Sharp global nonlinear stability for temperature dependent viscosity convection

Straughan, B.

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,
• Public URL: https://durham-repository.worktribe.com/output/1622271