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Volume 42 Issue 3
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Article Navigation >  Advances in Mechanics  > 2012  >  42(3): 231-251
ZHOU Quan, XIA Keqing. ADVANCES AND OUTLOOK IN TURBULENT RAYLEIGH-BÉNARD CONVECTION[J]. Advances in Mechanics, 2012, 42(3): 231-251. doi: 10.6052/1000-0992/11-163
Citation: ZHOU Quan, XIA Keqing. ADVANCES AND OUTLOOK IN TURBULENT RAYLEIGH-BÉNARD CONVECTION[J]. Advances in Mechanics, 2012, 42(3): 231-251. doi: 10.6052/1000-0992/11-163
shu

ADVANCES AND OUTLOOK IN TURBULENT RAYLEIGH-BÉNARD CONVECTION

doi: 10.6052/1000-0992/11-163
  • 1.

    Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

  • 2. Department of Physics, The Chinese University of Hong Kong, Hong Kong 00852, China

Funds:  The project was support by the Natural Science Foundation of China (11161160554 and 11002085), “Pu Jiang” Project of Shanghai (10PJ1404000), Shanghai Program for Innovative Research Team in Universities, and Research Grants Council of Hong Kong SAR (CUHK404808, 404409, 403811).
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  • Corresponding author: XIA Keqing
  • Received Date: 2011-11-29
  • Rev Recd Date: 2012-02-09
  • Publish Date: 2012-05-25
    Abstract
  • Turbulent Rayleigh-B閚ard (RB) convection, a fluid layer heated from below and cooled from above, has become a paradigm for the study of general convection phenomena that occurs ubiquitously in nature and in many engineering applications. This paper presents an overview of recent advances in the following major areas of RB convection: turbulent heat transport, thermal plumess, large-scale circulation, and small-scale properties of velocity and temperature fields. A brief description of recent developments in the studies using non-traditional RB configurations is also presented. We end by pointing out main remaining issues and challenges and giving an outlook on the future development.

     

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  • 1 余荔, 宁利中, 魏炳乾, 等. Rayleigh-Bénard 对流及其在工 程中的应用. 水资源与水工程学报, 2008, 19: 52-54
    2 Bénard H. Les tourbillons cellularies dans une nappe liquide. Rev. Gen. Sci. Pure Appl., 1900, 11: 1261-1271
    3 Rayleigh L. On convection currents in a horizontal layer of fluid when higher temperature is on the under side. Philos. Mag., 1916, 32: 529-543
    4 Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability. New York: Dover, 1981
    5 Drazin P, ReidWH. Hydrodynamic Stability. Cambridge: Cambridge University Preee, 1981
    6 Getling A V. Rayleigh-Bénard Convection: Structures and Dynamics. Singapore: World Scientific, 1998
    7 Bodenschatz E, Pesch W, Ahlers G. Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech.,2000, 32: 709-778
    8 Heslot F B, Castaing B, Libchaber A. Transition to turbulence in helium gas. Phys. Rev. A, 1987, 36: 5870-5873
    9 Castaing B, Gunaratne G, Heslot F, et al. Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech., 1989, 204: 1-30
    10 Sano M, Wu X Z, Libchaber A. Turbulence in helium-gas gree-convection. Phys. Rev. A, 1989, 40: 6421-6430
    11 Siggia E D. High Rayleigh number convection. Annu. Rev. Fluid Mech., 1994, 26: 137-168
    12 王晋军, 夏克青. Rayleigh-Bénard 湍流对流实验研究进展. 力学进展, 1999, 29(4): 557-566
    13 周全, 孙超, 郗恒东, 等. 湍流热对流中的若干问题. 物理,2007, 36(9): 657-663
    14 Ahlers G, Grossmann S, Lohse D. Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys., 2009, 81: 503-537
    15 Lohse D, Xia K Q. Small-Scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech.,2010, 42: 335-364
