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Acta Mechanica Sinica 1992年第4期8卷 289-294页

作者：是长春黄永念陈耀松 Peking University Beijing 100871China

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 *** 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 ***,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 *** find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.

关键词： beltrami flow sufficient and necessary condition spherica vortex chaotic trajectory

SOME PROPERTIES OF THREE-DIMENSIONAL beltrami flowS

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Acta Mechanica Sinica 1991年第4期7卷 289-294页

作者：是长春黄永念 Peking University Beijing 100871China

The investigation of beltrami flows is important for the research on the mechanism of turbulent *** this paper the general solutions of the beltrami flows are given,which depend explicitly on the solutions of three independent Helmholtz equations with scalar *** fields of beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equa- *** 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 *** interesting examples of beltrami flows other than'ABC flows','Kolmogolov flows','Rayleigh-Bernard flows','Q-flows' are *** detailed analytic results of these examples will be published in the near future.

关键词： beltrami flow Euler equation Navier-Stokes equation exact solution

THE TENSOR DENOTATION OF beltrami SPHERICAL VORTICES AND THEIR SYMMETRY ANALYSIS

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Applied Mathematics and Mechanics(English Edition) 2002年第1期23卷 13-17页

作者： HUANG Yong-nian(黄永年) HU Xin(胡欣) Department of Mechanics and Engineering Science State Key Laboratory for Turbulence Research Peking University Beijing 100871 P R China Department of Mechanics and Engineering Science State Key Laboratory for Turbulence Research Peking University Beijing 100871 P R China

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.

关键词： beltrami flow tensor denotation symmetry chaotic phenomena

Exact solutions for different vorticity functions of couple stress fluids

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第5期9卷 672-680页

作者： Saeed ISLAM Chao-ying ZHOU Xiao-juan RAN Department of Mechanical Engineering and Automation Harbin Institute of Technology Shenzhen Graduate School Shenzhen 518055 China COMSATS Institute of lnformation Technology Islamabad 44000 Pakistan

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).

关键词： Exact solutions Vorticity functions beltrami flow Couple stress fluid

A method for exploring some new solutions of complex lamellar flow

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Communications in Nonlinear Science and Numerical Simulation 2000年第1期5卷 17-20页

作者： Xin HU Yongnian HUANG and Yi ZENG Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence Research, Peking University, Beijing 100871, China Basic Department, Jiaotong University of Eastern China, Nanchang 330013, China Dept. of Mechanics and Eng. Science State Key Lab. for Turbulence Res. Peking University Beijing 100871 China Basic Department Jiaotong University of Eastern China Nanchang 330013 China

Complex lamellar flow is a typical flow in fluid mechanics. Its research has high theoretical value. Generally speaking, there are only two typical flows in nature: one is beltrami flow, the other is complex lamellar flow. We have known much about the former. But the solutions of the latter are hard to obtain because it is difficult to solve the N-S equation or Euler equation. From the incompressible condition, if we let the form of the velocity satisfy some special conditions, we would obtain some new solutions of this flow.

关键词： beltrami flow complex lamellar flow exact solution incompressible condition