在极端一维的汉堡流中三元相的对齐
Bartosz Protas1, Di Kang1, Miguel D Bustamante2
1Department of Mathematics and Statistics, <a href="https://ror.org/02fa3aq29">McMaster University</a>, Hamilton, Ontario, Canada, L8S 4L8.
Physical review. E
|June 22, 2024
概括
汉堡流中的非线性模态相互作用显示了相对齐,最大限度地将能量转移到较小的尺度上. 一些关键的相互作用主导着这种能量流,这表明了流体动力学的缩小模型.
科学领域:
- 流体动力学 流体动力学
- 非线性动力学是一种非线性动力学.
- 计算物理 计算物理
背景情况:
- 汉堡流作为欧勒和纳维埃-斯托克斯方程的简化模型,对于理解流体动力学至关重要.
- 非线性模态相互作用,特别是三元相互作用,控制流体系统中跨尺度的能量转移.
- 了解这些相互作用中的相位对齐是预测能量流和系统行为的关键.
研究的目的:
- 分析无和粘性Burgers流中的非线性模态相互作用的细结构.
- 在三元相互作用中研究福里埃模式的偏好相位对齐.
- 开发诊断工具,探测三元相互作用的连贯性及其对能量流的影响.
主要方法:
- 分析1D无粘性和粘性汉堡流,具有各种初始条件 (单模,极端,通用).
- 开发和应用诊断工具来量化三元相互作用中的连贯性.
- 确定主导三合体,负责不同波数的能量流.
主要成果:
- 涉及含有能量的里叶模式的三合体始终对齐相位,以最大限度地使能量流向小尺度.
- 一个普遍的统计分布显示,少数三合体实现了大部分的能量流.
- 主导三合体包括局部和非局部相互作用的混合物,随着时间的推移,非局部相互作用变得越来越重要.
结论:
- 结果表明,有可能构建具有较少自由度的 Burgers 流动的减少模式表示.
- 在初始数据中随机化空间连贯性不会显著改变三元交互动态或能量流.
- 这些发现提供了关于乱和混乱系统中能量转移的基本机制的见解.
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