Short wavelength local instabilities of a circular Couette flow with radial temperature gradient

TL;DR

This study analyzes how radial temperature gradients influence the stability of circular Couette flow, revealing that inward gradients can destabilize otherwise stable flows through different bifurcation mechanisms.

Contribution

It provides a detailed linear stability analysis considering both thermal and viscous effects, including axisymmetric and nonaxisymmetric perturbations, which is novel in the context of radial temperature gradients.

Findings

Inward temperature gradient destabilizes Rayleigh stable flow.

Destabilization occurs via Hopf bifurcation for highly conductive fluids.

Destabilization occurs via steady bifurcation when viscosity dominates.

Abstract

We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with the radial temperature gradient. Axisymmetric and nonaxisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of the asymmetry of the heating both on the centrifugally unstable flows and on the onset of the instabilities of the centrifugally stable flows, including the flow with the Keplerian shear profile, is thoroughly investigated. It is found that the inward temperature gradient destabilizes the Rayleigh stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.