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
The investigation of Beltrami flows is important for the research on the mechanism of turbulent structure.In this paper the general solutions of the Beltrami flows are given,which depend explicitly on the solutions of...The investigation of Beltrami flows is important for the research on the mechanism of turbulent structure.In this paper the general solutions of the Beltrami flows are given,which depend explicitly on the solutions of three independent Helmholtz equations with scalar unknowns.Velocity fields of Beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equa- tions.On the basis of the exact solutions of Euler equations given above,we obtain one kind of exact solu- tions of non-steady Navier-Stokes equations which are also the Beltrami flows.Some interesting examples of Beltrami flows other than'ABC flows','Kolmogolov flows','Rayleigh-Bernard flows','Q-flows' are given.The detailed analytic results of these examples will be published in the near future.展开更多
In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows...In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the <em>rz</em>-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.展开更多
One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisy...One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisymmetric Beltrami spherical vortices. From these aspects, it is shown that the tensor denotation has more meaningful characters and nonaxisymmetric Beltrami shperical vortices are various and very complex.展开更多
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
In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The so...In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).展开更多
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.
文摘The investigation of Beltrami flows is important for the research on the mechanism of turbulent structure.In this paper the general solutions of the Beltrami flows are given,which depend explicitly on the solutions of three independent Helmholtz equations with scalar unknowns.Velocity fields of Beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equa- tions.On the basis of the exact solutions of Euler equations given above,we obtain one kind of exact solu- tions of non-steady Navier-Stokes equations which are also the Beltrami flows.Some interesting examples of Beltrami flows other than'ABC flows','Kolmogolov flows','Rayleigh-Bernard flows','Q-flows' are given.The detailed analytic results of these examples will be published in the near future.
文摘In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the <em>rz</em>-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.
文摘One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisymmetric Beltrami spherical vortices. From these aspects, it is shown that the tensor denotation has more meaningful characters and nonaxisymmetric Beltrami shperical vortices are various and very complex.
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.
文摘In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).
