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

Straughan, B.

doi:10.1007/s12215-020-00588-1

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

Straughan, B.

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
Public URL	https://durham-repository.worktribe.com/output/1244053

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