Linear coupling of modes in 2D radially stratified astrophysical discs

TL;DR

This paper analyzes how different linear modes in radially stratified astrophysical discs interact and couple, revealing mechanisms that can generate vortical structures influencing disc dynamics.

Contribution

It introduces a three-mode formalism to study asymmetric coupling of vorticity, entropy, and compressional modes in 2D stratified discs, highlighting new mode interactions.

Findings

P-modes can generate potential vorticity through mode coupling.

Asymmetric coupling occurs between S, W, and P modes.

Compressional perturbations influence vortical structure development.

Abstract

We investigate mode coupling in a two dimensional compressible disc with radial stratification and differential rotation. We employ the global radial scaling of linear perturbations and study the linear modes in the local shearing sheet approximation. We employ a three-mode formalism and study the vorticity (W), entropy (S) and compressional (P) modes and their coupling properties. The system exhibits asymmetric three-mode coupling: these include mutual coupling of S and P-modes, S and W-modes, and asymmetric coupling between the W and P-modes. P-mode perturbations are able to generate potential vorticity through indirect three-mode coupling. This process indicates that compressional perturbations can lead to the development of vortical structures and influence the dynamics of radially stratified hydrodynamic accretion and protoplanetary discs.