complex coastline and topography. A high-resolution 3-D hydrodynamic model is developed and verified, and the results from the model agree well with the field data. Based on the hydrodynamic model, the Lagrangian residual current is computed by using the particle tracking method. A concept based on the dynamical systems theory, the Lagrangian coherent structures （LCSs）, is introduced to uncover the underlying structures which act as the transport barriers in the flow. The finite-time Lyapunov exponent （FTLE） fields are computed from the hydrodynamic model results to extract the LCSs. The results indicate that the LCSs act as the internal structures of the Lagrangian residual current and the Lagrangian residual current displays the residual current speed and direction of different water regimes separated by the LCSs. The water masses with different transport characteristics can be identified and their exchange ability with other water masses can be estimated by combining the Lagrangian particle tracking with the LCSs methods. The comprehensive applications of these Lagrangian methods reveal the underlying structures and the inhomogeneous characteristics of the water transport in Xiangshan Bay.

3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis

In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model（FBDCM）, a turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures（LCSs）. Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.

Flow and magnetic structures in a kinematic ABC-dynamo

Dynamo theory describes the magnetic field induced by the rotating,convecting and electrically conducting fluid in a celestial body.The classical ABC-flow model represents fast dynamo action,required to sustain such a magnetic field.In this letter,Lagrangian coherent structures(LCSs)in the ABC-flow are detected through Finite-time Lyapunov exponents(FTLE).The flow skeleton is identified by extracting intersections between repelling and attracting LCSs.For the case A=B=C=1,the skeleton structures are made up from lines connecting two different types of stagnation points in the ABC-flow.The corresponding kinematic ABC-dynamo problem is solved using a spectral method,and the distribution of cigar-like magnetic structures visualized.Inherent links are found to exist between LCSs in the ABC-flow and induced magnetic structures,which provides insight into the mechanism behind the ABC-dynamo.

Evolution of the Lagrangian drift and vortex added-mass of a growing vortex ring

The vortex-based propulsive systems’ enhanced performance greatly contributes to the vortex added-mass effect, which was initially developed to explain the added drag when a solid body accelerates in fluids. However, the solution of the instantaneous vortex added-mass coefficient is still remaining a question because vortices always do not have a stable geometric shape like solid bodies. In this paper, the formation of a canonical vortex ring is performed to investigate the nature of vortex added-mass and explore a solution for estimating the vortex added-mass coefficient. The vortex ring is generated by a piston-cylinder apparatus, and the time-dependent flow fields are recorded by particle image velocimetry technique. The ridges of finite-time Lyapunov exponent are applied to identify the Lagrangian boundary of the vortex ring. It is found that a part of the ambient fluids is entrained by the vortex ring when it propagates downstream, resulting in the growth of the vortex ring. Besides, a significant drift of the ambient fluid is observed to bypass the Lagrangian boundary of the vortex ring and reveals the nature of the vortex added-mass. Thus, the added-mass coefficient of the vortex is redefined as the ratio of the volume of the Lagrangian drift fluids in finite time interval step to the vortex volume at that instant. By referring to McPhaden’s method to estimate the added-mass of a solid body, a method based on the multiple material lines with relative-timestep is developed to estimate the volume of Lagrangian drift fluids induced by the vortex added-mass. Then, an empirical criterion for determining the material line number and the finite time interval step is suggested for the vortex ring flow, and the eventual vortex added-mass coefficient calculated by the volume of Lagrangian drift fluids is found to well agree with the results of Brennen. Moreover, the method based on multiple material lines for calculating Lagrangian drift fluids’ volume suggests a potential solution for estimating the added-mass coefficient of arbitrary vortex structures.

Unsteady Flow Separation and High Performance of Airfoil with Local Flexible Structure at Low Reynolds Number

The unsteady flow separation of airfoil with a local flexible structure(LFS)is studied numerically in Lagrangian frames in detail,in order to investigate the nature of its high aerodynamic performance.For such aeroelastic system,the characteristicbased split(CBS)scheme combined with arbitrary Lagrangian-Eulerian(ALE)framework is developed firstly for the numerical analysis of unsteady flow,and Galerkin method is used to approach the flexible structure.The local flexible skin of airfoil,which can lead to self-induced oscillations,is considered as unsteady perturbation to the flow.Then,the ensuing high aerodynamic performances and complex unsteady flow separation at low Reynolds number are studied by Lagrangian coherent structures(LCSs).The results show that the LFS has a significant influence on the unsteady flow separation,which is the key point for the lift enhancement.Specifically,the oscillations of the LFS can induce the generations of moving separation and vortex,which can enhance the kinetic energy transport from main flow to the boundary layer.The results could give a deep understand of the dynamics in unsteady flow separation and flow control for the flow over airfoil.

