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

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.