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| 1 | Third generation of vortex identification methods:Omega and Liutex/Rortex based systems显示文摘A vortex is intuitively recognized as the rotational/swirling motion of fluids,but a rigorous and universally-accepted definition is still not available.Vorticity tube/filament has been regarded equivalent to a vortex since Helmholtz proposed the concepts of vorticity tube/filament in 1858 and the vorticity-based methods can be categorized as the first generation of vortex identification methods.During the last three decades,a lot of vortex identification methods,including 0,A,and Aci criteria,have been proposed to overcome the problems associated with the vorticity-based methods.Most of these criteria are based on the Cauchy-Stokes decomposition and/or eigenvalues of the velocity gradient tensor and can be considered as the second generation of vortex identification methods.Starting from 2014,the Vortex and Turbulence Research Team at the University of Texas at Arlington(the UTA team)focus on the development of a new generation of vortex identification methods.The first fruit of this effort,a new Omega(/2)vortex identification method,which defined a vortex as a connected region where the vorticity overtakes the deformation,was published in 2016.In 2017 and 2018,a Liutex(previously called Rortex)vector was proposed to provide a mathematical definition of the local rigid rotation part of the fluid motion,including both the local rotational axis and the rotational strength.Liutex/Rortex is a new physical quantity with scalar,vector and tensor forms exactly representing the local rigid rotation of fluids.Meanwhile,a decomposition of the vorticity to a rotational part namely Liutex/Rortex and an anti-symmetric shear part(RS decomposition)was introduced in 2018,and a universal decomposition of the velocity gradient tensor to a rotation part(7?)and a non-rotation part(NR、was also given in 2018 as a counterpart of the traditional Cauchy-Stokes decomposition.Later in early 2019,a Liutex/Rortex based Omega method called Omega-Liutex,which combines the respective advantages of both Liutex/Rortex and Omega methods,was developed.And a latest objective Omega method,which is still under development,is also briefly introduced.These advances are classified as the third generation of vortex identification methods in the current paper.To elaborate the advantages of the third-generation methods,six core issues for vortex definition and identification have been raised,including:(1)the absolute strength,(2)the relative strength,(3)the rotational axis,(4)the vortex core center location,(5)the vortex core size,(6)the vortex boundary.The new third generation of vortex identification methods can provide reasonable answers to these questions,while other vortex identification methods fail to answer all questions except for the approximation of vortex boundaries.The purpose of the current paper is to summarize the main ideas and methods of the third generation of vortex identification methods rather than to conduct a comprehensive review on the historical development of vortex identification methods. | Chaoqun Liu Yi-sheng Gao Xiang-rui Dong Yi-qian Wang Jian-ming Liu Yu-ning Zhang Xiao-shu Cai Nan Gui | 2019 | Journal of Hydrodynamics2019，31，2： | 82 |
| 2 | New omega vortex identification method显示文摘A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity. | ChaoQun Liu YiQian Wang Yong Yang ZhiWei Duan | 2016 | Science China(Physics,Mechanics & Astronomy)2016，59，8： | 49 |
| 3 | Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition显示文摘In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (2c.) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector. | Yi-qian Wang Yi-sheng Gao Jian-ming Liu Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，3： | 38 |
| 4 | Determination of epsilon for Omega vortex identification method显示文摘In the present paper, epsilon(ε) in the Omega vortex identification criterion( Ω method) is defined as an explicit function in order to apply the Ω method to different cases and even different time steps for the unsteady cases. In our method, e is defined as a function relating with the flow without any subjective adjustment on its coefficient. The newly proposed criteria for the determination of ε is tested in several typical flow cases and is proved to be effective in the current work. The test cases given in the present paper include boundary layer transition, shock wave and boundary layer interaction, and channel flow with different Reynolds numbers. | 董祥瑞 王义乾 陈小平 Yinlin Dong 张宇宁 Chaoqun Liu | 2018 | Journal of Hydrodynamics2018，30，4： | 32 |