    16 Malkus M V R. The heat transport and spectrum of thermal turbulence. Proc. R. Soc. London, Ser. A, 1954,225: 196-212
    17 Cioni S, Ciliberto S, Sommeria J. Strongly turbulent Rayleigh-Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech.,1997, 335: 111-140
    18 Zhou S Q, Xia K Q. Plume statistics in thermal turbulence： Mixing of an active scalar. Phy. Rev. Lett., 2002,89: 184502
    19 Zhou Q, Sun C, Xia K Q. Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2007, 98: 074501
    20 Zhou Q, Xia K Q. Physical and geometrical properties of thermal plumes in turbulent Rayleigh-Bénard convection. New J. Phys., 2010, 12: 075006
    21 Shraiman B I, Siggia E D. Heat transport in high- Rayleigh-number convection. Phys. Rev. A, 1990, 42:3650-3653
    22 du Puits R, Resagk C, Thess A. Mean velocity profile in confined turbulent convection. Phys. Rev. Lett., 2007,99: 234504
    23 Grossmann S, Lohse D. Scaling in thermal convection：A unifying view. J. Fluid Mech., 2000, 407: 27-56
    24 Grossmann S, Lohse D. Thermal convection for large Prandtl number. Phys. Rev. Lett., 2001, 86: 3316-3319
    25 Grossmann S, Lohse D. Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E, 2002, 66: 016305
    26 Grossmann S, Lohse D. Fluctuations in turbulent Rayleigh-Bénard convection: The role of plumes. Phys. Fluids, 2004, 16: 4462-4472
    27 Zhang J, Childress S, Libchaber A. Non-Boussinesq effect: Thermal convection with broken symmetry. Phys. Fluids,1997, 9: 1034-1042
    28 Xi H D, Lam S, Xia K Q. From laminar plumes to organized flows: The onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech., 2004, 503: 47-56
    29 Ahlers G, Xu X. Prandtl-number dependence of heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2001, 86: 3320-3323
    30 Qiu X L, Tong P. Onset of coherent oscillations in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2001,87: 094501
    31 Funfschilling D, Brown E, Nikolaenko A, et al. Heat transport by turbulent Rayleigh-Bénard convection in cylindrical cells with aspect ratio one and larger. J. Fluid Mech.,2005, 536: 145-154
    32 Xia K Q, Lam S, Zhou S Q. Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2002, 88: 064501
    33 Kraichnan R H. Turbulent thermal convection at arbritrary Prandtl number. Phys. Fluids, 1962, 5: 1374-1389
    34 Spiegel E A. Convection in stars. Annu. Rev. Astron. Astrophys., 1971, 9: 323-352
    35 Doering C R, Constantin P. Variational bounds on energy dissipation in incompressible flows：III. Convection. Phys. Rev. E, 1996, 53: 5957-5981
    36 Otero J, Wittenberg R W, Worthing R A, et al. Bounds on Rayleigh-Bénard convection with an imposed heat flux. J. Fluid Mech., 2002, 473: 191-199
    37 Landau L D, Lifshitz E M. Fluid Mechanics. Oxford: Pergamon, 1987
    38 Sun C, Cheung Y H, Xia K Q. Experimental studies of the viscous boundary layer properties in turbulent Rayleigh- Bénard convection. J. Fluid Mech., 2008, 605: 79-113
    39 Glazier J A, Segawa T, Naert A, Sano M. Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers. Nature, 1999, 398: 307-310
    40 Verzicco R. Effects of nonperfect thermal sources in turbulent thermal convection. Phys. Fluids, 2004, 16: 1965-1979
    41 Brown E, Nikolaenko A, Funfschilling D, et al. Heat transport in turbulent Rayleigh-Bénard convection: effect of finite top- and bottom-plate conductivities. Phys. Fluids,2005, 17: 075108
    42 Chavanne X, Chilla F, Chabaud B, et al. High Rayleigh number convection with gaseous helium at low temperature. J. Low Temp. Phys., 1996, 104: 109-129
