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

泰勒-库埃特装置中的轴向密度分层允许满足瑞利稳定性准则的流动对小扰动变得不稳定。线性分析，这些层旋转不稳定性（SRI）已进行主要是在无粘性流体的背景下，在狭窄的差距，只有很少的研究超出了这个制度的参数空间的小区域。然而，Luke Robin博士（利兹，2017年）的论文包括线性分析的发展，以覆盖粘性和非粘性流体的参数空间的更大区域。他确定了不同性质的不稳定模式，发生在不同的区域的参数空间，并显示存在封闭的不稳定域在k-Re spaces.Here，我们建议扩展的稳定性分析卢克罗宾斯进行的非线性制度，通过高性能计算，使用数值代码访问学术界（如NEK 5000）。这个问题是相关的流体力学的基本过程的理解与潜在的直接应用理论的吸积盘。

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.