1209.0470 (Min-Kai Lin)

Non-barotropic linear Rossby wave instability in three-dimensional disks    [PDF]

Min-Kai Lin

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 Rossby wave instability (RWI). The linearized fluid equations are solved numerically as a partial differential equation eigenvalue problem. It is found that when the polytropic index is fixed and adiabatic index varied, 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.

View original: http://arxiv.org/abs/1209.0470