The excitation of inertial-acoustic waves through turbulent fluctuations in accretion discs I: WKBJ theory

Content Provider	Semantic Scholar
Author	Heinemann, Tobias Papaloizou, John C. B.
Copyright Year	2008
Abstract	We study and elucidate the mechanism of inertial-acoustic wave excitation in a turbulent, differentially rotating flow. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these using a WKBJ method. It is found that, for a particular azimuthal wave length, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Pairs of trailing waves of equal amplitude propagating in opposite directions are produced and give rise to an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wave length. By solving the wave amplitude equations numerically we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation approach completely the important wave source terms need to be specified. Assuming conditions of weak non-linearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wave lengths, the optimal azimuthal wave length produced is found to be determined solely by the WKBJ response and is estimated to be 2pi H, with H being the putative disc scale height. In a following paper by Heinemann & Papaloizou, we perform direct three dimensional simulations and compare results manifesting the wave excitation process and its source with the assumptions made and the theory developed here in detail, finding excellent agreement.
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Alternate Webpage(s)	http://arxiv.org/pdf/0812.2068v2.pdf
Alternate Webpage(s)	http://arxiv.org/pdf/0812.2068v1.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article