Analysis of inviscid shear instability of axisymmetric flows

Abstract: Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for stability improves upon the classical result of \cite{Batchelor_Gill_1962}, following the idea of the second Kelvin-Arnol'd stability theorem. A novel sufficient condition for instability is also derived by extending the recently proposed hurdle theorem for parallel flows \citep{Deguchi_Hirota_Dowling_2024}. These analytical criteria are applied to annular and pipe model flows and are shown to effectively predict the neutral parameters obtained from eigenvalue computations of the stability problem.