Temperature Statistics in Turbulent Rayleigh-Bénard Convection

Abstract

Rayleigh-Bénard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of the Lundgren-Monin-Novikov hierarchy known from homogeneous isotropic turbulence. The unclosed terms arising in the form of conditional averages are estimated from direct numerical simulations. Focusing on the statistics of temperature, the theoretical framework allows to interpret the statistical results in an illustrative manner, giving deeper insight into the connection between dynamics and statistics of Rayleigh-Bénard convection. The results are discussed in terms of typical flow features and the relation to the heat transfer.

This is an author-created, un-copyedited version of an article accepted for publication in New J. Phys. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at DOI:10.1088/1367-2630/13/1/015002

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Cited by in corpus (6)

• The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
• Resolved energy budget of superstructures in Rayleigh-Bénard convection
• Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space
• Generalized vortex-model for the inverse cascade of two-dimensional turbulence
• Two-Point Vorticity Statistics in the Inverse Turbulent Cascade
• Transport and mixing in control volumes through the lens of probability