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 rotatio...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.展开更多
As a potential mineral resource, the clay minerals enriched in rare earth elements including yttrium（REY） in the deep sea have been attracting great attention. However, the enrichment mechanism of REY remains unclea...As a potential mineral resource, the clay minerals enriched in rare earth elements including yttrium（REY） in the deep sea have been attracting great attention. However, the enrichment mechanism of REY remains unclear. To understand the geochemical characteristics and factors controlling REY enrichment in zeolite clay in the deep sea, we conducted mineral identification by XRD, major and trace element measurements by XRF and REY analyses by ICP-MS on a 1.4-m-long sediment core（GC02） located in the Central Indian Oceanic Basin（CIOB）. The main findings include：（1） the core sediments in GC02 possess elevated REY contents and exhibited a strong negative Ce anomaly, an apparent MREE bulge and positive Y anomaly. These were comparable with typical REY-rich clays in the Pacific Ocean, indicating the similar REY enrichment mechanism and the presence of REY-rich clays in the CIOB;（2） in comparison with the dataset from the Wharton Basin and DSDP site 213, the higher content of REY and stronger PAAS（Post Archean Australian Shale） normalization patterns in the GC02 sediments were likely caused by the weaker impact of terrigenous materials of GC02. The CIOB was suggested to be a promising place hosting REY rich pelagic sediments.展开更多
基金This work was mainly supported by the Department of Mathematics of University of Texas at Arlington where the corresponding author,Dr.Chaoqun Liu,is the full-time professor。
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.
基金supported by the National Natural Science Foundation of China(41773005)China Ocean Mineral Resources R&D Association(COMRA)Research Program(DY125-11-R-01,DY125-22-02),the Research Center for Air Pollution and Health(RCAPH)of Zhejiang University
文摘As a potential mineral resource, the clay minerals enriched in rare earth elements including yttrium（REY） in the deep sea have been attracting great attention. However, the enrichment mechanism of REY remains unclear. To understand the geochemical characteristics and factors controlling REY enrichment in zeolite clay in the deep sea, we conducted mineral identification by XRD, major and trace element measurements by XRF and REY analyses by ICP-MS on a 1.4-m-long sediment core（GC02） located in the Central Indian Oceanic Basin（CIOB）. The main findings include：（1） the core sediments in GC02 possess elevated REY contents and exhibited a strong negative Ce anomaly, an apparent MREE bulge and positive Y anomaly. These were comparable with typical REY-rich clays in the Pacific Ocean, indicating the similar REY enrichment mechanism and the presence of REY-rich clays in the CIOB;（2） in comparison with the dataset from the Wharton Basin and DSDP site 213, the higher content of REY and stronger PAAS（Post Archean Australian Shale） normalization patterns in the GC02 sediments were likely caused by the weaker impact of terrigenous materials of GC02. The CIOB was suggested to be a promising place hosting REY rich pelagic sediments.
