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 BatchelorGill1962, 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 DeguchiHirotaDowling2024. 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.
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