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

Journal Article · Wed Mar 25 00:00:00 EDT 2020 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1922794117· OSTI ID:1606457

Iyer, Kartik P. ^[1]; Scheel, Janet D. ^[2]; Schumacher, Jörg ^[3]; Sreenivasan, Katepalli R. ^[4]

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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

Significance

The heat transport law in turbulent convection remains central to current research in the field. Our present knowledge of the heat transport law for $\mathrm{R}\mathrm{a}>10^{12}$ is inconclusive, where the Rayleigh number $\mathrm{R}\mathrm{a}$ is a measure of the strength of convection. Massively parallel simulations of the three-dimensional convection have progressed to $\mathrm{R}\mathrm{a}=10^{15}$ in slender cells. We resolve velocity gradients inside thin boundary layers and show that the turbulent heat transport continues to follow the classical $1/3$ scaling law with no transition to the so-called “ultimate” state that is variously argued to have $1/2$ scaling. Our work suggests that the boundary layers remain marginally stable and continue to act as the bottleneck for global heat transport.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1606457
• Alternate ID(s): OSTI ID: 1625066
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 14 Vol. 117; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of Sciences
• Country of Publication: United States
• Language: English

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