Using the C-mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross Pitaevskii theory in （3＋l）-dimensional space-time. We obtain the reduced dynamic equ...Using the C-mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross Pitaevskii theory in （3＋l）-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the function indicates that the vortices can only be generated from the zero points of Ф and are quantized in terms of the Hopf indices and Brouwer degrees. The C-mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.展开更多
Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are diff...Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of 未 function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a 未-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.展开更多
In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the to...In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.展开更多
Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two t...Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term n^→·（Эin^→×Эjn^→）, and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons.展开更多
Observational analyses and convection-permitting simulations are conducted to study an extreme event of damaging surface winds within a bow-shaped squall line over South China.Prevailing explanations for the formation...Observational analyses and convection-permitting simulations are conducted to study an extreme event of damaging surface winds within a bow-shaped squall line over South China.Prevailing explanations for the formation of damaging surface winds were applied to investigate the detailed processes at the mature stage of a squall line in a complicated real-world scenario.It is shown that environmental vertical wind shear was adequately strong to cause a shearing vorticity,and the shearing vorticity was comparable to the baroclinic vorticity by a cold pool.The balance led to strong upward motions at the leading edge of the squall line and brought plenty of rainfall.The descending rainfall cooled the surrounding air and entrained the upper-level cold air downward to the lower level,strengthening the cold pool by excessive evaporation and melting.The cold pool accelerated the propagation speed of the squall line and caused extensive wind damage at the surface.Meanwhile,the horizontal vortex lines at the leading edge of the cold pool were lifted by frontal updrafts and tilted to form the anti-cyclonic vortex at the middle level.This maintained and intensified the rearinflow jet behind the apex of bow echo in association with a notable midlevel pressure gradient.The rear-inflow jet was then transported downward to the surface by descending condensate,leading to damaging winds there.Other factors,such as environmental flows,however,contributed less to the damaging surface winds.展开更多
The in-line （IL） vortex-induced vibration （VIV） that occurs frequently in ocean engineering may cause severe fatigue damage in slender marine structures. To the best knowledge of the authors, in existing literatur...The in-line （IL） vortex-induced vibration （VIV） that occurs frequently in ocean engineering may cause severe fatigue damage in slender marine structures. To the best knowledge of the authors, in existing literatures, there is no efficient analytical model for predicting pure IL VIV. In this paper, a wake oscillator model capable of analyzing the IL VIV of slender marine structures has been developed. Two different kinds of van der Pol equations are used to describe the near wake dynamics related to the fluctuating nature of symmetric vortex shedding in the first excitation region and alternate vortex shedding in the second one. Some comparisons are carried out between the present model results and experimental data. It is found that many phenomena observed in experiments could be reproduced by the present wake oscillator model.展开更多
The traditional Kelvin-Helmholtz notion of studying the shear instability is not suitable for the case associated with shear line with the strong wind shear in the vortex sheet. Since then, the shear instability becom...The traditional Kelvin-Helmholtz notion of studying the shear instability is not suitable for the case associated with shear line with the strong wind shear in the vortex sheet. Since then, the shear instability becomes theinstability of the vortex sheet. If the velocity is induced by the vortex sheet, the inequalities (1? R r + Ri d)> 0 and U(v,t)> U(A(t)) become the criterion of the vortex sheet instability. This criterion indicates that 1) the disposition of environment field restrains the disturbance developing along the shear line. 2) There exist multi—scale interactions in the unstable process of the shear line. The calculation of the necessary condition for the instability is also presented in this paper. Key words Shear line - Induced velocity - Instability of the vortex sheet This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climate and weather disaster in China under Grant G 1998040907 and by the key project on the Dynamic Study of Severe Mesoscale Covective Systems sponsored by the National Natural Science Foundation of China under Grant No.49735180.展开更多
In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flo...In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flow where the mass and natural frequencies are precisely the same in both X- and Y-direction. The fluid speed varies from low to high with the corresponding vortex shedding frequency varying from below the first natural frequency to above the second natural frequency of the flexible pipe. Particular emphasis was placed on the investigation of the relationship between in-line and cross-flow vibration. The experimental results analyzed by using these measurements exhibits several valuable features.展开更多
The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of th...The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations （VIV） of the riser are analyzed in time domain in this papar. The numencal shnulation results of the riser＇s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser＇s VIV. Finally, the effects of the riser＇s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.展开更多
By using the conventional data,the rainfall data in the automatic weather station and so on,a regional heavy rainstorm which happened in the northwest and north central region of Shandong Province during May 9-10,2009...By using the conventional data,the rainfall data in the automatic weather station and so on,a regional heavy rainstorm which happened in the northwest and north central region of Shandong Province during May 9-10,2009 was analyzed.The results showed that the cooling shear line in low altitude was the main system which caused the heavy rainstorm.The rainstorm mainly happened on the left front of jet stream in low altitude,the right of cooling shear line in low altitude and the northeast quadrant of vortex.The southwest jet stream in the west of subtropical high established a water vapor passage from the South China Sea to the center of North China.It not only provided warm and wet air and energy for the development of heavy rainstorm,but also was the necessary condition which shear line in low altitude stagnated for a long time.Ground frontal cyclone was the trigger mechanism of rainstorm.The northeast wet and cold air joined with the southwest warm and wet air in Shandong after the front,which prompted the development of convection and the release of instable energy to form the rainstorm.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10905026 and 10905027)the Program of Science and Technology Development of Lanzhou, China (Grant No. 2010-1-129)
文摘Using the C-mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross Pitaevskii theory in （3＋l）-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the function indicates that the vortices can only be generated from the zero points of Ф and are quantized in terms of the Hopf indices and Brouwer degrees. The C-mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10905026 and 10905027)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090211120030)the Lanzhou Development of Science and Technology Program,China(Grant No.2010-1-129)
文摘Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of 未 function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a 未-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475034 and the Doctor Education Fund of the Educational Department of China.Acknowledgments It is a great pleasure to thank Dr. Y.X. Liu and Dr. Z.G. Huang for many useful discussions.
