Hydrodynamic response of rotationally supported flows in the small shearing box model

• Published in: Astronomy and astrophysics (Berlin) Vol. 486; no. 2; pp. 341 - 345
• Main Authors: Sternberg, A., Umurhan, O. M., Gil, Y., Regev, O.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.08.2008
• Subjects: accretion; accretion disks; Astronomy; Earth, ocean, space; Exact sciences and technology; hydrodynamics; Functionals; Box models; accretion, accretion disks; Eigenmode; Disturbances; Boundary conditions; Nonlinear problems; Initial value problems; hydrodynamics; Accretion disks; Bessel functions
• ISSN: 0004-6361; 1432-0746
• DOI: 10.1051/0004-6361:20077484

We examine the hydrodynamic response of the inviscid small shearing box model of a midplane section of a rotationally supported astrophysical disk. We formulate an energy functional ${\cal E}$ for the general nonlinear problem. We find that the fate of disturbances is related to the conservation of this quantity which, in turn, depends on the boundary conditions utilized: ${\cal E}$ is conserved for channel boundary conditions, while it is not conserved, in general, for shearing box conditions. Linearized disturbances subject to channel boundary conditions have normal-modes described by Bessel Functions and are qualitatively governed by a quantity Σ, which is a measure of the ratio between the azimuthal and vertical wavelengths. Inertial oscillations ensue if Σ > 1 – otherwise disturbances must be treated generally as an initial value problem. We reflect upon these results and offer a speculation.