Non-barotropic linear Rossby wave instability in three-dimensional disks

TL;DR

This study extends the understanding of Rossby wave instability in three-dimensional astrophysical disks by including baroclinic effects through an energy equation, revealing the influence of entropy distribution on vortex formation.

Contribution

It generalizes previous 3D linear RWI analysis to include non-uniform entropy, showing how baroclinity affects instability growth and vortex dynamics in stratified disks.

Findings

Non-uniform entropy has negligible effect on RWI growth rate when adiabatic index increases.

Pressure and density perturbations near pressure bumps increase away from the midplane.

Buoyancy forces significantly influence the internal flow of Rossby vortices.

Abstract

Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to disk-planet interaction, may be subject to the non-axisymmetric Rossby wave instability (RWI) that lead to vortex-formation. The linear instability has recently been demonstrated in three-dimensional (3D) barotropic disks. It is the purpose of this study to generalize the 3D linear problem to include an energy equation, thereby accounting for baroclinity in three-dimensions. Linear stability calculations are presented for radially structured, vertically stratified, geometrically-thin disks with non-uniform entropy distribution in both directions. Polytropic equilibria are considered but adiabatic perturbations assumed. The unperturbed disk has a localized radial density bump making it susceptible to the RWI. The linearized fluid equations are solved numerically as a partial differential equation eigenvalue problem. Emphasis on the ease of method implementation is given. It is found that when the polytropic index is fixed and adiabatic index increased, non-uniform entropy has negligible effect on the RWI growth rate, but pressure and density perturbation magnitudes near a pressure enhancement increases away from the midplane. The associated meridional flow is also qualitatively changed from homentropic calculations. Meridional vortical motion is identified in the nonhomentropic linear solution, as well as in a nonlinear global hydrodynamic simulation of the RWI in an initially isothermal disk evolved adiabatically. Numerical results suggest buoyancy forces play an important role in the internal flow of Rossby vortices.