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Fixed-flux Rayleigh–Bénard convection in doubly periodic domains: generation of large-scale shear

Published online by Cambridge University Press:  11 January 2024

Chang Liu Open the ORCID record for Chang Liu [Opens in a new window] ,
Manjul Sharma Open the ORCID record for Manjul Sharma [Opens in a new window] ,
Keith Julien Open the ORCID record for Keith Julien [Opens in a new window]  and
Edgar Knobloch Open the ORCID record for Edgar Knobloch [Opens in a new window]
Chang Liu*
Affiliation:
Department of Physics, University of California, Berkeley, CA 94720, USA School of Mechanical, Aerospace, and Manufacturing Engineering, University of Connecticut, Storrs, CT 06269, USA
Manjul Sharma
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
Keith Julien
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
Edgar Knobloch
Affiliation:
Department of Physics, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: chang_liu@uconn.edu
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Abstract

This work studies two-dimensional fixed-flux Rayleigh–Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyses its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For $Pr=1$, where $Pr$ is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behaviour between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated travelling waves without flow reversal. Single-mode equations reproduce this moderate Rayleigh number behaviour well. At high Rayleigh numbers, chaotic behaviour dominated by modulated travelling waves appears. These transitions are characteristic of high wavenumber elevator modes since the vertical wavenumber of the secondary instability is linearly proportional to the horizontal wavenumber of the elevator mode. At a low $Pr$, relaxation oscillations between the conduction state and the elevator mode appear, followed by quasi-periodic and chaotic behaviour as the Rayleigh number increases. In the high $Pr$ regime, the large-scale shear weakens, and the flow shows bursting behaviour that can lead to significantly increased heat transport or even intermittent stable stratification.

JFM classification

Convection: Buoyancy-driven instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A19
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© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Liu et al. supplementary movie 1

Temperature deviation $T(x,z,t)$ corresponding to Figure 3.
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Liu et al. supplementary movie 2

Temperature deviation $T(x,z,t)$ corresponding to Figure 17.
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Supplementary material: File

Liu et al. supplementary movie 3

Temperature deviation $T(x,z,t)$ corresponding to Figure 25.
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