    43 Chavanne X, Chilla F, Castaing B, et al. Observation of the ultimate regime in Rayleigh-Bénard convection. Phys. Rev. Lett., 1997, 79: 3648-3651
    44 Chavanne X, Chilla F, Chabaud B, et al. Turbulent Rayleigh-Bénard convection in gaseous and liquid He. Phys. Fluids, 2001, 13: 1300-1320
    45 Niemela J J, Sreenivasan K R. Confined turbulent convection. J. Fluid Mech., 2003, 481: 355-384
    46 Niemela J J, Skrbek L, Sreenivasan K R, et al. Turbulent convection at very high Rayleigh numbers. Nature, 2000,404: 837-840
    47 Funfschilling D, Bodenschatz E, Ahlers G. Search for the “ultimate state” in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2009, 103: 014503
    48 Ahlers G, Funfschilling D, Bodenschatz E. Transitions in heat transport by turbulent convection at Rayleigh numbers up to 1015. New J. Phys., 2010, 11: 123001
    49 Lohse D, Toschi F. The ultimate state of thermal convection. Phys. Rev. Lett., 2003, 90: 034502
    50 Calzavarini E, Lohse D, Toschi F, et al. Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Bénard turbulence. Phys. Fluid, 2005, 17: 055107
    51 Roche P E, Castaing B, Chabaud B, et al. Observation of the 1/2 power law in Rayleigh-Bénard convection. Phys. Rev. E, 2001, 63: 045303(R)
    52 Qiu X L, Xia K Q, Tong P. Experimental study of velocity boundary layer near a rough conducting surface in turbulent natural convection. J. Turbulence, 2005, 6: 30
    53 Gibert M, Pabiou H, Chilla F, et al. High-Rayleighnumber convection in a vertical channel. Phys. Rev. Lett.,2006, 96: 084501
    54 Gibert M, Pabiou H, Tisserand J C, et al. Heat convection in a vertical channel：Plumes versus turbulent diffusion. Phys. Fluid, 2009, 21: 035109
    55 Shang X D, Qiu X L, Tong P, et al. Measured local heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2003, 90: 074501
    56 Shang X D, Qiu X L, Tong P, et al. Measurements of the local convective heat flux in turbulent Rayleigh-Bénard convection. Phys. Rev. E, 2004, 70: 026308
    57 Shang X D, Tong P, Xia K Q. Scaling of the local convective heat flux in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2008, 100: 244503
    58 Ashkenazi S, Steinberg V. High Rayleigh number turbulent convection in a gas near the gas-liquid critical point. Phys. Rev. Lett., 1999, 83: 3641-3644
    59 Roche P E, Castaing B, CHabaud B, et al. Prandtl and Rayleigh numbers dependences in Rayleigh-Bénard convection. Europhys. Lett., 2002, 58: 693-698
    60 Verzicco R, Camussi R. Prandtl number effects in convective turbulence. J. Fluid Mech., 1999, 383: 55-73
    61 Kerr R M, Herring J R. Prandtl number dependence of Nusselt number in direct numerical simulations. J. Fluid Mech., 2000, 419: 325-344
    62 Breuer M, Wessling S, Schmalzl J, et al., Effect of inertia in Rayleigh-Bénard convection. Phys. Rev. E, 2004, 69:026302
    63 Silano G, Sreenivasan K R, Verzicco R. Numerical simulations of Rayleigh-Bénard convection for Prandtl numbers between 10??1 and 104 and Rayleigh numbers between 105 and 109. J. Fluid Mech., 2010, 662: 409-446
    64 Wu X Z, Libchaber A. Scaling relations in thermal turbulence： The aspect ratio dependence. Phys. Rev. A, 1992,45: 842-845
    65 Fleischer A S, Goldstein R J. High-Rayleigh-number convection of pressurized gases in a horizontal enclosure. J. Fluid Mech., 2002, 469: 1-12
    66 Sun C, Ren L Y, Song H, et al. Heat transport by turbulent Rayleigh-Bénard convection in 1 m diameter cylindrical cells of widely varying aspect ratio. J. Fluid Mech.,2005, 542: 165-174
