Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

doi:10.1088/1674-1056/ac012f

Abstract We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection in a square cavity by direct numerical simulations. The Rayleigh number range is ${1\times }{{10}}^{{8}}\le Ra\le 1\times {{10}}^{{13}}$, and the Prandtl number is selected as $Pr=0.7$ and $Pr=4.3$. It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns. In the thermal boundary layer, the normalized fluctuation $\theta_{\rm rms}/\theta_{\rm rms,max}$ is independent of Ra and a power law relation is identified, $i.e.$, $\theta _{\rm rms}/\theta_{\rm rms,max}\sim \left( z / \delta \right)^{0.99\pm 0.01}$, where $z / \delta $ is a dimensionless distance to the boundary ($\delta $ is the thickness of thermal boundary layer). Out of the boundary layer, when $Ra\le 5\times {10}^{9}$, the profiles of $\theta _{\rm rms}/\theta_{\rm rms,max}$ descend, then ascend, and finally drop dramatically as $z / \delta $ increases. While for $Ra\ge 1\times {10}^{10}$, the profiles continuously decrease and finally overlap with each other. The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls. Besides, there is a critical value of Ra indicating the transition, beyond which the fluctuation $\langle \theta_{\rm rms}\rangle _{V}$ has a power law dependence on Ra, given by $\langle \theta_{\rm rms}\rangle _{V}{\sim }{Ra}^{-0.14\pm 0.01}$.

Keywords: Rayleigh-Bénard temperature fluctuation distribution patterns critical value

Received: 11 March 2021
Revised: 11 May 2021
Accepted manuscript online: 14 May 2021

PACS:

47.27.te

(Turbulent convective heat transfer)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11772362), the Shenzhen Fundamental Research Program (Grant No. JCYJ20190807160413162), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University, China (Grant No. 19lgzd15).

Corresponding Authors: Yun Bao
E-mail: stsby@mail.sysu.edu.cn

Cite this article:

Ming-Wei Fang(方明卫), Jian-Chao He(何建超), Zhan-Chao Hu(胡战超), and Yun Bao(包芸) Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection 2022 Chin. Phys. B 31 014701

[1] Ahlers G, Grossmann S and Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Lohse D and Xia K Q 2010 Annu. Rev. Fluid Mech. 42 335
[3] Chillá F and Schumacher J 2012 Eur. Phys. J. E. 35 58
[4] Xia K Q 2013 Theor. Appl. Mech. Lett. 3 052001
[5] Grossmann S and Lohse D 2000 J. Fluid Mech. 407 27
[6] Grossmann S and Lohse D 2001 Phys. Rev. Lett. 86 3316
[7] Grossmann S and Lohse D 2002 Phys. Rev. E 66 016305
[8] Krishnamurti R and Howard L N 1981 Natl. Acad. Sci. USA 78 1981
[9] Qiu X L and Tong P 2001 Phys. Rev. E 64 036304
[10] Xia K Q, Sun C and Zhou S Q 2003 Phys. Rev. E 68 066303
[11] Kaminski E and Jaupart C 2003 J. Fluid Mech. 478 287
[12] Zhou Q, Sun C and Xia K Q 2007 Phys. Rev. Lett. 98 074501
[13] van der Poel E P, Verzicco R, Grossmann S and Lohse D 2015 J. Fluid Mech. 772 5
[14] Shang X D, Qiu X L, Tong P and Xia K Q 2003 Phys. Rev. Lett. 90 074501
[15] Shang X D, Tong P and Xia K Q 2008 Phys. Rev. Lett. 100 244503
[16] Gasteuil Y, Shew W L, Gibert M, Chilla F, Castaing B and Pinton J F 2007 Phys. Rev. Lett. 99 234302
[17] Bao Y, He J C and Gao Z Y 2019 Acta Phys. Sin. 68 164701 (in Chinese)
[18] Grossmann S and Lohse D 2004 Phys. Fluids. 16 4462
[19] Castaing B, Gunaratne G, Heslot F, et al. 1989 J. Fluid Mech. 204 1
[20] Adrian R J 1996 Int. J. Heat Mass Transfer 39 2303
[21] Wang Y, He X and Tong P 2016 Phys. Rev. Fluids 1 082301
[22] Wang Y, Xu W, He X and Tong P 2018 J. Fluid Mech. 840 408
[23] He Y H and Xia K Q 2019 Phys. Rev. Lett. 122 014503
[24] Deardorff J W 1970 J. Atmos. Sci. 27 1211
[25] Xie Y C, Cheng B Y C, Hu Y B and Xia K Q 2019 J. Fluid Mech. 878 R1
[26] Wang J and Xia K Q 2003 Eur. Phys. J. B 32 127
[27] Sun C, Cheung Y H and Xia K Q 2008 J. Fluid Mech. 605 79
[28] Belmonte A, Tilgner A and Libchaber A 1994 Phys. Rev. E 50 269
[29] Fernandes R L J and Adrian R J 2002 Exp. Therm. Fluid Sci. 26 355
[30] Lakkaraju R, Stevens R J A M, Verzicco R, et al. 2012 Phys. Rev. E 86 056315
[31] Du Y B and Tong P 2001 Phys. Rev. E 63 046303
[32] Huang S D and Xia K Q 2016 J. Fluid Mech. 794 639
[33] Zhang Y Z, Sun C, Bao Y and Zhou Q 2018 J. Fluid Mech. 836 R2
[34] Bao Y, Luo J and Ye M 2018 J. Mech. 34 159
[35] Zhou Q and Xia K Q 2013 J. Fluid Mech. 721 199
[36] Song H and Tong P 2010 Europhys. Lett. 90 44001
[37] Sun C and Xia K Q 2007 J. Fluid Mech. 570 479
[38] Sugiyama K, Ni R, Stevens R J A M, et al. 2010 Phys. Rev. Lett. 105 034503
[39] Chandra M and Verma M K 2013 Phys. Rev. Lett. 110 114503

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Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

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