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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 R a —the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for R a 1 0 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 N u = ( 0.0525 ± 0.006 ) × R a 0.331 ± 0.002 up to R a = 1 0 15 . Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all R a considered here, increasing with increasing R a , and suggest that an abrupt transition of the boundary layer to turbulence does not take place.

Authors:
; ORCiD logo; ORCiD logo;
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; 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

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. doi: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. doi: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 three-dimensional 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1073/pnas.1922794117

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Cited by: 2 works
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Figures / Tables:

Fig. 1 Fig. 1: Global scaling laws of turbulent trans- A B C port. (A) Turbulent heat transport law Nu(Ra) for two datasets on log–log coordinates. The present data (open circles) are for Pr = 1 and Γ=0.1 for 108 ≤ Ra ≤1015. Open squares representing DNS at Pr=0.7 and Γ=1 formore » 3 x 105 ≤ Ra ≤1010 are taken from ref. 23. Also added is the power-law fit of Nu= (0.0525 ± 0.006) x Ra0.331±0.002 which is obtained for 1010 ≤ Ra ≤1015. (B) Linear–log plot of the data of A, displayed in the form of compensated classical power law of 1/3 slope, with error bars computed from the standard deviation of the time series Nu(t), obtained at $\tilde{z}$= z/H=0 (bottom) and $\tilde{z}$=1 (top). The plot shows that the power-law exponent is smaller (0.29 ± 0.01) for Ra ≤ 109 and is 1/3 in the high-Ra range, with no tendency to a larger slope as would be required of the possible progression to the ultimate state. The dashed line corresponds to prefactor 0.0525, in close agreement with the classical prediction of 0.073 (6, 7). (C) Compensated power-law plot of the turbulent momentum transport law Re(Ra). A fit over the same Rayleigh number range as in B gives Re=(0.1555 ± 0.006) x Ra0.458 ± 0.006. Symbols mean the same in A–C.« less

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