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 $\mathrm{R}\mathrm{a}\gtrsim 1{0}^{12}$have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of threedimensional 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 $\mathrm{R}\mathrm{a}=1{0}^{15}$. 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:

 Tandon School of Engineering, New York University, New York, NY 11201,
 Department of Physics, Occidental College, Los Angeles, CA 90041,
 Tandon School of Engineering, New York University, New York, NY 11201,, Department of Mechanical Engineering, Technische Universität Ilmenau, D98684 Ilmenau, Germany,
 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:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1606457
 Alternate Identifier(s):
 OSTI ID: 1625066
 Grant/Contract Number:
 AC02_06CH11357; AC0206CH11357
 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 00278424
 Publisher:
 Proceedings of the National Academy of Sciences
 Country of Publication:
 United States
 Language:
 English
 Subject:
 Science & Technology  Other Topics
Citation Formats
Iyer, Kartik P., Scheel, Janet D., Schumacher, Jörg, and Sreenivasan, Katepalli R. Classical 1/3 scaling of convection holds up to Ra = 10 15. United States: N. p., 2020.
Web. doi:10.1073/pnas.1922794117.
Iyer, Kartik P., Scheel, Janet D., Schumacher, Jörg, & Sreenivasan, Katepalli R. Classical 1/3 scaling of convection holds up to Ra = 10 15. United States. https://doi.org/10.1073/pnas.1922794117
Iyer, Kartik P., Scheel, Janet D., Schumacher, Jörg, and Sreenivasan, Katepalli R. Wed .
"Classical 1/3 scaling of convection holds up to Ra = 10 15". United States. https://doi.org/10.1073/pnas.1922794117.
@article{osti_1606457,
title = {Classical 1/3 scaling of convection holds up to Ra = 10 15},
author = {Iyer, Kartik P. and Scheel, Janet D. and Schumacher, Jörg and Sreenivasan, Katepalli R.},
abstractNote = {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 numberRa—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells forRa≳1012have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of threedimensional turbulent Rayleigh–Bénard convection flows in a slender cylindrical cell of aspect ratio1/10, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law ofNu=(0.0525±0.006)×Ra0.331±0.002up toRa=1015. Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at allRaconsidered here, increasing with increasingRa, and suggest that an abrupt transition of the boundary layer to turbulence does not take place.},
doi = {10.1073/pnas.1922794117},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 14,
volume = 117,
place = {United States},
year = {2020},
month = {3}
}
https://doi.org/10.1073/pnas.1922794117
Web of Science
Figures / Tables:
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