Stability of density-stratified viscous Taylor-Couette flows

Free access article

Issue		A&A Volume 438, Number 2, August I 2005


Page(s)		411 - 417
Section		Astrophysical processes
DOI		http://dx.doi.org/10.1051/0004-6361:20042492

A&A 438, 411-417 (2005)
DOI: 10.1051/0004-6361:20042492

Stability of density-stratified viscous Taylor-Couette flows

D. Shalybkov^{1, 2} and G. Rüdiger^{1, 3}

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: gruediger@aip.de
² A.F. Ioffe Institute for Physics and Technology, 194021 St. Petersburg, Russia
³ Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK

(Received 7 December 2004 / Accepted 21 April 2005)

Abstract
We consider the stability of density-stratified viscous Taylor-Couette flow using the Boussinesq approximation, but without any use of the short-wave approximation. Flows which are unstable according to the Rayleigh criterion ( $\hat \mu<\hat \eta^2$ , with $\hat \mu={\it\Omega}_{\rm out}/{\it\Omega}_{\rm in }$ and $\hat \eta=R_{\rm in}/R_{\rm out}$ ), now develop overstable axisymmetric Taylor vortices. However, for the wide-gap container considered here, we find that nonaxisymmetric modes are preferred. These nonaxisymmetric modes are unstable also beyond the Rayleigh line. For such modes the instability condition seems simply to be $\hat\mu<1$ , as stressed by Yavneh, McWilliams & Molemaker (2001). However, if the rotation law is too flat, fulfilling the condition $\hat \mu>\hat \eta$ , we never found unstable modes. The Reynolds numbers grow rapidly to very large values as this limit is approached (see Figs. 3 and 4). Also striking is that the marginal stability lines for the higher m penetrate less and less into the region beyond the Rayleigh line, so that we have to consider the stratorotational instability as a "low-m instability". Finally, we briefly discuss the applicability of these results to the stability problem of accretion disks, with their strong density stratification and rapid rotation.

Key words: accretion, accretion disks -- hydrodynamics -- turbulence

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