A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

Xiaozhou He; Eberhard Bodenschatz; Guenter Ahlers

Theoretical and Applied Mechanics Letters (Feb 2021)

A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

Xiaozhou He,
Eberhard Bodenschatz,
Guenter Ahlers

Affiliations

Xiaozhou He: School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen 518055, China; Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany; International Collaboration for Turbulence Research; Corresponding author.
Eberhard Bodenschatz: Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany; International Collaboration for Turbulence Research; Institute for Nonlinear Dynamics, University of Göttingen, D-37073 Göttingen, Germany; Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Guenter Ahlers: Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany; International Collaboration for Turbulence Research; Department of Physics, University of California, Santa Barbara, CA 93106, USA

Journal volume & issue: Vol. 11, no. 2
p. 100237

Abstract

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We propose a theoretical model for spatial variations of the temperature variance σ2(z,r) (z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC). Adapting the “attached-eddy” model of shear flow to the plumes of RBC, we derived an equation for σ2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z/λth, where λth is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr, but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.

Published in Theoretical and Applied Mechanics Letters

ISSN: 2095-0349 (Print)
Publisher: Elsevier
Country of publisher: China
LCC subjects: Technology: Engineering (General). Civil engineering (General)
Website: http://www.journals.elsevier.com/theoretical-and-applied-mechanics-letters/

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