2005/01/01 by Bryan M. Johnson, Charles F. Gammie · 5 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics and Star Formation Studies #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.1086/430081
published as Astrophys.J. 626 (2005) 978-990 · 28 pages, 1 figure, submitted to the Astrophysical Journal
arxiv created 2005/01/01 · openalex publication_date 2005/06/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We consider the nonaxisymmetric linear theory of radially stratified disks. We work in a shearing-sheet-like approximation, in which the vertical structure of the disk is neglected, and develop equations for the evolution of a plane-wave perturbation comoving with the shear flow (a shearing wave, or "shwave"). We calculate a complete solution set for compressive and incompressive short-wavelength perturbations in both the stratified and unstratified shearing-sheet models. We develop expressions for the late-time asymptotic evolution of an individual shwave, as well as for the expectation value of the energy for an ensemble of shwaves that are initially distributed isotropically in k -space. We find that (1) incompressive, short-wavelength perturbations in the unstratified shearing sheet exhibit transient growth and asymptotic decay, but the energy of an ensemble of such shwaves is constant with time; (2) short-wavelength compressive shwaves grow asymptotically in the unstratified shearing sheet, as does the energy of an ensemble of such shwaves; (3) incompressive shwaves in the stratified shearing sheet have density and azimuthal velocity perturbations δΣ, δ v y ~ t -Ri (for |Ri| ≪ 1), where Ri ≡ N /( Ω) 2 is the Richardson number, N is the square of the radial Brunt-Väisälä frequency, and Ω is the effective shear rate; and (4) the energy of an ensemble of incompressive shwaves in the stratified shearing sheet behaves asymptotically as Ri t 1-4Ri for |Ri| ≪ 1. For Keplerian disks with modest radial gradients, |Ri| is expected to be ≪1, and there is therefore weak growth in a single shwave for Ri < 0 and near-linear growth in the energy of an ensemble of shwaves, independent of the sign of Ri.