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Linear and non-linear stability thresholds for thermal convection in a box

Hill, Antony A.; Straughan, B.

Authors

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Antony Hill Antony.Hill@uwe.ac.uk
College Dean of Learning and Teaching

B. Straughan



Abstract

We analyse the problem of finding instability thresholds and global non-linear stability bounds for thermal convection in a linearly viscous fluid in a finite box. The vertical walls are maintained at different temperatures which gives rise to a non-uniform temperature field in steady state. This problem was previously analysed by Georgescu and Mansutti (Int. J. Non-Linear Mech. 1999; 34:603-613). In our work we determine the linear instability threshold to be well above the global stability boundary found by an energy method. Since the perturbed system is not symmetric we expect this to be the case, and our analysis yields a parameter region where possible sub-critical instabilities may be found. Copyright © 2006 John Wiley & Sons, Ltd.

Citation

Hill, A. A., & Straughan, B. (2006). Linear and non-linear stability thresholds for thermal convection in a box. Mathematical Methods in the Applied Sciences, 29(17), 2123-2132. https://doi.org/10.1002/mma.770

Journal Article Type Article
Publication Date Nov 25, 2006
Journal Mathematical Methods in the Applied Sciences
Print ISSN 0170-4214
Electronic ISSN 1099-1476
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 29
Issue 17
Pages 2123-2132
DOI https://doi.org/10.1002/mma.770
Keywords energy method, subcritical instabilities, spectral methods
Public URL https://uwe-repository.worktribe.com/output/1044163
Publisher URL http://dx.doi.org/10.1002/mma.770