Nonlinear Evolution of Strato-Rotational Instabilities in Taylor-Couette Flows

Taylor-Couette 流中层旋转不稳定性的非线性演化

• 批准号: 2106301
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2106301
• 关键词: Nonlinear; Evolution; Strato; Rotational; Instabilities

Axial density stratification in the Taylor-Couette set-up allows for flows which satisfy the Rayleigh stability criterion to become unstable to small perturbations. The linear analysis of these Strato-Rotational Instabilities (SRI) has been performed primarily in the context of inviscid fluids in narrow gaps, with only very few studies going beyond this regime for small regions of the parameter space. However, Luke Robin PhD (Leeds, 2017) thesis consisted in the development of the linear analysis to cover a larger region of the parameter space for both viscous and inviscid fluids. He identified unstable modes of a different nature, occurring in distinct regions of the parameter space, and also showed the existence of closed unstable domains in k-Re space.Here, we propose to extend the stability analysis performed by Luke Robins to the nonlinear regime, by means of High Performance Computations, using numerical codes accessible to the academic community (e.g. NEK5000). This problem is relevant to the understanding of fundamental processes in fluid mechanics with potentially direct applications to the theory of accretion discs.

泰勒-库埃特装置中的轴向密度分层允许满足瑞利稳定准则的流动在小扰动下变得不稳定。这些层旋转不稳定性（SRI）的线性分析主要是在窄间隙中的无粘性流体的情况下进行的，只有很少的研究超出了参数空间的小区域。然而，Luke Robin博士（Leeds, 2017）的论文包括了线性分析的发展，以覆盖粘性和非粘性流体参数空间的更大区域。他发现了不同性质的不稳定模态，出现在参数空间的不同区域，并证明了k-Re空间中存在封闭的不稳定域。在这里，我们建议将Luke Robins进行的稳定性分析扩展到非线性状态，通过高性能计算，使用学术界可访问的数值代码（例如NEK5000）。这个问题与理解流体力学的基本过程有关，并可能直接应用于吸积盘理论。