Year: 2025
Type: article
Abstract: The linear and nonlinear dynamics of centrifugal instability in Taylor–Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) of cylindrical Couette flow confirms that the stabilising role of stratification in centrifugal instability is suppressed by strong thermal diffusion (i.e. low Prandtl number $Pr$ ). For $Pr\ll 1$ , it is verified that the instability dependence on thermal diffusion and stratification with the non-dimensional Brunt–Väisälä frequency $N$ can be prescribed by a single rescaled parameter $P_{N}=N^{2}Pr$ . From direct numerical simulation (DNS), various nonlinear features such as axisymmetric Taylor vortices at saturation, secondary instability leading to non-axisymmetric patterns or transition to chaotic states are investigated for various values of $Pr\leqslant 1$ and Reynolds number $Re_{i}$ . Two-dimensional bi-global LSA of axisymmetric Taylor vortices, which appear as primary centrifugal instability saturates nonlinearly, is also performed to find the secondary critical Reynolds number $Re_{i,2}$ at which the Taylor vortices become unstable by non-axisymmetric perturbation. The bi-global LSA reveals that $Re_{i,2}$ increases (i.e. the onset of secondary instability is delayed) in the range $10^{-3}\lt Pr\lt 1$ at $N=1$ or as $N$ increases at $Pr=0.01$ . Secondary instability leading to highly non-axisymmetric or irregular chaotic patterns is further investigated by three-dimensional DNS. The Nusselt number $Nu$ is also computed from the torque at the inner cylinder for various $Pr$ and $Re_{i}$ at $N=1$ to describe how the angular momentum transfer increases with $Re_{i}$ and how $Nu$ varies differently for saturated and chaotic states.
Source: Journal of Fluid Mechanics
DOI: 10.1017/jfm.2025.261
Author: Junho Park
Institution: Coventry University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4409948909