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The high-resolution numerical simulations of two-dimensional (2D) turbulent Rayleigh-Bnard convection are conducted by using the Parallel direct method of DNS (PDM-DNS) with Ra=1010 and Pr in a range from 0.05 to 20. Using the flow visualization technique, the effects of Pr on the structure of plumes and large scale circulation (LSC) are investigated. With Pr decreasing, plumes become more active and the flow turns more turbulent. When Pr4.3, pronounced LSC and corner vortex exist. The thickness of thermal boundary layer varies slightly with the value of Pr changing, which obeys a scaling law. Nusselt number (Nu) increases with Pr value increasing when Pr value is low and becomes independent when Pr value is high. Furthermore, two definitions of Reynolds number (Re) are given. The Re〈u〉 angle is calculated from the fluctuation of horizontal velocity near the center of bottom plate, and the ReUmax is calculated from maximal horizontal velocity in the mean field. Both of them follow the same scaling Re~Pr0.81.
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Keywords:
- Rayleigh-Bnard convection /
- Prandtl number /
- turbulence /
- thermal boundary layer
[1] Ahlers G, Grossmann S, Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Grossmann S, Lohse D 2000 J. Fluid Mech. 407 27
[3] Grossmann S, Lohse D 2001 Phys. Rev. Lett. 86 3316
[4] Shishkina O, Horn S, Wagner S, Ching E S C 2015 Phys. Rev. Lett. 114 114302
[5] Wang Y, He X Z, Tong P 2016 Phys. Rev. Fluids 1 08230
[6] Salort J, Liot O, Rusaouen E 2014 Phys. Fluids 26 015112
[7] Wei P, Chan T S, Ni R, Zhao X Z 2014 J. Fluid Mech. 740 28
[8] Xie Y C, Xia K Q 2017 J. Fluid Mech. 825 573
[9] Wagner S, Shishkina O 2015 J. Fluid Mech. 763 109
[10] Toppaladoddi S, Succi S, Wettlaufer J S 2017 Phys. Rev. Lett. 118 074503
[11] Zhu X J, Stevens R J A M, Verzicco R, Lohse D 2017 Phys. Rev. Lett. 119 154501
[12] He X Z, Funfschilling D, Nobach H, Bodenschatz E, Ahlers G 2012 Phys. Rev. Lett. 108 024502
[13] Zhou Q, Xia K Q 2010 Phys. Rev. Lett. 104 104301
[14] Stevens R J A M, Lohse D, Verzicoo R 2011 J. Fluid Mech. 688 31
[15] Huang M J, Bao Y 2016 Acta Phys. Sin. 20 204702(in Chinese) [黄茂静, 包芸 2016 物理学报 20 204702]
[16] Zhou H Y, Xu W, Bao Y 2014 J. Hydrodyn. 29 34(in Chinese) [邹鸿岳, 徐炜, 包芸 2014 水动力学研究与进展 A辑29 34]
[17] Bao Y, Ning H, Xu W 2014 Acta Phys. Sin. 63 154703(in Chinese) [包芸, 宁浩, 徐炜 2014 物理学报 63 154703]
[18] van der Poel E P, Stevens R J A M, Lohse D 2013 J. Fluid Mech. 736 177
[19] Bao Y, Chen J, Liu B F 2015 J. Fluid Mech. 784 R5
[20] Chen J, Bao Y, Yin Z X 2017 Int. J. Heat Mass Tran.. 115 556
[21] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1(in Chinese) [徐炜, 包芸 2013 力学学报 45 1]
[22] Sun X H, Zhang W 2004 IEEE Trans. Parall. Distr. 15 97
[23] Bao Y, Luo J H, Ye M X 2017 J. Mech. (Received)
[24] Breuer M, Wessling S, Schmalzl J, Hansen U 2004 Phys. Rev.. 69 026302
[25] Verzicco R, Camussi R 1999 J. Fluid Mech. 383 55
[26] Stevens R J A M, van der Poel E P, Grossmann S, Lohse D 2013 J. Fluid Mech. 730 295
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[1] Ahlers G, Grossmann S, Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Grossmann S, Lohse D 2000 J. Fluid Mech. 407 27
[3] Grossmann S, Lohse D 2001 Phys. Rev. Lett. 86 3316
[4] Shishkina O, Horn S, Wagner S, Ching E S C 2015 Phys. Rev. Lett. 114 114302
[5] Wang Y, He X Z, Tong P 2016 Phys. Rev. Fluids 1 08230
[6] Salort J, Liot O, Rusaouen E 2014 Phys. Fluids 26 015112
[7] Wei P, Chan T S, Ni R, Zhao X Z 2014 J. Fluid Mech. 740 28
[8] Xie Y C, Xia K Q 2017 J. Fluid Mech. 825 573
[9] Wagner S, Shishkina O 2015 J. Fluid Mech. 763 109
[10] Toppaladoddi S, Succi S, Wettlaufer J S 2017 Phys. Rev. Lett. 118 074503
[11] Zhu X J, Stevens R J A M, Verzicco R, Lohse D 2017 Phys. Rev. Lett. 119 154501
[12] He X Z, Funfschilling D, Nobach H, Bodenschatz E, Ahlers G 2012 Phys. Rev. Lett. 108 024502
[13] Zhou Q, Xia K Q 2010 Phys. Rev. Lett. 104 104301
[14] Stevens R J A M, Lohse D, Verzicoo R 2011 J. Fluid Mech. 688 31
[15] Huang M J, Bao Y 2016 Acta Phys. Sin. 20 204702(in Chinese) [黄茂静, 包芸 2016 物理学报 20 204702]
[16] Zhou H Y, Xu W, Bao Y 2014 J. Hydrodyn. 29 34(in Chinese) [邹鸿岳, 徐炜, 包芸 2014 水动力学研究与进展 A辑29 34]
[17] Bao Y, Ning H, Xu W 2014 Acta Phys. Sin. 63 154703(in Chinese) [包芸, 宁浩, 徐炜 2014 物理学报 63 154703]
[18] van der Poel E P, Stevens R J A M, Lohse D 2013 J. Fluid Mech. 736 177
[19] Bao Y, Chen J, Liu B F 2015 J. Fluid Mech. 784 R5
[20] Chen J, Bao Y, Yin Z X 2017 Int. J. Heat Mass Tran.. 115 556
[21] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1(in Chinese) [徐炜, 包芸 2013 力学学报 45 1]
[22] Sun X H, Zhang W 2004 IEEE Trans. Parall. Distr. 15 97
[23] Bao Y, Luo J H, Ye M X 2017 J. Mech. (Received)
[24] Breuer M, Wessling S, Schmalzl J, Hansen U 2004 Phys. Rev.. 69 026302
[25] Verzicco R, Camussi R 1999 J. Fluid Mech. 383 55
[26] Stevens R J A M, van der Poel E P, Grossmann S, Lohse D 2013 J. Fluid Mech. 730 295
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