We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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

Straughan, B. (2021) 'Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order.', Rendiconti del Circolo Matematico di Palermo Series 2 .


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.

Item Type:Article
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution 4.0.
Download PDF
Publisher Web site:
Publisher 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
Date accepted:28 December 2020
Date deposited:21 April 2021
Date of first online publication:18 January 2021
Date first made open access:21 April 2021

Save or Share this output

Look up in GoogleScholar