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Sharp global nonlinear stability for temperature dependent viscosity convection

Straughan, B.

Authors

B. Straughan



Abstract

With regard to the dependence of viscosity on temperature, an unconditional non-linear energy-stability analysis for thermal convection according to Navier-Stokes theory has not yet been developed. We here analyse three models of fluid behaviour proposed by O. A. Ladyzhenskaya. We show that by using these theories we can develop an unconditional analysis directly. Two of the models lead directly to an unconditional development employing L2 theory, while the third necessitates the introduction of a generalized energy also involving an L3 term. The nonlinear stability boundaries in all three cases are sharp when compared with the instability thresholds of linear theory.

Citation

Straughan, B. (2002). Sharp global nonlinear stability for temperature dependent viscosity convection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458(2023), 1773-1782. https://doi.org/10.1098/rspa.2001.0945

Journal Article Type Article
Publication Date Jul 8, 2002
Deposit Date Apr 23, 2007
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 458
Issue 2023
Pages 1773-1782
DOI https://doi.org/10.1098/rspa.2001.0945
Keywords Unconditional, Stability, Temperature-dependent viscosity, Thermal convection, Ladyzhenskaya's models,

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