Skip to main content

Research Repository

Advanced Search

Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms

Straughan, Brian

Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms Thumbnail


Authors

Brian Straughan



Abstract

We present models for convection in a mixture of viscous fluids when the layer is heated from below and simultaneously the pointwise volume concentration of one of the fluids is heavier below. This configuration produces a problem of competitive double diffusion since heating from below promotes instability, but the greater density of fluid below is stabilizing. The fluids are of linear viscous type which may contain Kelvin–Voigt terms, but density gradients due to the mixture appear strongly in the governing equations. The density gradients give rise to Korteweg stresses, but may also be described by theory due to Kazhikhov and Smagulov. The systems of equations which appear are thus highly nonlinear. The instability surface threshold is calculated and this is found to have a complex nonlinear shape, very different from the linear ones found in classical thermohaline convection in a Navier–Stokes fluid. It is shown that the Kazhikhov–Smagulov terms, Korteweg terms and Kelvin–Voigt term play a key role in acting as stabilizing agents but the associated effect is very nonlinear. Quantitative values of the instability surface are displayed showing the effect Korteweg terms, Kazhikhov–Smagulov terms, and the Kelvin Voigt term have. The nonlinear stability problem is addressed by means of a generalized energy theory deriving different results depending on which underlying theory is employed.

Citation

Straughan, B. (2023). Effect of Temperature Upon Double Diffusive Instability in Navier–Stokes–Voigt Models with Kazhikhov–Smagulov and Korteweg Terms. Applied Mathematics and Optimization, 87(54), Article 54. https://doi.org/10.1007/s00245-023-09964-6

Journal Article Type Article
Acceptance Date Jan 2, 2023
Online Publication Date Mar 13, 2023
Publication Date 2023
Deposit Date Apr 17, 2023
Publicly Available Date Apr 17, 2023
Journal Applied Mathematics & Optimization
Print ISSN 0095-4616
Electronic ISSN 1432-0606
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 87
Issue 54
Article Number 54
DOI https://doi.org/10.1007/s00245-023-09964-6

Files

Published Journal Article (493 Kb)
PDF

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.




You might also like



Downloadable Citations