| 一个新的平面不可压缩的Navier-Stokes方程的八模类Lorenz方程组截断 |
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| 引用本文： | 崔妍,王贺元.一个新的平面不可压缩的Navier-Stokes方程的八模类Lorenz方程组截断[J].辽宁工学院学报,2007,27(6):416-420. |
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| 作者姓名： | 崔妍 王贺元 |
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| 作者单位： | 辽宁工业大学数理科学系 辽宁锦州121001 |
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| 基金项目： | 辽宁省教育厅资金资助项目(200401081) |
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| 摘 要： | 通过对平面正方形区域上不可压缩的Navier-Stokes方程进行傅立叶展开后截断得到一个新的八模类Lorenz方程组,给出了该方程组的定常解及吸引子存在性和全局稳定性的证明。同时,数值模拟了雷诺数在一定范围内变化时方程组的基本动力学行为和混沌轨线。系统通过一系列的分岔展现了复杂的随机行为。
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| 关 键 词： | Navier-Stokes方程 奇怪吸引子 李雅谱诺夫函数 分歧 混沌 |
| 文章编号： | 1005-1090（2007）06-0416-05 |
| 收稿时间： | 2007-03-26 |
| 修稿时间： | 2007年3月26日 |
Eight-modes Truncation of Plane Incompressible Navier-Stokes Equations |
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| CUI Yan, WANG He-yuan.Eight-modes Truncation of Plane Incompressible Navier-Stokes Equations[J].Journal of Liaoning Institute of Technology(Natural Science Edition),2007,27(6):416-420. |
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| Authors: | CUI Yan WANG He-yuan |
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| Abstract: | A new eight-modes Lorenz-like system was obtained by Fourier expansion through a suitable eight-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus.Several issues such as some basic dynamical behaviors,the existence of attractor and the global stability of the equations were proposed.The changes in a certain range about Reynolds involved in basic clynamical behaviors and Chaos of the equations were imitated numerically.And the system exhibited a stochastic behavior approached through an involved sequence of bifurcations. |
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| Keywords: | Navier-Stokes equations strange attractor Lyapunov function bifurcation Chaos |
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