| 5 | A selected review of vortex identification methods with applications显示文摘In the present review, recent progress on the vortex identification methods are introduced with a focus on the newly proposed omega method( Ω method). The advantages of Ω method are summarized with many illustrating examples. Furthermore, comparing with other existing methods(e.g., Q criterion and λ_2 criterion), one of the characteristics of Ω method is its independence on the chosen threshold values for vortex identifications. The important parameters involved for the practical applications of Ω method are further discussed in detail together with the physical interpretation of the Ω and some suggestions of the future work. Other emerging topics(e.g., Lagrangian coherent structure and Rortex) are also introduced with comments. | 张宇宁 裘勖 陈飞鹏 刘凯华 张宇宁 董祥瑞 Chaoqun Liu | 2018 | Journal of Hydrodynamics2018，30，5： | 25 |
| 6 | Liutex (vortex) core definition and automatic identification for turbulence vortex structures显示文摘As a milestone research in vortex identification(VI),the physical quantity of Liutex,including its forms of scalar,vector and tensor,was systematically explored and rigorously obtained as the third-generation(3G)of the vortex definition and identification methods distinguished from the first generation(1G)by vorticity and the second generation(2G)by the vortex identification(VI)criteria solely dependent on the velocity gradient tensor eigenvalues.Based on these findings,the vortex-core lines were abstracted from the well-defined Liutex,and for the first time,were automatically generated and massively visualized using computer.The distinctive characteristics of these vortex cores with the intriguing threshold-independency make them be the uniquely appropriate entity to represent and to depict the vortex structures in turbulence.The letter made use of the DNS data for the natural transition in a zero-pressure gradient flat-plate(Type-A turbulent boundary layer(TBL))and the fully-developed turbulence in a square annular duct(Type-B TBL)to demonstrate the vortex structure represented by the vortex-core lines.The 3G VI approach based on the vortex-core lines is capable of profoundly uncovering the vortex natures.Moreover,the capability of automatically identifying the vortex cores and massively visualizing the large number of vortex-core behaviors in a transient way will enable the fluid-mechanics and other related-science communities to step into a new era to explore the intrinsic natures of the centennial puzzle of turbulence and other vortex-related phenomena in future. | Hongyi Xu Xiao-shu Cai Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，5： | 21 |
| 7 | A Liutex based definition and identification of vortex core center lines显示文摘Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the criterion and the Acj criterion etc., are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient. | Yi-sheng Gao Jian-ming Liu Yi-fei Yu Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，3： | 19 |
| 8 | Orthogonal experiment design of EMI of security monitoring system in coal mines显示文摘 | Xiang Liu Chaoqun Jiao Aifen Yao | 2015 | International Journal of Coal Science & Technology2015，2，4： | 19 |
| 9 | An HBV-encoded miRNA activates innate immunity to restrict HBV replication显示文摘We previously identified that hepatitis B virus(HBV)encodes a microRNA(HBV-miR-3)that restrains HBV replication by targeting the HBV transcript.However,whether HBV-miR-3 affects host innate immunity to modulate HBV replication remains unclear.Here,we examined the vital functions of HBV-miR-3 in the innate immune response after HBV infection.We found that HBV-miR-3 expression gradually increased in a dose-and time-dependent manner in HBV-infected HepG2-NTCP cells.HBV-miR-3 activated the JAK/STAT signaling pathway by downregulating SOCS5 in hepatocytes,thereby enhancing the IFN-induced anti-HBV effect.In addition,HBVmiR-3 in exosomes facilitated the Ml polarization of macrophages.Furthermore,exosomes containing HBV-miR-3 enhanced the secretion of IL-6 via inhibiting the SOCS5-mediated ubiquitination of EGFR.In short,these results demonstrate that HBV-miR-3 activates the innate immune response to restrain HBV replication by multiple pathways,which may suppress HBV-induced acute liver cell injury and affect the progression of persistent HBV infection. | Xiaoqing Zhao Lu Sun Ting Mu Jianying Yi Chaoqun Ma Hong Xie Min Liu Hua Tang | 2020 | Journal of Molecular Cell Biology2020，12，4： | 17 |
| 10 | Liutex theoretical system and six core elements of vortex identification显示文摘The third-generation vortex identification method of Liutex(previously called Rortex)was introduced by the team led by Prof.Chaoqun Liu from University of Texas at Arlington to mathematically extract the rigid rotation part from the fluid motion,and thus to define and visualize vortices.Unlike the vorticity-based first generation and the scalar-valued second generation,Q,λ2,Δandλci methods for example,the Liutex vector provides a unique,mathematical and systematic way to define vortices and visualize vortical structures from multiple perspectives without ambiguity.In this article,we summarize the recent developments of the Liutex framework and discuss the Liutex theoretical system including its existence,uniqueness,stability,Galilean