We diagnose characteristics of the quasi-balanced flow and secondary circulation（SC） of tropical storm Bilis（2006） using the potential vorticity（PV）-ω inversion method.We further analyze how secondary steering ...We diagnose characteristics of the quasi-balanced flow and secondary circulation（SC） of tropical storm Bilis（2006） using the potential vorticity（PV）-ω inversion method.We further analyze how secondary steering flows associated with mesoscale convective systems affected the track of tropical storm Bilis after it made landfall.The quasi-balanced asymmetric and axisymmetric circulation structures of tropical storm Bilis are represented well by the PV-w inversion.The magnitude of the nonlinear quasi-balanced vertical velocity is approximately 75%of the magnitude simulated using the Weather Research and Forecasting（WRF） model.The SC of Bilis（2006） contained two strong regions of ascending motion,both of which were located in the southwest quadrant of the storm.The first（150-200 km southwest of the storm center） corresponded to the eyewall region,while the second（approximately 400 km southwest of the storm center） corresponded to latent heat release associated with strong precipitation in major spiral rainbands.The SC was very weak in the northeast quadrant（the upshear direction）.Dynamical processes related to the environmental vertical wind shear produced an SC that partially offset the destructive effects of the environmental vertical wind shear（by 20%-25%）.This SC consisted of upward motion in the southwest quadrant and subsidence in the northeast quadrant,with airflow oriented from southwest to northeast at high altitudes and from northeast to southwest at lower levels.The inverted secondary zonal and meridional steering flows associated with continuous asymmetric mesoscale convective systems were about-2.14 and-0.7 m s^（-1）,respectively.These steering flows contributed substantially to the zonal（66.15%） and meridional（33.98%） motion of the storm at 0000 UTC15 July 2006.The secondary steering flow had a significant influence on changing the track of Bilis from southward to northward.The direction of the large-scale meridional steering flow（3.02 m s^（-1）） was opposite to the actual meridional motion（-2.06 m s^（-1））.展开更多
In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditio...In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（super） linearity are assumed. W＇e present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property （X^＋）, which is very important for the existence of periodic solutions and oscillation theory.展开更多
In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞（0,t;H2（G）） is rigorously justified by analysis of asymp...In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞（0,t;H2（G）） is rigorously justified by analysis of asymptotic expansions.展开更多
We are concerned with the existence of quasi-periodic solutions for the following equation x" + Fx (x, t)x' + ω2x + φ(x,t) = 0,where F and φ are smooth functions and 2π-periodic in t, ω＞ 0 is a constant...We are concerned with the existence of quasi-periodic solutions for the following equation x" + Fx (x, t)x' + ω2x + φ(x,t) = 0,where F and φ are smooth functions and 2π-periodic in t, ω＞ 0 is a constant. Under some assumptions on the parities of F and φ, we show that the Dancer's function, which is used to study the existence of periodic solutions, also plays a role for the existence of quasi-periodic solutions and the Lagrangian stability (i.e. all solutions are bounded).展开更多
In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness ...In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness theorems of limit cycles for bounded quadratic systems. As well, we prove that any bounded quadratic system can not have (2, 2)-distribution of limit cycles according to these uniqueness theorems.展开更多
基金Supported by the National(Key)Basic Research and Development(973)Program of China(2009CB421503)International Cooperating Program of Science and Technology(2010DFA24650)+1 种基金National Natural Science Foundation of China(41375098 and 41175061)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘We diagnose characteristics of the quasi-balanced flow and secondary circulation（SC） of tropical storm Bilis（2006） using the potential vorticity（PV）-ω inversion method.We further analyze how secondary steering flows associated with mesoscale convective systems affected the track of tropical storm Bilis after it made landfall.The quasi-balanced asymmetric and axisymmetric circulation structures of tropical storm Bilis are represented well by the PV-w inversion.The magnitude of the nonlinear quasi-balanced vertical velocity is approximately 75%of the magnitude simulated using the Weather Research and Forecasting（WRF） model.The SC of Bilis（2006） contained two strong regions of ascending motion,both of which were located in the southwest quadrant of the storm.The first（150-200 km southwest of the storm center） corresponded to the eyewall region,while the second（approximately 400 km southwest of the storm center） corresponded to latent heat release associated with strong precipitation in major spiral rainbands.The SC was very weak in the northeast quadrant（the upshear direction）.Dynamical processes related to the environmental vertical wind shear produced an SC that partially offset the destructive effects of the environmental vertical wind shear（by 20%-25%）.This SC consisted of upward motion in the southwest quadrant and subsidence in the northeast quadrant,with airflow oriented from southwest to northeast at high altitudes and from northeast to southwest at lower levels.The inverted secondary zonal and meridional steering flows associated with continuous asymmetric mesoscale convective systems were about-2.14 and-0.7 m s^（-1）,respectively.These steering flows contributed substantially to the zonal（66.15%） and meridional（33.98%） motion of the storm at 0000 UTC15 July 2006.The secondary steering flow had a significant influence on changing the track of Bilis from southward to northward.The direction of the large-scale meridional steering flow（3.02 m s^（-1）） was opposite to the actual meridional motion（-2.06 m s^（-1））.
文摘In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（super） linearity are assumed. W＇e present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property （X^＋）, which is very important for the existence of periodic solutions and oscillation theory.
基金Supported by National Basic Research Program of China(973 Program,Grant No.2011CB808002)National Natural Sciences Fundation of China(Grant No.11371042)+3 种基金BNSF(No.1132006)Beijing Education Committee Foundation(No.CIT&TCD20130312)HNNSF(112300410251,132300410250,132300410084)KYTF of Henan Education Commitee(2011GGJS-210)
文摘In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞（0,t;H2（G）） is rigorously justified by analysis of asymptotic expansions.
基金supported by the Special Funds for Major State Basic Research Projects(973 Projects)NSFC(Grant No.10325103)TRAPOYT.
文摘We are concerned with the existence of quasi-periodic solutions for the following equation x" + Fx (x, t)x' + ω2x + φ(x,t) = 0,where F and φ are smooth functions and 2π-periodic in t, ω＞ 0 is a constant. Under some assumptions on the parities of F and φ, we show that the Dancer's function, which is used to study the existence of periodic solutions, also plays a role for the existence of quasi-periodic solutions and the Lagrangian stability (i.e. all solutions are bounded).
文摘In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness theorems of limit cycles for bounded quadratic systems. As well, we prove that any bounded quadratic system can not have (2, 2)-distribution of limit cycles according to these uniqueness theorems.