文摘In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.
基金supported by the National Natural Science Foundation of Chinathe Cuiying Programme of Lanzhou University
文摘Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term n^→·（Эin^→×Эjn^→）, and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons.
基金Research(2020B0301030004)National Natural Science Foundation of China(42275002)+3 种基金Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0890)Scientific and Technological Project of Chongqing Meteorological Service(YWJSGG-202124)Key Innovation Team of China Meteorological Administration(CMA2022ZD09)Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(SML2023SP209)。
文摘Observational analyses and convection-permitting simulations are conducted to study an extreme event of damaging surface winds within a bow-shaped squall line over South China.Prevailing explanations for the formation of damaging surface winds were applied to investigate the detailed processes at the mature stage of a squall line in a complicated real-world scenario.It is shown that environmental vertical wind shear was adequately strong to cause a shearing vorticity,and the shearing vorticity was comparable to the baroclinic vorticity by a cold pool.The balance led to strong upward motions at the leading edge of the squall line and brought plenty of rainfall.The descending rainfall cooled the surrounding air and entrained the upper-level cold air downward to the lower level,strengthening the cold pool by excessive evaporation and melting.The cold pool accelerated the propagation speed of the squall line and caused extensive wind damage at the surface.Meanwhile,the horizontal vortex lines at the leading edge of the cold pool were lifted by frontal updrafts and tilted to form the anti-cyclonic vortex at the middle level.This maintained and intensified the rearinflow jet behind the apex of bow echo in association with a notable midlevel pressure gradient.The rear-inflow jet was then transported downward to the surface by descending condensate,leading to damaging winds there.Other factors,such as environmental flows,however,contributed less to the damaging surface winds.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP)(20100032120047)the Independent Innovation Fund of Tianjin University (2010XJ-0098)+2 种基金State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (1104)the National High Technology Research and Development Program of China(863 Program) ( 2012AA051705)the National Natural Science Foundation of China (51209161)
文摘The in-line （IL） vortex-induced vibration （VIV） that occurs frequently in ocean engineering may cause severe fatigue damage in slender marine structures. To the best knowledge of the authors, in existing literatures, there is no efficient analytical model for predicting pure IL VIV. In this paper, a wake oscillator model capable of analyzing the IL VIV of slender marine structures has been developed. Two different kinds of van der Pol equations are used to describe the near wake dynamics related to the fluctuating nature of symmetric vortex shedding in the first excitation region and alternate vortex shedding in the second one. Some comparisons are carried out between the present model results and experimental data. It is found that many phenomena observed in experiments could be reproduced by the present wake oscillator model.
基金This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climat
文摘The traditional Kelvin-Helmholtz notion of studying the shear instability is not suitable for the case associated with shear line with the strong wind shear in the vortex sheet. Since then, the shear instability becomes theinstability of the vortex sheet. If the velocity is induced by the vortex sheet, the inequalities (1? R r + Ri d)> 0 and U(v,t)> U(A(t)) become the criterion of the vortex sheet instability. This criterion indicates that 1) the disposition of environment field restrains the disturbance developing along the shear line. 2) There exist multi—scale interactions in the unstable process of the shear line. The calculation of the necessary condition for the instability is also presented in this paper. Key words Shear line - Induced velocity - Instability of the vortex sheet This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climate and weather disaster in China under Grant G 1998040907 and by the key project on the Dynamic Study of Severe Mesoscale Covective Systems sponsored by the National Natural Science Foundation of China under Grant No.49735180.
基金This project was financially supported by the High Technology Research and Developmant Programof China (GrantNo.2006AA09Z356) the National Natural Science Foundation of China (Grant No.503795)
文摘In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flow where the mass and natural frequencies are precisely the same in both X- and Y-direction. The fluid speed varies from low to high with the corresponding vortex shedding frequency varying from below the first natural frequency to above the second natural frequency of the flexible pipe. Particular emphasis was placed on the investigation of the relationship between in-line and cross-flow vibration. The experimental results analyzed by using these measurements exhibits several valuable features.
基金supported by the High Technology Research and Development Program of China (863 Pro-gram, Grant No.2010AA09Z303)the Key Project of National Natural Science Foundation of China (Grant No.50739004)
文摘The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations （VIV） of the riser are analyzed in time domain in this papar. The numencal shnulation results of the riser＇s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser＇s VIV. Finally, the effects of the riser＇s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.
文摘By using the conventional data,the rainfall data in the automatic weather station and so on,a regional heavy rainstorm which happened in the northwest and north central region of Shandong Province during May 9-10,2009 was analyzed.The results showed that the cooling shear line in low altitude was the main system which caused the heavy rainstorm.The rainstorm mainly happened on the left front of jet stream in low altitude,the right of cooling shear line in low altitude and the northeast quadrant of vortex.The southwest jet stream in the west of subtropical high established a water vapor passage from the South China Sea to the center of North China.It not only provided warm and wet air and energy for the development of heavy rainstorm,but also was the necessary condition which shear line in low altitude stagnated for a long time.Ground frontal cyclone was the trigger mechanism of rainstorm.The northeast wet and cold air joined with the southwest warm and wet air in Shandong after the front,which prompted the development of convection and the release of instable energy to form the rainstorm.
