The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regio...The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regions and ordered islands on the Poincare sections. Interpretations of these phenomena are also given.展开更多
To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary condition...To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified.The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity.Finally,we find a class of spherical vortices of Beltrami flows,where the mo- tion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells.We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.展开更多
文摘The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regions and ordered islands on the Poincare sections. Interpretations of these phenomena are also given.
基金The project is supported by the National Foundamental Research Programme of State Commission of Sciences and Technology.
文摘To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified.The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity.Finally,we find a class of spherical vortices of Beltrami flows,where the mo- tion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells.We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.
