Potential vorticity dynamics in the framework of disk shallow-water theory: II. Mixed Barotropic-Baroclinic Instability

We extend exploration of potential vorticity instabilities in cold astrophysical disks whose mean states are baroclinic. In particular, we seek to demonstrate the potential existence of traditional baroclinic instabilities of meteorological studies in a simplified two-layer Philips Disk Model. Each disk layer is of constant but differing densities. The resulting mean azimuthal velocity profile shows a variation in the vertical direction implying that the system is baroclinic in the mean state. The stability of the system is treated in the context of disk shallow water theory wherein azimuthal disturbances are much longer than the corresponding radial or vertical scales. The normal-mode problem is solved numerically using two different methods. The results of a symmetric single layer barotropic model is considered and it is found that instability persists for models in which the potential vorticity profiles are not symmetric, consistent with previous results. The instaiblity is interpreted in terms of interacting Rossby waves. For a two layer system in which the flow is fundamentally baroclinic we report here that instability takes on the form of mixed barotropic-baroclinic type: instability occurs but it qualitatively follows the pattern of instability found in the barotropic models. Instability arises because of the phase locking and interaction of the Rossby waves between the two layers. The strength of the instability weakens as the density contrast between layers increases. (For full abstract see article.)