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Non-axisymmetric α2Ω-dynamo Waves in Thin Stellar Shells


Bassom, AP and Kuzanyan, KM and Sokoloff, D and Soward, AM, Non-axisymmetric α2Ω-dynamo Waves in Thin Stellar Shells, Geophysical and Astrophysical Fluid Dynamics, 99, (4) pp. 309-336. ISSN 0309-1929 (2005) [Refereed Article]

Copyright Statement

Copyright 2005 Taylor & Francis Group Ltd.

DOI: doi:10.1080/03091920500159887


Linear α2Ω-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. (Griffiths, G.L., Bassom, A.P., Soward, A.M. and Kuzanyan, K.M., Nonlinear α2Ω-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85-133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local α-effect and radial gradient of the zonal shear flow. These effects are measured at latitude θ by the magnetic Reynolds numbers Rαf(θ) and RΩg(θ). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude θp under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Ω*(θ) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number Dc = RαRΩ is minimised by axisymmetric modes in the αΩ-limit (Rα→0). On the other hand, when Rα ≠ 0 there may exist a band of wave numbers 0 < m < m for which the non-axisymmetric modes have a smaller Dc than in the axisymmetric case. Here m is regarded as a continuous function of Rα with the property m→0 as Rα→0 and the band is only non-empty when m >1, which happens for sufficiently large Rα. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the α2Ω-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude θp not only propagates equatorwards but also westwards relative to the local angular velocity Ω*(θp). Since the critical dynamo number Dc = RαRΩ is O (1) for small Rα, the condition m > 1 for non-axisymmetric mode preference imposes an upper limit on the size of |dΩ*/dθ|.

Item Details

Item Type:Refereed Article
Keywords:planar vortex; inviscid relaxation; spiral wind-up; elliptical streamlines
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107126
Year Published:2005
Web of Science® Times Cited:12
Deposited By:Mathematics and Physics
Deposited On:2016-03-04
Last Modified:2016-07-26

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