invariance,locality and globality,decomposition in tensor and vector forms,Liutex similarity in turbulence,and multiple Liutex-based vortex visualization methods including Liutex lines,Liutex magnitude iso-surfaces,Liutex-Ωmethod,and Liutex core line method,etc..Thereafter,the six core elements of vortex identification,including(1)absolute strength,(2)relative strength,(3)local rotational axis,(4)vortex rotation axes,(5)vortex core size,(6)vortex boundary,are used as touchstones against which the Liutex vortex identification system is examined.It is demonstrated with illustrative examples that the Liutex system is able to give complete and precise information of all six core elements in contrast to the failure and inaccuracy of the first and second-generation methods.The important concept that vorticity cannot represent vortex and the superiority of the Liutex system over previous methods are reiterated and stated in appropriate places throughout the paper.Finally,the article concludes with future perspectives,especially the application of the Liutex system in studying turbulence mechanisms encouraged by the discovery of Liutex similarity law.As a newly defined physical quantity,Liutex may open a door for quantified vortex and turbulence research including Liutex(vortex)dynamics and lead the community out of the shadow of turbulence research which traditionally relies on observations,graphics,assumptions,hypotheses,and other qualitative analyses.An optimistic projection is that the Liutex system could be critical to investigation of the vortex dynamics in applications from hydrodynamics,aerodynamics,oceanography,meteorology,etc.and to research of the generation,sustenance,modelling and controlling of turbulence. | Yi-qian Wang Yi-sheng Gao Hongyi Xu Xiang-rui Dong Jian-ming Liu Wen-qian Xu Meng-long Chen Chaoqun Liu | 2020 | Journal of Hydrodynamics2020，32，2： | 17 |
| 11 | Comparisons and analyses of vortex identification between Omega method and Q criterion显示文摘The present paper presents comparisons of the vortex identification between the Omega method and the Q criterion based on the data of a classical flow.From the comparisons of the vortex structure together with the flow statistics,some important conclusions are drawn on the validity of the two methods,as follows.The Omega method can identify various kinds of vortices with different intensities(e.g.,the strong vortex,the medium vortex and the weak vortex).For the Q criterion,due to the subjective threshold selection,only the strong vortex with weak deformations could be identified.Finally,some emerging topics related with the advanced vortex identification methods are briefly discussed. | Yu-ning Zhang Xiao-yu Wang Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，2： | 8 |
| 12 | Liutex similarity in turbulent boundary layer显示文摘Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence theory.The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon,however,cannot generally be met in practice,and thus discrepancy is often observed between the f law and direct numerical simulation(DNS)results of boundary layers in wall bounded turbulence,especially for moderate to low Reynolds number flows.Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion.Actually,Liutex is free from viscous dissipation and thus independent of Reynolds number,relaxing the very high Reynold number assumption of K41.Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000),both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law,which is obviously much better than the turbulence energy spectrum,while vorticity and other popular vortex identification methods,Q criterion for example,do not possess such a distinguished feature due to stretching and shearing contamination. | Wen-qian Xu Yi-qian Wang Yi-sheng Gao Jian-ming Liu Hua-shu Dou Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，6： | 8 |
| 13 | A natural variation in Ribonuclease H-like gene underlies Rht8 to confer“Green Revolution”trait in wheat显示文摘Dear Editor,Introduction of gibberellin(GA)-insensitive Reduced height(Rht)genes,Rht-B1b and Rht-D1b,has resulted in the“Green Revolution”in modern wheat cultivars(Triticum aestivum)that has skyrocketed wheat grain yields worldwide since the 1960s(Peng et al.,1999;Velde et al.,2021).However,Rht-B1b/D1b also reduce coleoptiles,which is undesired in dryland regions where deep planting is essential for seedling establishment(Rebetzke et al.,1999,Rebetzke et al.,2001;Ellis et al.,2004). | Lingling Chai Mingming Xin Chaoqun Dong Zhaoyan Chen Huijie Zhai Junhong Zhuang Xuejiao Cheng Naijiao Wang Jia Geng Xiaobo Wang Ruolin Bian Yingyin Yao Weilong Guo Zhaorong Hu Huiru Peng Guihua Bai Qixin Sun Zhenqi Su Jie Liu Zhongfu Ni | 2022 | Molecular Plant2022，15，3： | 8 |
