Inertial waves near corotation in 3D hydrodynamical disks

TL;DR

This paper investigates inertial waves in 3D hydrodynamical disks, showing that many cannot form trapped modes due to corotation singularities, which instead lead to continuous spectra and shearing waves, impacting understanding of disk oscillations.

Contribution

It reveals that a broad class of inertial waves cannot be trapped as normal modes near corotation, clarifying their spectral nature and stability in 3D disks.

Findings

Many inertial waves are part of a continuous spectrum.

Corotation singularities prevent trapping of certain inertial modes.

Corotation stabilizes perturbations in slender tori.

Abstract

This paper concerns the interaction between non-axisymmetric inertial waves and their corotation resonances in a hydrodynamical disk. Inertial waves are of interest because they can localise in resonant cavities circumscribed by Lindblad radii, and as a consequence exhibit discrete oscillation frequencies that may be observed. It is often hypothesised that these trapped eigenmodes are affiliated with the poorly understood QPO phenomenon. We demonstrate that a large class of non-axisymmetric 3D inertial waves cannot manifest as trapped normal modes. This class includes any inertial wave whose resonant cavity contains a corotation singularity. Instead, these `singular' modes constitute a continuous spectrum and, as an ensemble, are convected with the flow, giving rise to shearing waves. Lastly, we present a simple demonstration of how the corotation singularity stabilizes three-dimensional perturbations in a slender torus.