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Rotating convection in a higher gradient Navier–Stokes fluid

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Abstract

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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Acknowledgements

This work was supported by an Emeritus Fellowship of the Leverhulme Trust, EM-2019-022/9.

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  1. Department of Mathematical Sciences, University of Durham, Stockton Road, Durham, DH1 3LE, UK

    Brian Straughan

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  1. Brian Straughan
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Correspondence to Brian Straughan.

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Straughan, B. Rotating convection in a higher gradient Navier–Stokes fluid. Eur. Phys. J. Plus 138, 640 (2023). https://doi.org/10.1140/epjp/s13360-023-04284-8

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