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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 42 ›› Issue (6): 1047-1062.doi: 10.3969/j.issn.1005-3085.2025.06.005cstr: 32411.14.cjem.CN61-1269/O1.2025.06.005

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流动系统的混沌机理分析及能量演化仿真研究

王贺元1,2   

  1. 1. 广东科技学院通识教育学院，东莞 523083

    2. 沈阳师范大学数学学院，沈阳 110034

  • 收稿日期:2023-02-04 接受日期:2023-07-20 出版日期:2025-12-15 发布日期:2026-02-15
  • 基金资助:
    国家自然科学基金(11572146)；广东科技学院重点科研基金(GKY-2025KYZDK-25).

Chaos Mechanism Analysis and Energy Evolution Simulation of Flow System

WANG Heyuan1,2   

  1. 1. College of General Education, Guangdong University of Science and Technology, Dongguan 523083
    2. College of Mathematics, Shenyang Normal University, Shenyang 110034
  • Received:2023-02-04 Accepted:2023-07-20 Online:2025-12-15 Published:2026-02-15
  • Supported by:
    The National Natural Science Foundation of China (11572146); the Research Projects Foundation of Guangdong University of Science and Technology (GKY-2025KYZDK-25).

摘要：

为了探讨流动系统混沌的生成机理，采用力矩分析方法研究了平面五模类Lorenz方程组的动力学机理和能量转换问题。把五模类Lorenz混沌系统转换成柯尔莫哥洛夫(Kolmogorov)系统，将系统的力矩分为惯性力矩，耗散力矩和外力矩(驱动力矩)三种类型。通过力矩不同的耦合模式分析和探讨流动系统产生混沌的力学机理，探讨能量与外力矩间的关系。通过卡西米尔函数分析系统的动力学行为演化和能量转换，并估计混沌吸引子的边界。初步阐释流动失稳和湍流发生的物理机制。

关键词: 动力学机理, Kolmogorov系统, 混沌, 全局稳定性, 力矩, Hamiltonian能量

Abstract:

In order to study the generation mechanism of chaos in flow system, the dynamical mechanism and energy conversion of plane five-mode Lorenz-like equations are studied by moment analysis method. The five-mode system was transformed into a Kolmogorov type system, which is decomposed into three types of torques: inertial torque, dissipation and external torque (drive torque). Through the coupling of different torques, the mechanism of chaos and the relation between energy and external torques were analyzed. Dynamic behavior evolution and energy conversion of the system are analyzed by Casimir function, and the bound of chaotic attractor is estimated. The physical mechanism of flow instability and turbulence is preliminarily explained.

Key words: dynamical mechanism, Kolmogorov system, chaos, global stability, torque, Hamiltonian energy

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