    67 Niemela J, Sreenivasan K R. Turbulent convection at high Rayleigh numbers and aspect ratio 4. J. Fluid Mech.,2006, 557: 411-422
    68 Bailon-Cuba J, Emran M S, Schumacher J. Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection. J. Fluid Mech., 2010, 655: 152-173
    69 Tilgner A, Belmonte A, Libchaber A. Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E, 1993, 47: R2253-R2256
    70 Belmonte A, Tilgner A, Libchaber A. Boundary layer length scales in thermal turbulence. Phys. Rev. Lett.,1993, 70: 4067-4070
    71 Chilla F, Ciliberto S, Innocenti C, et al. Boundary layer and scaling properties in turbulent thermal convection. IL Nuovo Cimento, 1993, 15: 1229-1249
    72 Xin Y B, Xia K Q, Tong P. Measured velocity boundary layers in turbulent convertion. Phys. Rev. Lett., 1996,77: 1266-1269
    73 Xin Y B, Xia K Q. Boundary layer length scales in convective turbulence. Phys. Rev. E, 1997, 56: 3010-3015
    74 Naert A, Segawa T, Sano M. High-Reynolds-number thermal turbulence in mercury. Phys. Rev. E, 1997, 56: R1302-R1305
    75 Lui S L, Xia K Q, Spatial structure of the thermal boundary layer in turbulent convection. Phys. Rev. E, 1998,57: 5494-5503
    76 Qiu X L, Xia K Q. Viscous boundary layers at the sidewall of a convection cell. Phys. Rev. E, 1998, 58: 486-491
    77 Xia K Q, Zhou S Q. Temperature power spectra and the viscous boundary layer in thermal turbulence：the role of Prandtl number. Physica A, 2000, 288: 308-314
    78 Fernandes R L J, Adrian R J. Scaling of velocity and temperature fluctuations in turbulent thermal convection. Expl. Thermal Fluid Sci., 2002, 26: 355-360
    79 Lam S, Shang X D, Zhou S Q, et al. Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh-Bénard convection. Phys. Rev. E,2002, 65: 066306
    80 Wang J J, Xia K Q. Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection. Eur. Phys. J. B, 2003, 32: 127-136
    81 du Puits R, Resagk C, Tilgner A. Structure of thermal boundary layer for turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2007, 572: 231-254
    82 Maystrenko A, Resagk C, Thess A. Structure of the thermal boundary layer for turbulent Rayleigh-Bénard convection of air in a long rectangular enclosure. Phys. Rev. E, 2007, 75: 066303
    83 Zhou Q, Xia K Q. Measured instantaneous viscous boundary layer in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2010, 104: 104301
    84 Shishkina O, Thess A. Mean temperature profiles in turbulent Rayleigh-Bénard convection of water. J. Fluid Mech., 2009, 633: 449-460
    85 Sugiyama K, Calzavarini E, Grossmann S, et al. Flow organization in non-oberbeck-boussinesq Rayleigh-Bénard convection in water. J. Fluid Mech., 2009, 637: 105-135
    86 Stevens R J A M, Verzicco R, Lohse D. Radial boundary layer structure and Nusselt number in Rayleigh-Bénard convection. J. Fluid Mech., 2010, 643: 493-507
    87 Zhou Q, Stevens R J A M, Sugiyama K, et al. Prandtl- Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Bénard convection. J. Fluid Mech.,2010, 664: 297-312
    88 Gasteuil Y, Shew W L, Gibert M, et al. Lagrangian temperature, velocity, and local heat flux measurement in Rayleigh-Bénard convection. Phys. Rev. Lett., 2007, 99:234302
    89 Jellinek A M, Manga M. Links between long-lived hot spots, mantle plumes, D”, and plate tectonics. Rev. Geo- phys., 2004, 42: RG3002
    90 程雪玲, 胡非. 大气边界层内羽流扩散研究. 力学学报, 2005,37: 148-156
    91 Kaczorowski M, Wagner C. Analysis of the thermal plumes in turbulent Rayleigh-Bénard convection based on well-resolved numerical simulations. J. Fluid Mech., 2009,618: 89-112
