EDP Sciences
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Volume 486, Number 2, August I 2008
Page(s) 341 - 345
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20077484
Published online 27 May 2008

A&A 486, 341-345 (2008)
DOI: 10.1051/0004-6361:20077484

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

A. Sternberg1, O. M. Umurhan1, 2, 3, Y. Gil1, and O. Regev1, 4

1  Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
    e-mail: phassaf@techunix.technion.ac.il
2  Department of Geophysics and Space Sciences, Tel-Aviv University, Tel-Aviv, Israel
3  Department of Astronomy, City College of San Francisco, San Francisco, CA 94112, USA
4  Department of Astronomy, Columbia University, New York, NY 10025, USA

Received 15 March 2007 / Accepted 1 April 2008

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 $\Sigma$, which is a measure of the ratio between the azimuthal and vertical wavelengths. Inertial oscillations ensue if $\Sigma$ > 1 - otherwise disturbances must be treated generally as an initial value problem. We reflect upon these results and offer a speculation.

Key words: accretion, accretion disks -- hydrodynamics

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