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Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order

Straughan, B.

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Authors

B. Straughan



Abstract

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.

Citation

Straughan, B. (2022). Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order. Rendiconti del Circolo Matematico di Palermo Series 2, 71(1), 187-206. https://doi.org/10.1007/s12215-020-00588-1

Journal Article Type Article
Acceptance Date Dec 28, 2020
Online Publication Date Jan 18, 2021
Publication Date 2022-04
Deposit Date Apr 21, 2021
Publicly Available Date Apr 21, 2021
Journal Rendiconti del Circolo Matematico di Palermo Series 2
Print ISSN 0009-725X
Electronic ISSN 1973-4409
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 71
Issue 1
Pages 187-206
DOI https://doi.org/10.1007/s12215-020-00588-1

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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/.




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