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Thermal convection in a higher-gradient Navier–Stokes fluid

Straughan, Brian

Thermal convection in a higher-gradient Navier–Stokes fluid Thumbnail


Brian Straughan


We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing models for thermal convection, analysing these in detail, and deriving critical Rayleigh and wave numbers for the onset of convective fluid motion. In addition to linear instability theory we present a careful analysis of fully nonlinear stability theory. The theories analysed all possess a bi-Laplacian term in addition to the normal spatial derivative term. The theories discussed are Stokes couple stress theory, dipolar fluid theory, Green–Naghdi theory, Fried–Gurtin–Musesti theory, and a second theory of Fried and Gurtin. We show that the Stokes couple stress theory and the Fried–Gurtin–Musesti theory involve the same partial differential equations while those of Green–Naghdi and dipolar theory are similar. However, we concentrate on boundary conditions which are crucial to understand all five theories and their differences.


Straughan, B. (2023). Thermal convection in a higher-gradient Navier–Stokes fluid. European Physical Journal Plus, 138(60),

Journal Article Type Article
Acceptance Date Dec 24, 2022
Online Publication Date Jan 21, 2023
Publication Date 2023
Deposit Date Jan 30, 2023
Publicly Available Date Jan 30, 2023
Journal The European Physical Journal Plus
Electronic ISSN 2190-5444
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 138
Issue 60


Published Journal Article (554 Kb)

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