https://doi.org/10.1140/epjp/s13360-023-04284-8
Regular Article
Rotating convection in a higher gradient Navier–Stokes fluid
Department of Mathematical Sciences, University of Durham, Stockton Road, Durham, DH1 3LE, UK
a
brian.straughan@durham.ac.uk
Received:
9
May
2023
Accepted:
14
July
2023
Published online:
22
July
2023
We present a model for thermal convection in a horizontal layer rotating about a vertical axis, when the fluid is an incompressible Navier–Stokes fluid of Fried–Gurtin–Musesti type. This means the constitutive theory involves the second velocity gradient in addition to the velocity gradient itself. The governing equations then contain a hyperviscosity term which involves the bi-Laplacian operator. It is shown that the effect of rotation and the hyperviscosity effect both stabilize thermal convection when acting separately. However, when the rotation rate is sufficiently high the hyperviscosity can act to destabilize. This is an unexpected, counter intuitive effect.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
