On reversals in 2D turbulent Rayleigh-Bénard convection: insights from embedding theory and comparison with Proper Orthogonal Decomposition analysis

Abstract : Turbulent Rayleigh-Bénard convection in a 2D square cell is characterized by the existence of a large-scale circulation which varies intermit- tently. We focus on a range of Rayleigh numbers where the large-scale circulation experiences rapid non-trivial reversals from one quasi-steady (or meta-stable) state to another. In previous work [B. Podvin and A. Sergent, J. Fluid Mech. 766, 172201 (2015); B. Podvin and A. Sergent, Phys. Rev. E 95, 013112 (2017)], we applied proper orthogonal decomposition (POD) to the joint temperature and velocity fields at a given Rayleigh number, and the dynamics of the flow were characterized in a multi-dimensional POD space. Here, we show that several of those findings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of the embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specifically, the embedding theory confirms that the switches among meta-stable states are uncorrelated. It also shows that, despite the large number of degrees of freedom of the turbulent Rayleigh Bénard flow, a low dimensional description of its physics can be derived with low computational efforts, providing that a single global observable reflecting the symmetry of the system is identified. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established.
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Submitted on : Monday, July 1, 2019 - 4:29:43 PM
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  • HAL Id : hal-02170060, version 1

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Davide Faranda, Bérengère Podvin, Anne Sergent. On reversals in 2D turbulent Rayleigh-Bénard convection: insights from embedding theory and comparison with Proper Orthogonal Decomposition analysis. Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP, 2019, 29, pp.1-18. ⟨hal-02170060⟩

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