    92 Zhou Q, Xia K Q. Physical and geometrical properties of thermal plumes in turbulent Rayleigh-Bénard convection. New J. Phys., 2010, 12: 075006
    93 Nikolaenko A, Ahlers G. Nusselt number measurements for turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2003, 91: 084501
    94 Moses E, Zocchi G, Libchaber A. An experimental study of laminar plumes.J. Fluid Mech., 1993, 251: 581-601
    95 Kaminski E, Jaupart C. Laminar starting plumes in high- Prandtl-number fluids. J. Fluid Mech., 2003, 478: 287-298
    96 Zocchi G, Moses E, Libchaber A. Coherent structures in turbulent convection：an experimental study. Physica A,1990, 166: 387-407
    97 Gluckman B J, Willaime H, Gollub J P. Geometry of isothermal and isoconcentration on surfaces in thermal turbulence. Phys. Fluids A, 1993, 5: 647-661
    98 Ciliberto S, Cioni S, Laroche C. Large-scale flow properties of turbulent thermal convection. Phys. Rev. E, 1996,54: R5901-R5904
    99 Du Y B, Tong P. Enhanced heat transport in turbulent convection over a rough surface. Phys. Rev. Lett., 1998,81: 987-990
    100 Tanaka H, Miyata H. Turbulent natural convection in a horizontal water layer heated from below. Int. J. Heat Mass Transfer, 1980, 23: 1273-1281
    101 Haramina T, Tilgner A. Coherent structures in boundary layers of Rayleigh-Bénard convection. Phys. Rev. E,2004, 99: 056306
    102 Puthenveettil B A, Arakeri J H. Plume structure in high- Rayleigh-number convection. J. Fluid Mech., 2005, 542:217-249
    103 Funfschilling D, Brown E, Ahlers G. Torsional oscillations of the large-scale circulation in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2008, 607: 119-139
    104 Krishnamurti R, Howard L N. Large scale flow generation in turbulent convection. Proc. Natl. Acad. Sci. U.S.A.,1981, 78: 1981-1985
    105 Qiu X L, Tong P. Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E, 2001, 64: 036304
    106 Qiu X L, Shang X D, Tong P, et al. Velocity oscillations in turbulent Rayleigh-Bénard convection. Phys. Fluids,2004, 16: 412-423
    107 Xia K Q, Sun C, Zhou S Q. Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E, 2003, 68: 066303
    108 Sun C, Xia K Q, Tong P. Three-dimensional flow structures and dynamics of turbulent thermal convection in a cylindrical cell. Phys. Rev. E, 2005, 72: 026302
    109 Sun C, Xi H D, Xia K Q. Azimuthal symmetry, flow dynamics, and heat flux in turbulent thermal convection in a cylinder with aspect ratio one-half. Phys. Rev. Lett.,2005, 95: 074502
    110 Xi H D, Xia K Q. Azimuthal motion, reorientation, cessation and reversal of the large-scale circulation in turbulent thermal convection: a comparison between aspec ratio one and one-half geometries. Phys. Rev. E, 2008,78: 036306
    111 Qiu X L, Tong P. Temperature oscillations in turbulent Rayleigh-Bénard convection. Phys. Rev. E, 2002, 66:026308
    112 Takeshita T, Segawa T, Glazier J A, et al. Thermal turbulence in mercury. Phys. Rev. Lett., 1996, 76: 1465-1468
    113 Niemela J J, Skrbek L, Sreenivasan K R, et al. The wind in confined thermal convection. J. Fluid Mech., 2001, 449:169-178
    114 Funfschilling D, Ahlers G. Plume motion and large-scale circulation in a cylindrical Rayleigh-Bénard cell. Phys. Rev. Lett., 2004, 92: 194502
    115 Sun C, Xia K Q. Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E, 2005, 72: 067302
    116 Brown E, Funfschilling D, Ahlers G. Anomalous Reynoldsnumber scaling in turbulent Rayleigh-Bénard convection. J. Stat. Mech., 2007, 10: P10005
