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<p>In this paper, we study the instability threshold of Rayleigh number for the Rayleigh–Bénard (buoyancy driven) convection problem with temperature-dependent viscosity in an infinite layer. Of interest, we revisit the linear results of Pla et al. (Phys. D 239:1108–1119, 2010) and of Lafitte (C. R. Math. Acad. Sci. Paris 359:1165–1178, 2021) to obtain the critical Rayleigh number with variable viscosity, extending that one of as reported by Chandrasekhar (Hydrodynamics and Hydromagnetic Stability, Oxford University Press, London, 1961) for the classical Rayleigh–Bénard problem with constant viscosity. Hence, we prove the nonlinear instability of a conductive state in the supercritical regime of Rayleigh number with a wide class of initial data, based on the spectral analysis of Lafitte (C. R. Math. Acad. Sci. Paris 359:1165–1178, 2021).</p>

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Nonlinear instability of Rayleigh–Bénard convection with temperature-dependent viscosity

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Tien-Tai Nguyen

摘要

In this paper, we study the instability threshold of Rayleigh number for the Rayleigh–Bénard (buoyancy driven) convection problem with temperature-dependent viscosity in an infinite layer. Of interest, we revisit the linear results of Pla et al. (Phys. D 239:1108–1119, 2010) and of Lafitte (C. R. Math. Acad. Sci. Paris 359:1165–1178, 2021) to obtain the critical Rayleigh number with variable viscosity, extending that one of as reported by Chandrasekhar (Hydrodynamics and Hydromagnetic Stability, Oxford University Press, London, 1961) for the classical Rayleigh–Bénard problem with constant viscosity. Hence, we prove the nonlinear instability of a conductive state in the supercritical regime of Rayleigh number with a wide class of initial data, based on the spectral analysis of Lafitte (C. R. Math. Acad. Sci. Paris 359:1165–1178, 2021).