On vortex rings around vortices: an optimal mechanism

Abstract

Stable columnar vortices subject to hydrodynamic noise (\eg turbulence) present some recurrent behaviours like the systematic development of vortex rings at the periphery of the vortex core. This phenomenon still lacks a comprehensive explanation, partly because it is not associated to an instability \textit{stricto sensu}. The aim of the present paper is to identify the physical mechanism triggering this intrinsic feature of vortices using an optimal perturbation analysis as a tool of investigation. We found that the generation of vortex rings is linked to the intense and rapid amplification of specific disturbances in the form of azimuthal velocity streaks that eventually evolve into azimuthal vorticity rolls generated by the rotational part of the local Coriolis force. This evolution thus appears to follow a scenario opposite to the classical lift-up view, where rolls give rise to streaks.