Thermosolutal Convection with a Navier–Stokes–Voigt Fluid

Straughan, Brian

Abstract

We present a model for convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a dissolved salt field in a complex viscoelastic fluid of Navier–Stokes–Voigt type. The Kelvin–Voigt parameter is seen to play a very important role in acting as a stabilizing agent when the convection is of oscillatory type. The quantitative size of this effect is displayed. Nonlinear stability is also discussed, and it is briefly indicated how the global nonlinear stability limit may be increased, although there still remains a region of potential sub-critical instability, especially when the Kelvin–Voigt parameter increases.

Citation

Straughan, B. (2021). Thermosolutal Convection with a Navier–Stokes–Voigt Fluid. Applied Mathematics and Optimization, 84(3), 2587-2599. https://doi.org/10.1007/s00245-020-09719-7

• Journal Article Type: Article
• Online Publication Date: Sep 20, 2020
• Publication Date: 2021-12
• Deposit Date: Oct 7, 2020
• Publicly Available Date: Oct 7, 2020
• Journal: Applied Mathematics and Optimization
• Print ISSN: 0095-4616
• Electronic ISSN: 1432-0606
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 84
• Issue: 3
• Pages: 2587-2599
• DOI: https://doi.org/10.1007/s00245-020-09719-7
• Public URL: https://durham-repository.worktribe.com/output/1260278