Journal Article

A weakly non-linear theory for spiral density waves excited by accretion disc turbulence

T. Heinemann and J. C. B. Papaloizou

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 419, issue 2, pages 1085-1096
Published in print January 2012 | ISSN: 0035-8711
Published online December 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19763.x
A weakly non-linear theory for spiral density waves excited by accretion disc turbulence

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We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly non-linear regime. Such waves are generically found to be excited in simulations of turbulent accretion discs, in particular if the said turbulence arises from the magneto-rotational instability (MRI). We derive a modified Burgers equation governing their dynamics, which includes the effects of non-linear steepening, dispersion and a bulk viscosity to support shocks. We solve this equation approximately to obtain non-linear sawtooth solutions that are asymptotically valid at late times. In this limit, the presence of shocks is found to cause the wave amplitude to decrease with time as t−2. The validity of the analytic description is confirmed by direct numerical solution of the full non-linear equations of motion. The asymptotic forms of the wave profiles of the state variables are also found to occur in MRI simulations, indicating that dissipation due to shocks plays a significant role apart from any effects arising from direct coupling to the turbulence.

Keywords: accretion, accretion discs; turbulence; waves

Journal Article.  9026 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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