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

Taylor-Couette装置中的轴向密度分层允许满足Rayleigh稳定性准则的流动在小扰动下变得不稳定。对这些直转不稳定性(SRI)的线性分析主要是在窄间隙中无粘流体的背景下进行的，只有极少数研究超出了参数空间的小区域。然而，Luke Robin PhD(Leeds，2017)的论文包括了线性分析的发展，以涵盖粘性和无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出现在参数空间的不同区域，并证明了k-Re空间中闭合不稳定域的存在。在这里，我们建议将Luke Robins所做的稳定性分析扩展到非线性区域，通过高性能计算的方法，使用学术界可用的数值代码(例如NEK5000)。这个问题与理解流体力学中的基本过程有关，有可能直接应用于吸积盘理论。

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.