| 14 | New ideas on governing equations of fluid dynamics显示文摘Classical fluid kinematics or Cauchy-Stokes decomposition mistreated vorticity as fluid rotation and mixed flow stretching with shearing.Classical fluid dynamics or Navier-Stokes(N-S)equations are based on the classical kinematics and treated vorticity as null in contribution of forces and mixed the stretching force with the shearing force,which is not consistent with the Galilean invariancy.N-S equations also neglect the flow rotation.It is believed that N-S equations may work for incompressible and laminar flow but are not satisfied for turbulent flow and compressible flow especially for high-speed flow.Based on Liutex,new fluid kinematics has been established by Liu in 2021,which gives a Liutex-based principal coordinate system and a new principal decomposition in that system,which has been transferred back to the original Cartesian coordinate system.The principal decomposition of velocity gradient tensor has four parts which are called rotation,stretching,anti-symmetric shearing and symmetric shearing.Four forces are derived according to the four parts of the velocity gradient tensor.According to the new fluid kinematics,it is reported in this letter that based on the principal decomposition,a new relation between the velocity gradient tensor and stress-rate tensor has been established to form a new fluid dynamics equation to govern fluid flow.The new governing equation may be applicable to both laminar flow and turbulent flow,and both incompressible flow and compressible flow including high-speed flow for reasonable results with reasonable grids.Further numerical experiment is needed to verify. | Chaoqun Liu | 2021 | Journal of Hydrodynamics2021，33，4： | 7 |
| 15 | Global methane and nitrous oxide emissions from terrestrial ecosystems due to multiple environmental changes显示文摘Greenhouse gas(GHG)-induced climate change is among the most pressing sustainability challenges facing humanity today,posing serious risks for ecosystem health.Methane(CH_(4))and nitrous oxide(N_(2)O)are the two most important GHGs after carbon dioxide(CO_(2)),but their regional and global budgets are not well known.In this study,we applied a process-based coupled biogeochemical model to concurrently estimate the magnitude and spatial and temporal patterns of CH_(4)and N_(2)O fluxes as driven by multiple environmental changes,including climate variability,rising atmospheric CO_(2),increasing nitrogen deposition,tropospheric ozone pollution,land use change,and nitrogen fertilizer use.The estimated CH_(4)and N_(2)O emissions from global land ecosystems during 1981-2010 were 144.39±12.90 Tg C/yr(mean 62 SE;1 Tg=1012 g)and 12.52±0.74 Tg N/yr,respectively.Our simulations indicated a significant(P,0.01)annually increasing trend for CH_(4)(0.43±0.06 Tg C/yr)and N_(2)O(0.14±0.02 Tg N/yr)in the study period.CH_(4)and N_(2)O emissions increased significantly in most climatic zones and continents,especially in the tropical regions and Asia.The most rapid increase in CH_(4)emission was found in natural wetlands and rice fields due to increased rice cultivation area and climate warming.N_(2)O emission increased substantially in all the biome types and the largest increase occurred in upland crops due to increasing air temperature and nitrogen fertilizer use.Clearly,the three major GHGs(CH_(4),N_(2)O,and CO_(2))should be simultaneously considered when evaluating if a policy is effective to mitigate climate change. | Hanqin Tian Guangsheng Chen Chaoqun Lu Xiaofeng Xu Wei Ren Bowen Zhang Kamaljit Banger Bo Tao Shufen Pan Mingliang Liu Chi Zhang Lori Bruhwiler Steven Wofsy | 2015 | Ecosystem Health and Sustainability2015，1，1： | 7 |
| 16 | Galilean invariance of Omega vortex identification method显示文摘In the new vortex identification method(Liu et al.2016)to represent the rotation level and capture and visualize the vortices,proposed in our previous study,the independence of the reference frame and the Galilean invariant were not proved.In the present study,the Galilean invariance of the omega vortex identification method is proved and several examples are presented to verify the conclusion. | Jian-ming Liu Yi-qian Wang Yi-sheng Gao Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，2： | 6 |
| 17 | Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method显示文摘The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube. | Cong Trieu Tran Xin-ping Long Bin Ji Chaoqun Liu | 2020 | Journal of Hydrodynamics2020，32，3： | 6 |
| 18 | Hydrogel-based artificial enzyme for combating bacteria and accelerating wound healing显示文摘Artificial enzymes have provided great antimicrobial activity to combat wound infection.However,the lack of tissue repair capability compromised their treatment effect.Therefore,development of novel artificial enzyme concurrently with the excellent antibacterial activity and the property of promoting wound healing are required.Here,we demonstrated the hydrogel-based artificial enzyme composed of copper and amino acids possessed intrinsic peroxidase-like catalytic activity,which could combat wound pathogen effectively and accelerate wound healing by stimulating angiogenesis and collagen deposition.Furthermore,the system possesses good biocompatibility for practical application.The synergic effect of the hydrogel-based artificial enzyme promises the system as a new paradigm in bacteria-infected wound healing therapy. | Hao Qiu Fang Pu Zhengwei Liu Xuemeng Liu Kai Dong Chaoqun Liu Jinsong Ren Xiaogang Qu | 2020 | Nano Research2020，13，2： | 6 |