    117 Niemela J J, Sreenivasan K R. Rayleigh-number evolution of large-scale coherent motion in turbulent convection. Europhys. Lett., 2003, 62: 829-833
    118 Qiu X L, Yao Y S, Tong P. Large-scale coherent rotation and oscillation in turbulent thermal convection. Phys. Rev. E, 2000, 61: R6075-R6078
    119 Xi H D, Zhou Q, Xia K Q. Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E,2006, 73: 056312
    120 Brown E, Ahlers G. Rotations and cessations of the largescale circulation in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2006, 568: 351-386
    121 Brown E, Ahlers G. Effect of the Earth’s Coriolis force on the large-scale circulation of turbulent Rayleigh-Bénard convection. Phys. Fluids, 2006, 18: 125108
    122 Xi H D, Xia K Q. Cessations and reversals of the largescale circulation in turbulent thermal convection. Phys. Rev. E, 2007, 75: 066307
    123 Sreenivasan K R, Bershadskii A, Niemela J J. Mean wind and its reversal in thermal convection. Phys. Rev. E,2002, 65: 056306
    124 Brown E, Nikolaenko A, Ahlers G. Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2005, 95: 084503
    125 Sugiyama K, Ni R, Stevens R J A M, et al. Flow reversals in thermally driven turbulence. Phys. Rev. Lett., 2010,105: 034503
    126 Benzi R. Flow reversal in a simple dynamical model of turbulence. Phys. Rev. Lett., 2005, 95: 024502
    127 Fontenele A, Grossmann S, Lohse D. Wind reversals in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett.,2005, 95: 084502
    128 Resagk C, du Puits R, Thess A, et al. Oscillations of the large scale wind in turbulent thermal convection. Phys. Fluids, 2006, 18: 095105
    129 Brown E, Ahlers G. Large-scale circulation model for turbulent Rayleigh-Bénard convection. Phys. Rev. Lett.,2007, 98: 134501
    130 Brown E, Ahlers G. A dynamical model of the largescale circulation in turbulent Rayleigh-Bénard convection： Azimuthal asymmetries. Phys. Fluids, 2008, 20:105105
    131 Zhou Q, Xi H D, Zhou S Q, et al. Oscillations of the largescale circulation in turbulent Rayleigh-Bénard convection: the sloshing mode and its relationship with the torsional mode. J. Fluid Mech., 2009, 630: 367-390
    132 Xi H D, Zhou S Q, Zhou Q, et al. Origin of the temperature oscillation in turbulent thermal convection. Phys. Rev. Lett., 2009, 102: 044503
    133 Brown E, Ahlers G. The origin of oscillations of the largescale circulation in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2009, 638: 383-400
    134 Kolmogorov A N. The local structure of turbulence in imcompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR, 1941, 30: 299-303
    135 Arneodo A, Baudet C, Belin F, et al. Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett., 1996, 34: 411-416
    136 Obukhov A M. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR Ser. Geog. Geo z,1949, 13: 58-69
    137 Corrsin S. On the spectrum of isotropic temprature fluctuations in anisotropic turbulence. J. Appl. Phys., 1951,22: 469-473
    138 Warhaft Z. Passive scalars in turbulent flows. Annu. Rev. Fluid Mech., 2000, 32: 203-240
    139 Bolgiano R. Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res., 1959, 64: 2226-2229
    140 Obukhov A M. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR Ser. Geog. Geo z.,1959, 13: 58-69
    141 Wu X Z, Kadanoff L, Libchaber A, et al. Frequency power spectrum of temperature fluctuations in free convection. Phys. Rev. Lett., 1990, 64: 2140-2143
    142 Tong P, Shen Y. Relative velocity fluctuations in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 1992,69: 2066-2069
