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
Abstract
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
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. |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & 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 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:982 |