Gravito-inertial waves in a differentially rotating spherical shell

TL;DR

This paper analyzes gravito-inertial waves in a differentially rotating spherical shell, revealing complex wave behaviors, potential instabilities driven by differential rotation, and a rich spectrum with implications for rotating stars and planets.

Contribution

It provides a detailed analysis of gravito-inertial wave propagation and stability in a differentially rotating spherical shell, highlighting new instability mechanisms and spectral properties.

Findings

Waves often focus around short-period attractors or are trapped by turning surfaces.

Some eigenmodes are weakly affected by viscosity and heat diffusion, resembling regular modes.

Differential rotation can destabilize certain axisymmetric and non-axisymmetric modes.

Abstract

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.