We explore the various instabilities that potentially assail vortex cores in the presence of rotation and/or radially drifting solids. We first revisit the classical elliptical instability of rotating purely hydrodynamic vortices, showing that, in certain natural limits, the problem is governed by the ‘inverted Matthieu equation’, which provides a novel and remarkably simple way to conceptualise the parametric instability of the non-modal inertial waves. Second, we construct idealised vortex solutions involving a drifting dust fluid and a two-way drag force, using a multiple scales approach and the presence of a conserved ‘dusty potential vorticity’. These solutions are subject to new small-scale instabilities that can be categorised as ‘resonant drag instabilities’, involving a coupling between the dust advective mode and inertial waves, though as both are non-modal, the classical theory needs significant reworking.
De Geoffrey Vallis
De Luca Melzi
De Beatrice Pelloni
