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Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics

Beaume, Cédric and Bergeon, Alain and Knobloch, Edgar Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics. (2018) Journal of Fluid Mechanics, 840. 74-105. ISSN 0022-1120

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Official URL: https://doi.org/10.1017/jfm.2017.905

Abstract

Three-dimensional doubly diffusive convection in a closed vertically extended container driven by competing horizontal temperature and concentration gradients is studied by a combination of direct numerical simulation and linear stability analysis. No-slip boundary conditions are imposed on all six container walls. The buoyancy number is taken to be to ensure the presence of a conduction state. The primary instability is subcritical and generates two families of spatially localized steady states known as convectons. The convectons bifurcate directly from the conduction state and are organized in a pair of primary branches that snake within a well-defined range of Rayleigh numbers as the convectons grow in length. Secondary instabilities generating twist result in secondary snaking branches of twisted convectons. These destabilize the primary convectons and are responsible for the absence of stable steady states, localized or otherwise, in the subcritical regime. Thus all initial conditions in this regime collapse to the conduction state. As a result, once the Rayleigh number for the primary instability of the conduction state is exceeded, the system exhibits an abrupt transition to large-amplitude relaxation oscillations resembling bursts with no hysteresis. These numerical results are confirmed here by determining the stability properties of both convecton types as well as the domain-filling states. The number of unstable modes of both primary and secondary convectons of different lengths follows a pattern that allows the prediction of their stability properties based on their length alone. The instability of the convectons also results in a dramatic change in the dynamics of the system outside the snaking region that arises when the twist instability operates on a time scale faster than the time scale on which new rolls are nucleated. The results obtained are expected to be applicable in various pattern-forming systems exhibiting localized structures, including convection and shear flows.

Item Type:Article
Additional Information:Thanks to CUP editor. The original PDF of the article can be found at https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/threedimensional-doubly-diffusive-convectons-instability-and-transition-to-complex-dynamics/F186B5F652BDA190BDC8ED408D61ECDC
HAL Id:hal-01801735
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > University of Leeds (UNITED KINGDOM)
Other partners > University of California - UC Berkeley (USA)
Laboratory name:
Funders:
National Science Foundation
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Deposited By: Alain BERGEON
Deposited On:28 May 2018 14:18

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