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Near-onset dynamics in natural doubly diffusive convection

Published online by Cambridge University Press:  21 January 2022

Cédric Beaume Open the ORCID record for Cédric Beaume [Opens in a new window] ,
Alastair M. Rucklidge Open the ORCID record for Alastair M. Rucklidge [Opens in a new window]  and
Joanna Tumelty
Cédric Beaume*
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
Alastair M. Rucklidge
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
Joanna Tumelty
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the linear stability of the conductive state is known, but the convection patterns arising from the primary instability have only been studied for specific parameter values. We have extended this by determining the nature of the primary bifurcation for all values of the Lewis and Prandtl numbers using a weakly nonlinear analysis. The resulting convection branches are extended using numerical continuation and we find large-amplitude steady convection states can coexist with the stable conduction state for sub- and supercritical primary bifurcations. The stability of the convection states is investigated and attracting travelling waves and periodic orbits are identified using time stepping when these steady states are unstable.

JFM classification

Convection: Double diffusive convection Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A42
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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