Numerical analyses of ventilated cavitation over a 2-D NACA0015 hydrofoil using two turbulence modeling methods

The present paper studies the ventilated cavitation over a NACA0015 hydrofoil by numerical methods. The corresponding cavity evolutions are obtained at three ventilation rates by using the level set method. To depict the complicated turbulent flow structure, the filter-based density corrected model（FBDCM） and the modified partially-averaged Navier-Stokes（MPANS） model are applied in the present numerical analyses. It is indicated that the predicted results of the cavitation shedding dynamics by both turbulence models agree fairly well with the experimental data. It is also noted that the shedding frequency and the super cavity length predicted by the MPANS method are closer to the experiment data as compared to that predicted by the FBDCM model. The simulation results show that in the ventilated cavitation, the vapor cavity and the air cavity have the same shedding frequency. As the ventilated rate increases, the vapor cavity is depressed rapidly. The cavitation-vortex interaction in the ventilated cavitation is studied based on the vorticity transport equation（VTE） and the Lagrangian coherent structure（LCS）. Those results demonstrate that the vortex dilatation and baroclinic torque terms are highly dependent on the evolution of the cavitation. In addition, from the LCSs and the tracer particles in the flow field, one may see the process from the attached cavity to the cloud cavity.

圆和非圆湍流合成射流结构演化和质量输运的拉格朗日方法分析

旋涡卷吸特性对合成射流的流动控制应用具有重要意义.为了研究湍流合成射流涡环的结构演化和瞬态卷吸特性,采用时间解析层析粒子图像测速技术,测量了相同参数下,圆形和长宽比为3的矩形合成射流的三维流场.利用拉格朗日拟序结构方法,刻画了涡环的三维拓扑变形和质量输运过程,并量化了连续涡环的卷吸特性.特别是对矩形涡环,由于涡环的对流速度沿周向分布不均匀,导致传统的移动参考系方法无法有效计算卷吸.针对该问题,采用基于有限时间李雅普诺夫指数“脊线”辨识旋涡边界的方法,估计涡泡体积,从而计算涡环的卷吸和动能转换效率.结果表明,矩形涡环能够卷吸更多的周围流质,产生比圆形涡环更大的涡旋强度;此外,矩形涡环从孔口喷出的流质中获得了更多动能,以维持涡环的轴系转换,这些特征有利于增强射流掺混.上述工作通过发展旋涡动力学的数学描述,为量化流动控制中的旋涡卷吸特性提供了重要参考.

Study on Mass Transports in Evolution of Separation Bubbles Using LCSs and Lobe Dynamics

The lobe dynamics andmass transport between separation bubble andmain flow in flow over airfoil are studied in detail,using Lagrangian coherent structures(LCSs),in order to understand the nature of evolution of the separation bubble.For this problem,the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split(CBS)scheme,in combination with dual time stepping.Then,LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble andmain flow,from viewpoint of nonlinear dynamics.The results show that stablemanifolds and unstable manifolds could be tangledwith each other as time evolution,and the lobes are formed periodically to induce mass transport between main flow and separation bubble,with dynamic behaviors.Moreover,the evolution of the separation bubble depends essentially on themass transportwhich is induced by lobes,ensuing energy andmomentum transfers.As the results,it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics,and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

DualSmoke: Sketch-based smoke illustration design with two-stage generative model

The dynamic effects of smoke are impressive in illustration design,but it is a troublesome and challenging issue for inexpert users to design smoke effects without domain knowledge of fuid simulations.In this work,we propose DualSmoke,a two-stage globalto-local generation framework for interactive smoke illustration design.In the global stage,the proposed approach utilizes fluid patterns to generate Lagrangian coherent structures from the user's hand-drawn sketches.In the local stage,detailed flow patterns are obtained from the generated coherent structure.Finally,we apply a guiding force field to the smoke simulator to produce the desired smoke illustration.To construct the training dataset,DualSmoke generates flow patterns using finite-time Lyapunov exponents of the velocity fields.The synthetic sketch data are generated from the fow patterns by skeleton extraction.Our user study verifies that the proposed design interface can provide various smoke illustration designs with good user usability.Our code is available at https://github.com/shasph/DualSmoke.