| 19 | Nd-Sr Isotopic Geochemistry of the Late Archean-Paleoproterozoic Granitoids in the Lüliang-Wutai Terrain,North China Craton,and Implications for Petrogenesis显示文摘In this paper we report geochemical and Nd-Sr isotopic data for a late Archean gneissic granitic pluton (Hengling pluton), an early Paleoproterozoic complex (Xipan complex) and a late Paleoproterozoic granitic pluton (Yunzhongshan granites) from the Lüliang-Wutai terrain, North China, to trace the source of these late Archean-Paleoproterozoic granitoids and, particularly, to understand the nature and mechanism of continental growth at that time. The Hengling granitic gneisses (ca. 2.51 Ga) are characterized by high Na2O and LILEs, TTG-like REE patterns (highly depleted HREE and minor Eu anomalies) and moderately depleted Nd-Sr isotopic compositions (εNd(t) =1.2?2.7, ISr=0.7015?0.7019), and were considered as being products of arc magmatism that was developed upon the North China craton. The Xipan complex (ca. 2.2 Ga) contain gabbroic diorite and monzonite, mostly being Na2O-rich, highly fractionated REE patterns and isotopically enriched (εNd(t) =?1.5 to ?4.1, ISr=0.7038?0.706). The gabbroic diorites probably originated from melting of an enriched mantle source, but significantly contaminated by lower crustal material, and the monzonites probably represent a product of a mixture between the gabbroic dioritic magma and granitic melts of crustal origin. The Yunzhongshan post-collisional granitoids (ca. 1.8 Ga) are characterized by high-K affinity and highly-enriched and homogeneous Nd isotopic compositions (εNd(t)=?4.9 to ?5.7), although they split into two groups in terms of REE patterns: one group showing elevated HREE (and Sc, Y and Zr) with significant negative Eu anomalies and the other showing highly depleted HREE and, to a lesser extent, mid-REE with negligible Eu anomalies. These granites are genetically related to a process of extensional collapse of a thickened orogen. They formed through magma mixing between mantle- derived basaltic magmas and crust-derived granitic melts, followed by significant fractionation of ferromagnesian phases (like hornblende and Cpx) and feldspar and accessory zircons. Some Yunzhongshan granites show very old Nd model ages (2.9?3.0 Ga), suggesting the existence of continental crust older than 2.7 Ga, which is supported by our zircon Hf isotopic data for these granites. | CHEN Bin, LIU Shuwen, WANG Rui, CHEN Zhichao and LIU Chaoqun Key Laboratory of Orogenic Belts and Crustal Evolution, MOE School of Earth and Space Sciences, Peking University, Beijing 100871 | 2006 | Acta Geologica Sinica(English Edition)2006，80，6： | 4 |
| 20 | POD analysis on vortical structures in MVG wake by Liutex core line identification显示文摘The Liutex core line method, first combined with the snapshot proper orthogonal decomposition (POD), is utilized in a supersonic micro-vortex generator (MVG) wake flow at Ma = 2.5 and Reθ = 5 760 to reveal the physical significance of each POD mode of the flow field. Compared with other scalar-based vortex identification methods, the Liutex core line identification is verified to be the most appropriate approach that is threshold-free and provides full information of a fluid rotation motion. Meanwhile, the Liutex integration is employed to quantitatively track the evolution of the vortices in MVG wake and is applied to the determination of the effective control section of the MVG wake for the optimization study of MVG design. The physical mechanism of each POD mode for multi-scale and multi-frequency vortical structures is investigated by using Liutex core line identification to give some revelations. For the mean mode (mode 0) indicating the time-averaged velocity flowfield of the MVG wake flow, a pair of primary counter-rotating streamwise vortices and another pair of secondary vortices is uniquely identified by two pairs of Liutex core lines with Liutex magnitude. In contrast, mode 1 is featured by a fluctuated roll-up motion of streamwise vortex, and the streamwise component of the MVG wake is demonstrated to be dominant in terms of the total kinetic energy contribution. Meanwhile, a dominant shedding frequency of St = 0.072 is detected from the temporal behavior of mode 2, which has the organized arc-shaped vortex structures shedding from MVG induced by the K-H instability. Additionally, mode 4 subjects to low-frequency oscillations of the wall vortices and thus takes a relatively lower frequency of St = 0.044. | Xiang-rui Dong Xiao-shu Cai Yinlin Dong Chaoqun Liu | 2020 | Journal of Hydrodynamics2020，32，3： | 4 |
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