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Analysis of the shearing instability in nonlinear convection and magnetoconvection

Rucklidge, A.M. and Matthews, P.C. (1996) Analysis of the shearing instability in nonlinear convection and magnetoconvection. Nonlinearity, 9 (2). pp. 311-351. ISSN 1361-6544


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Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1996 IOP Publishing Ltd and LMS Publishing Ltd. This is an author produced version of an article published in Nonlinearity. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: A. M. Rucklidge
Date Deposited: 06 Feb 2006
Last Modified: 12 Jun 2014 13:00
Published Version: http://www.iop.org/EJ/abstract/0951-7715/9/2/003
Status: Published
Refereed: Yes
Identification Number: 10.1088/0951-7715/9/2/003
URI: http://eprints.whiterose.ac.uk/id/eprint/982

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