根据盖伊-卢萨克近似的3D洛伦兹模型的扩展
Caleb Monoran1, Clifford Watkins2, Sean Breckling1
1Advanced Analytics, Nevada National Security Sites (NNSS), North Las Vegas, Nevada 83090, USA.
Chaos (Woodbury, N.Y.)
|September 5, 2025
概括
这项研究通过使用Gay-Lussac近似来介绍流体对流的新动态系统,扩展了3D洛伦兹系统. 这些模型捕获非Boussinesq效应,同时保持不压缩性,以便更好地进行流体动力学研究.
科学领域:
- 流体动力学
- 非线性动力学
- 热力学
背景情况:
- 从Oberbeck-Boussinesq (OB) 近似得出的3D Lorenz (3DL) 系统是研究流体对流的基石.
- OB近似简化了流体密度变化,假设不压缩性和依赖温度的线性状态方程.
- 在许多现实场景中至关重要的非Boussinesq效应并未被标准的OB模型完全捕捉到.
研究的目的:
- 使用替代不可压缩的自然对流模型探索3D洛伦兹系统的扩展.
- 在Gay-Lussac (GL) 近似下研究来自雷利-贝纳德问题的动态系统.
- 分析这些新系统的行为,包括它们的稳定性和分叉性质.
主要方法:
- 应用盖伊-卢萨克 (GL) 近似法对雷利-贝纳德问题,放松奥伯贝克-布西内斯克 (OB) 假设.
- 开发一种新的不可压缩的动态系统,其中包括流体密度变化.
- 包括线性稳定性分析,莱普诺夫光谱和分叉图来描述系统动态.
主要成果:
- 基于GL近似的雷利-贝纳德问题已经制定了一个新的动态系统类.
- 这些系统成功地结合了非Boussinesq效应,同时保持了不可压缩性假设.
- 分析提供了这些扩展流体对流模型的稳定性和复杂行为.
结论:
- 盖伊-卢萨克近似为扩展经典流体动力学模型,如3D洛伦兹系统提供了有价值的框架.
- 开发的动态系统提供了更全面的自然对流,特别是当非Boussinesq效应显著时.
- 这项研究为在更广泛的物理条件下研究复杂流体现象和非线性动力学开辟了新的途径.
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