    143 Shang X D, Xia K Q. Scaling of the velocity power spectra in turbulent thermal convection. Phys. Rev. E, 2001, 64:065301(R)
    144 Zhou S Q, Xia K Q. Scaling properties of the temperature field in convective turbulence. Phys. Rev. Lett., 2001, 87:064501
    145 Taylor G I. The spectrum of turbulence. Proc. R. Soc. Lond. A, 1938, 164: 476-490
    146 Sun C, Zhou Q, Xia K Q. Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence. Phys. Rev. Lett., 2006, 97: 144504
    147 Zhou Q, Sun C, Xia K Q. Experimental investigation of homogeneity, isotropy, and circulation of the velocity field in buoyancy-driven turbulence. J. Fluid Mech., 2008, 598:361-372
    148 Kunnen R P J, Clercx H J H, Geurts B J, et al. Numerical and experimental investigation of structure-function scaing in turbulent Rayleigh-Bénard convection. Phys. Rev. E, 2008, 77: 016302
    149 Paladin G, Vulpiani A. Degrees of freedom of turbulence. Phys. Rev. A, 1987, 15: 1971-1973
    150 Yakhot V. Probability densities in strong turbulence. Physica D, 2006, 215: 166-174
    151 Biferale L. A note on the fluctuation of dissipative scale in turbulence. Phys. Fluids, 2008, 20: 031703
    152 Schumacher J. Sub-Kolmogorov-scale fluctuations in fluid turbulence. Europhys. Lett., 2007, 80: 54001
    153 Bailey S C C, Hultmark M, Schumacher J, et al. Measurement of local dissipation scales in turbulent pipe flow. Phys. Rev. Lett., 2009, 103: 014502
    154 Zhou Q, Xia K Q. Universality of local dissipation scales in buoyancy-driven turbulence. Phys. Rev. Lett., 2010,104: 124301
    155 Toschi F, Bodenschatz E. Lagrangian properties of particles in turbulence.Annu. Rev. Fluid Mech., 2009, 41:375-404
    156 Schumacher J. Lagrangian dispersion and heat transport in convective turbulence. Phys. Rev. Lett., 2008, 100:134502
    157 Schumacher J. Lagrangian studies in convective turbulence. Phys. Rev. E, 2009, 79: 056301
    158 Mohammad S E, Schumacher J. Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell. Phys. Rev. E, 2010, 82: 016303
    159 Kunnen R P J, Stevens R J A M, Overkamp J, et al. The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-Bénard convection. J. Fluid Mech., 2011, 688:422-442
    160 Julien K, Legg S, Mcwilliams J, et al. Rapidly rotating turbulent Rayleigh-Bénard convection. J. Fluid Mech.,1996, 322: 243-273
    161 Liu Y M, Ecke R E. Heat transport scaling in turbulent Rayleigh-Bénard convection：Effects of Rotation and Prandtl number. Phys. Rev. Lett., 1997, 79: 2257-2260
    162 King E M, Stellmach S, Noir J, et al. Boundary layer control of rotating convection systems. Nature, 2009, 457:301-304
    163 Liu Y M, Ecke R E. Heat transport measurements in turbulent rotating Rayleigh-Bénard convection. Phys. Rev.,2009, 80: 036314
    164 Zhong J Q, Stevens R J A M, Clercx H J H, et al. Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Bénard convection. Phys. Rev. Lett., 2009, 102: 044502
    165 Stevens R J A M, Zhong J Q, Clercx H J H, et al. Transitions between turbulent states in rotationg Rayleigh- Bénard convection. Phys. Rev. Lett., 2009, 103: 024503
    166 Niemela J J, Babuin S, Sreenivasan K R. Turbulent rotating convection at high Rayleigh and Taylor numbers. J. Fluid Mech., 2010, 649: 509-522
    167 Zhong J Q, Alhers G. Heat transport and the large-scale circulation in rotating turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2010, 665: 300-333
    168 Stevens R J A M, Clercx H J H, Lohse D. Boundary layers in rotating weakly turbulent Rayleigh-Bénard convection. Phys. Fluids, 2010, 22: 085103
