  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.
