Skip to main content Accessibility help

Moisture transfer by turbulent natural convection

  • Lu Zhang (a1) (a2), Kai Leong Chong (a1) and Ke-Qing Xia (a1) (a2)


We present an experimental and numerical study of natural convection with moist air as convecting fluid. By simplifying the system as two-component convection, an experimental method is proposed for indirectly measuring the moisture transfer rates in buoyancy-driven flows. We verify the results using direct numerical simulations. It is found that the non-dimensionalized transfer rates for both sensible heat ( $Nu_{T}$ ) and water vapour ( $Nu_{e}$ ) are essentially determined by a generalized Grashof number $Gr$ (the ratio of combined buoyancy generated by the imposed temperature and vapour pressure gradients to viscous force), and are only weakly dependent on the buoyancy ratio $\unicode[STIX]{x1D6EC}$ (the ratio of buoyancy induced by temperature variation to that due to vapour pressure variation). Moreover, we show that the full set of control parameters $\{Gr,\unicode[STIX]{x1D6EC},Pr,Sc\}$ is more suitable than other choices for characterizing the two-component system under investigation. As a special case, the Schmidt number dependence for passive scalar transport rates in buoyancy-driven flows is also deduced.


Corresponding author

Email address for correspondence:


Hide All
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503537.
Andrews, D. G. 2000 An Introduction to Atmospheric Physics. Cambridge University Press.
Arya, S. P. 1999 Air Pollution Meteorology and Dispersion. Oxford University Press.
Bergman, T. L., Incropera, F. P., DeWitt, D. P. & Lavine, A. S. 2011 Fundamentals of Heat and Mass Transfer. Wiley.
Bodenschatz, E., Malinowski, S. P., Shaw, R. A. & Stratmann, F. 2010 Can we understand clouds without turbulence? Science 327 (5968), 970971.
Bretherton, C. S. 1987 A theory for nonprecipitating moist convection between two parallel plates. Part I. Thermodynamics and linear solutions. J. Atmos. Sci. 44 (14), 18091827.
Bretherton, C. S. 1988 A theory for nonprecipitating convection between two parallel plates. Part II. Nonlinear theory and cloud field organization. J. Atmos. Sci. 45 (17), 23912415.
Cane, M. A., Clement, A. C., Kaplan, A., Kushnir, Y., Pozdnyakov, D., Seager, R., Zebiak, S. E. & Murtugudde, R. 1997 Twentieth-century sea surface temperature trends. Science 275 (5302), 957960.
Chandrakar, K. K., Cantrell, W., Chang, K., Ciochetto, D., Niedermeier, D., Ovchinnikov, M., Shaw, R. A. & Yang, F. 2016 Aerosol indirect effect from turbulence-induced broadening of cloud-droplet size distributions. Proc. Natl Acad. Sci. USA 113 (50), 1424314248.
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.
Chong, K.-L., Ding, G.-Y. & Xia, K.-Q. 2018 Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence. J. Comput. Phys. 375, 10451058.
Durack, P. J., Wijffels, S. E. & Matear, R. J. 2012 Ocean salinities reveal strong global water cycle intensification during 1950 to 2000. Science 336, 455458.
Emanuel, K. A. 1994 Atmospheric Convection. Oxford University Press.
Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A. & Edson, J. B. 2003 Bulk parameterization of air-sea fluxes updates and verification for the COARE algorithm. J. Clim. 16 (4), 571591.
Fairall, C. W., Bradley, E. F., Rogers, D. P., Edson, J. B. & Young, G. S. 1996 Bulk parameterization of air-sea fluxes for tropical ocean global atmosphere coupled ocean atmosphere response experiment. J. Geophys. Res. 101 (c2), 37473764.
Gent, P. R. & Mcwilliams, J. C. 1990 Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 20 (1), 150155.
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86, 33163319.
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66, 016305.
Hernandez-Duenas, G., Majda, A. J., Smith, L. M. & Stechmann, S. N. 2013 Minimal models for precipitating turbulent convection. J. Fluid Mech. 717, 576611.
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299329.
Landau, L. D. & Lifshitz, E. M. 2013 Fluid Mechanics. Elsevier Science.
Levitus, S., Antonov, J. I., Boyer, T. P. & Stephens, C. 2000 Warming of the world ocean. Science 287, 22252229.
Liu, W. T. 1979 Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci. 36 (9), 17221735.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42 (1), 335364.
Maidment, D. R. 1993 Handbook of Hydrology. McGraw Hill Professional.
Mangarella, P. A., Chambers, A. J., Street, R. L. & Hsu, E. Y. 1973 Laboratory studies of evaporation and energy transfer through a wavy air water interface. J. Phys. Oceanogr. 3 (1), 93101.
Murray, F. W. 1967 On the computation of saturation vapor pressure. J. Appl. Meteorol. 6 (1), 203204.
Pauluis, O. & Schumacher, J. 2011 Self-aggregation of clouds in conditionally unstable moist convection. Proc. Natl Acad. Sci. USA 108 (31), 1262312628.
Prabhakaran, P., Weiss, S., Krekhov, A., Pumir, A. & Bodenschatz, E. 2017 Can hail and rain nucleate cloud droplets? Phys. Rev. Lett. 119 (12), 128701.
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.
Sanders, C. J. & Holman, J. P. 1972 Franz Grashof and the Grashof number. Intl J. Heat Mass Transfer. 15 (3), 562563.
Schmitt, R. W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26 (1), 255285.
Schumacher, J. & Pauluis, O. 2010 Buoyancy statistics in moist turbulent Rayleigh–Bénard convection. J. Fluid Mech. 648, 509519.
Shishkina, O., Stevens, R. J. A. M., Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12 (7), 075022.
Sini, J. F., Anquetin, S. & Mestayer, P. G. 1996 Pollutant dispersion and thermal effects in urban street canyons. Atmos. Environ. 30 (15), 26592677.
Stevens, R. J. A. M., Lohse, D. & Verzicco, R. 2014 Sidewall effects in Rayleigh–Bénard convection. J. Fluid Mech. 741, 127.
Stevens, R. J. A. M., van der Poel, E. P., Grossmann, S. & Lohse, D. 2013 The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295308.
Vallis, G. K., Parker, D. J. & Tobias, S. M. 2019 A simple system for moist convection: the Rainy–Bénard model. J. Fluid Mech. 862, 162199.
Wei, P., Chan, T.-S., Ni, R., Zhao, X.-Z. & Xia, K.-Q. 2014 Heat transport properties of plates with smooth and rough surfaces in turbulent thermal convection. J. Fluid Mech. 740, 2846.
Weidauer, T., Pauluis, O. & Schumacher, J. 2010 Cloud patterns and mixing properties in shallow moist Rayleigh–Bénard convection. New J. Phys. 12, 105002.
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3 (5), 052001.
Yang, Y.-T., Verzicco, R. & Lohse, D. 2018 Two-scalar turbulent Rayleigh–Bénard convection: numerical simulations and unifying theory. J. Fluid Mech. 848, 648659.
Zhong, J. Q., Funfschilling, D. & Ahlers, G. 2009 Enhanced heat transport by turbulent two-phase Rayleigh–Bénard convection. Phys. Rev. Lett. 102 (12), 124501.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed