NONBAROTROPIC LINEAR ROSSBY WAVE INSTABILITY IN THREEDIMENSIONAL DISKS
Abstract
Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to diskplanet interaction, may be subject to the nonaxisymmetric Rossby wave instability (RWI) that leads to vortex formation. The linear instability has recently been demonstrated in threedimensional (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 nonuniform 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, nonuniform entropy has negligible effect on the RWI growth rate, but pressure and density perturbation magnitudes near a pressure enhancement increase 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 asmore »
 Authors:
 Canadian Institute for Theoretical Astrophysics, 60 St. George Street, Toronto, ON M5S 3H8 (Canada)
 Publication Date:
 OSTI Identifier:
 22127015
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 765; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ASTRONOMY; ASTROPHYSICS; AXIAL SYMMETRY; COMPUTERIZED SIMULATION; DISTURBANCES; EIGENVALUES; ENTROPY; HYDRODYNAMICS; INDEXES; INSTABILITY; PARTIAL DIFFERENTIAL EQUATIONS; PLANETS; PROTOPLANETS; THREEDIMENSIONAL CALCULATIONS; VORTICES
Citation Formats
Lin, MinKai, Email: mklin924@cita.utoronto.ca. NONBAROTROPIC LINEAR ROSSBY WAVE INSTABILITY IN THREEDIMENSIONAL DISKS. United States: N. p., 2013.
Web. doi:10.1088/0004637X/765/2/84.
Lin, MinKai, Email: mklin924@cita.utoronto.ca. NONBAROTROPIC LINEAR ROSSBY WAVE INSTABILITY IN THREEDIMENSIONAL DISKS. United States. doi:10.1088/0004637X/765/2/84.
Lin, MinKai, Email: mklin924@cita.utoronto.ca. 2013.
"NONBAROTROPIC LINEAR ROSSBY WAVE INSTABILITY IN THREEDIMENSIONAL DISKS". United States.
doi:10.1088/0004637X/765/2/84.
@article{osti_22127015,
title = {NONBAROTROPIC LINEAR ROSSBY WAVE INSTABILITY IN THREEDIMENSIONAL DISKS},
author = {Lin, MinKai, Email: mklin924@cita.utoronto.ca},
abstractNote = {Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to diskplanet interaction, may be subject to the nonaxisymmetric Rossby wave instability (RWI) that leads to vortex formation. The linear instability has recently been demonstrated in threedimensional (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 nonuniform 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, nonuniform entropy has negligible effect on the RWI growth rate, but pressure and density perturbation magnitudes near a pressure enhancement increase 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 that buoyancy forces play an important role in the internal flow of Rossby vortices.},
doi = {10.1088/0004637X/765/2/84},
journal = {Astrophysical Journal},
number = 2,
volume = 765,
place = {United States},
year = 2013,
month = 3
}

Numerical calculations of the linear Rossby wave instability (RWI) in global threedimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and twodimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggests the RWI is predominantly a 2D instabilitymore »

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Linear corotation torques in nonbarotropic disks
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