Reviews of topical problems

Transient dynamics of perturbations in astrophysical disks

 a, b,  b
a Lomonosov Moscow State University, Department of Physics, Vorobevy gory, Moscow, 119992, Russian Federation
b Lomonosov Moscow State University, Shternberg State Astronomical Institute, Universitetskii prosp. 13, Moscow, 119889, Russian Federation

This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational instability? In this case a rotational homogeneous inviscid flow with a Keplerian angular velocity profile is spectrally stable, making the transient growth of perturbations a candidate mechanism for energy transfer from the regular motion to perturbations. Transient perturbations differ qualitatively from perturbation modes and can grow substantially in shear flows due to the nonnormality of their dynamical evolution operator. Since the eigenvectors of this operator, alias perturbation modes, are mutually nonorthogonal, they can mutually interfere, resulting in the transient growth of their linear combinations. Physically, a growing transient perturbation is a leading spiral whose branches are shrunk as a result of the differential rotation of the flow. This paper discusses in detail the transient growth of vortex shearing harmonics in the spatially local limit as well as methods for identifying the optimal (fastest growth) perturbations. Special attention is given to obtaining such solutions variationally, by integrating the direct and adjoint equations forward and back in time, respectively. The material is presented in a newcomer-friendly style.

Text can be downloaded in Russian. English translation is available here.
Keywords: hydrodynamics, turbulence, accretion disks
PACS: 02.30.−f, 02.60.Pn, 47.32.C−, 97.10.Gz, 97.82.Jw, 98.62.Mw (all)
DOI: 10.3367/UFNe.0185.201511a.1129
Citation: Razdoburdin D N, Zhuravlev V V "Transient dynamics of perturbations in astrophysical disks" Phys. Usp. 58 1031–1058 (2015)
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Received: 18th, May 2015, revised: 1st, September 2015, 8th, September 2015

Оригинал: Раздобурдин Д Н, Журавлёв В В «Транзиентная динамика возмущений в астрофизических дисках» УФН 185 1129–1161 (2015); DOI: 10.3367/UFNr.0185.201511a.1129

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