Stability of stratified and highly-diffusive Taylor-Couette flow

Understanding the role of thermal diffusion is important for naturally-occurring systems where fluid flow is coupled with heat transfer. The thermal diffusion is characterized by the Prandtl number Pr=nu/kappa, the ratio between fluid kinematic viscosity nu and thermal diffusivity kappa. The Prandtl number varies; for instance, Pr of O(1) for the air, Pr of O(10^{-2}) in the liquid metal core of the Earth, or Pr of O(10^{-6}) in the interior of the Sun and stars. In stably stratified flows, it has been known that high thermal diffusivity at low Pr suppresses the stratification effect. Our study aims to explore the effect of thermal diffusion in the context of Taylor-Couette (TC) flow with axial stratification. We first conduct linear stability analysis with a particular focus on Prandtl-number dependence and demonstrate how the stability of stratified TC flow is modified with high thermal diffusivity. We will also describe a self-similar behavior observed for this TC flow. Furthermore, there will be discussion on the effect of fast thermal diffusion in nonlinear instability and secondary instability using generalized quasi-linear approximation and 2D global stability analysis.