Title: Classical 1/3 scaling of convection holds up to Ra = 10 ¹⁵

Abstract

The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number $\mathrm{R}\mathrm{a}$—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for $\mathrm{R}\mathrm{a}\gtrsim 10^{12}$have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh–Bénard convection flows in a slender cylindrical cell of aspect ratio $1/10$, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law of $\mathrm{N}\mathrm{u}=\left(0.0525\pm 0.006\right)\times {\mathrm{R}\mathrm{a}}^{0.331\pm 0.002}$up to $\mathrm{R}\mathrm{a}=10^{15}$. Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all $\mathrm{R}\mathrm{a}$considered here, increasing with increasing $\mathrm{R}\mathrm{a}$, and suggest that an abrupt transition of the boundary layer to turbulence does not take place.

Authors:

Iyer, Kartik P. ^[1]; Scheel, Janet D.  ^[2];

• Search DOE PAGES for author "Scheel, Janet D."
• Search DOE PAGES for ORCID "0000-0002-1669-4188"

Schumacher, Jörg  ^[3];

• Search DOE PAGES for author "Schumacher, Jörg"
• Search DOE PAGES for ORCID "0000-0002-1359-4536"

Sreenivasan, Katepalli R. ^[4]

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+ Show Author Affiliations

1. Tandon School of Engineering, New York University, New York, NY 11201,
2. Department of Physics, Occidental College, Los Angeles, CA 90041,
3. Tandon School of Engineering, New York University, New York, NY 11201,, Department of Mechanical Engineering, Technische Universität Ilmenau, D-98684 Ilmenau, Germany,
4. Tandon School of Engineering, New York University, New York, NY 11201,, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012,, Department of Physics, New York University, New York, NY 10012,, Center for Space Science, New York University Abu Dhabi, Abu Dhabi 129188, United Arab Emirates

Publication Date:

Wed Mar 25 00:00:00 EDT 2020

Research Org.:

Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1606457

Alternate Identifier(s):

OSTI ID: 1625066

Grant/Contract Number:  

AC02_06CH11357; AC02-06CH11357

Resource Type:

Published Article

Journal Name:

Proceedings of the National Academy of Sciences of the United States of America

Additional Journal Information:

Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 117 Journal Issue: 14; Journal ID: ISSN 0027-8424

Publisher:

Proceedings of the National Academy of Sciences

Country of Publication:

United States

Language:

English

Subject:

Science & Technology - Other Topics