    169 Stevens R J A M, Overkamp J, Lohse D, Clercx H J H. Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection. Phys. Rev. E,2011, 84: 056313
    170 Weiss S, Alhers G. Heat transport by turbulent rotating Rayleigh-Bénard convection and its dependence on the aspect ratio. J. Fluid Mech., 2011, 684: 407-426
    171 Vorobieff P, Ecke R E. Turbulent rotating convection：An experimental study. J. Fluid Mech., 2002, 458: 191-218
    172 Kunnen R P J, Clercx H J H, Geurts B J. Vortex statistics in turbulent rotation convection. Phys. Rev. E, 2010, 82:036306
    173 Weiss S, Alhers G. The large-scale flow structure in turbulent rotating Rayleigh-Bénard convection. J. Fluid Mech.,2011, 688: 461-492
    174 Stevens R J A M, Clercx H J H, Lohse D. Breakdown of the large-scale wind aspect ratio ?? = 1=2 rotating Rayleigh-Bénard flow. J. Fluid Mech., submitted
    175 Jin X L, Xia K Q. An experimental study of kicked thermal turbulence. J. Fluid Mech., 2008, 606: 133-151
    176 Niemela J J, Sreenivasan K R. Formation of the “Superconducting” core in turbulent thermal convection. Phys. Rev. Lett., 2008, 100: 184502
    177 Qiu C. Heat transfer measurement of multilayer immiscible fluid in turbulent thermal convection: [M. Thesis]. Hong Kong: The Chinese University of Hong Kong, 2010
    178 Zhao X Z. Experimental investigation of turbulent thermal convection with slip-free boundary conditions: [M. Thesis]. Hong Kong: The Chinese University of Hong Kong,2010
    179 Benzi R, Ching E S C, De Angelis E. Effect of polymer additives on heat transport in turbulent thermal convection. Phys. Rev. Lett., 2010, 104: 024502
    180 Ahlers G, Nikolaenko A. Effect of a polymer additive on heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2010, 104: 034503
    181 Wei P, Ni R, Xia K Q. Enhanced and reduced heat transport in turbulent thermal convection with polymer additives. Phys. Rev. Lett. E, submitted.
    182 Oresta P, Verzicco R, Lohse D. Heat transfer mechanisms in bubbly Rayleigh-Bénard convection. Phys. Rev. E,2009, 80: 026304
    183 Ni R, Zhou S Q, Xia K Q. An experimental investigation of turbulent thermal convection in water-based Alumina nanofluid. Phys. Fluids., 2011, 23: 022005
    184 Zhong J Q, Funfschilling D, Ahlers G. Enhanced heat transport by turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 2009, 102: 124501
    185 Zhou Q, Sugiyama K, Stevens R J A M, et al. Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh-Bénard convection. Phys. Fluids, 2011, 23: 125104
    186 Zhou Q, Li C M, Lu Z M, et al. Experimental investigation of longitudinal space-time correlations of the velocity field in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 2011, 683: 94-111
    187 Zhou Q, Xia K Q. Disentangle plume-induced anisotropy in the velocity field in buoyancy-driven turbulence. J. Fluid Mech., 2011, 684: 192-203
    188 Xia K Q. How heat transfer efficiencies in turbulent thermal convection depend on internal flow modes. J. Fluid Mech., 2011, 676: 1-4
    189 Ni R, Huang S D, Xia K Q. Lagrangian acceleration measurements in convective thermal turbulence. J. Fluid Mech., 2012, 692: 395-419
    190 Ni R, Huang S D, Xia K Q. Local energy dissipation rate balances local heat flux in the center of turbulent thermal convection. Phys. Rev. Lett., 2011, 107: 174503
    191 Stevens R J A M, Zhou Q, Grossmann S, et al. Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample. Phys. Rev E, 2012, 85:027301
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