Seven-Mode Truncation and Chaotic Characteristics of Kolmogorov Flow Model
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摘要: 为了给出Kolmogorov流动模型中混沌行为的数学描述,选取常数k=3,重新对描述该模型的Navier-Stokes方程进行截断,得到了一个新的七维混沌系统.数值模拟了控制参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,分析了其混沌特性.一方面证实了具有湍流特性的数学对象归因于低维混沌吸引子,另一方面有利于更好地了解湍流流动产生的机理.
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关键词:
- Kolmogorov流动模型 /
- 截断 /
- 分岔 /
- 混沌
Abstract: To provide a mathematical description of the chaotic behavior in Kolmogorov flow model,with k=3was researched,NavierStokes equation was truncated by seven basic modes and a new sevendimensional chaotic system described by ordinary differential equations was obtained. The basic dynamical behaviors and chaotic behaviors were simulated numerically according to control parameter changes and the chaotic characteristics were analyzed. The result verifies that the mathematical object which accounts for turbulence is attributed to lowdimensional chaotic attractors and this is helpful to understand turbulent flow.-
Key words:
- Kolmogorov flow model /
- truncation /
- bifurcation /
- chaos
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