Linear coupling of modes in two-dimensional radially stratified astrophysical discs

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: this includes 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.