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Two-scalar turbulent Rayleigh–Bénard convection: numerical simulations and unifying theory

  • Yantao Yang (a1) (a2), Roberto Verzicco (a2) (a3) and Detlef Lohse (a2) (a4)
Abstract

We conduct direct numerical simulations for turbulent Rayleigh–Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann–Lohse theory for traditional RB convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Phys. Rev. Lett., vol. 86 (15), 2001, pp. 3316–3319; Stevens et al., J. Fluid Mech., vol. 730, 2013, pp. 295–308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theory can successfully capture the overall trends for the fluxes of two scalars and the Reynolds number without introducing any new free parameters. In fact, for most of the parameter space explored here, the theory can even predict the absolute values of the fluxes and the Reynolds number with good accuracy. The current study extends the generality of the Grossmann–Lohse theory in the area of buoyancy-driven convection flows.

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Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email address for correspondence: yantao.yang@pku.edu.cn
References
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Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.
Bakhuis, D., Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R. & Lohse, D. 2018 Mixed insulating and conducting thermal boundary conditions in Rayleigh–Bénard convection. J. Fluid Mech. 835, 491511.
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86 (15), 33163319.
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66 (1), 016305.
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16 (12), 44624472.
Hage, E. & Tilgner, A. 2010 High Rayleigh number convection with double diffusive fingers. Phys. Fluids 22 (7), 076603.
Hieronymus, M. & Carpenter, J. R. 2016 Energy and variance budgets of a diffusive staircase with implications for heat flux scaling. J. Phys. Oceanogr. 46, 25532569.
Horn, S. & Shishkina, O. 2015 Toroidal and poloidal energy in rotating Rayleigh–Bénard convection. J. Fluid Mech. 762, 232255.
Jiang, H., Zhu, X., Mathai, V., Verzicco, R., Lohse, D. & Sun, C. 2018 Controlling heat transport flow structures in thermal turbulence using ratchet surfaces. Phys. Rev. Lett. 120, 044501.
Kellner, M. & Tilgner, A. 2014 Transition to finger convection in double-diffusive convection. Phys. Fluids 26 (9), 094103.
King, E. M., Stellmach, S., Noir, J., Hansen, U. & Aurnou, J. M. 2009 Boundary layer control of rotating convection systems. Nature 457, 301304.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.
Ostilla-Mónico, R., Yang, Y., van der Poel, E. P., Lohse, D. & Verzicco, R. 2015 A multiple resolutions strategy for direct numerical simulation of scalar turbulence. J. Comput. Phys. 301, 308321.
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.
Roche, P.-E., Castaing, B., Chabaud, B. & Hébral, B. 2001 Observation of the 1/2 power law in Rayleigh–Bénard convection. Phys. Rev. E 63, 045303R.
Salort, J., Liot, O., Rusaouen, E., Seychelles, F., Tisserand, J.-C., Creyssels, M., Castaing, B. & Chillà, F. 2014 Thermal boundary layer near roughnesses in turbulent Rayleigh–Bénard convection: flow structure and multistability. Phys. Fluids 26, 015112.
Shishkina, O. & Wagner, C. 2011 Modelling the influence of wall roughness on heat transfer in thermal convection. J. Fluid Mech. 686, 568582.
Shraiman, B. I. & Siggia, E. D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42 (6), 36503653.
Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495507.
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.
Turner, J. S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17 (1), 1144.
Wagner, S. & Shishkina, O. 2015 Heat flux enhancement by regular surface roughness in turbulent thermal convection. J. Fluid Mech. 763, 109135.
Wang, F., Huang, S.-D. & Xia, K.-Q. 2017 Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top. J. Fluid Mech. 817, R1.
Wei, P., Weiss, S. & Ahlers, G. 2015 Multiple transitions in rotating turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 114, 114506.
Xie, Y.-C. & Xia, K.-Q. 2017 Turbulent thermal convection over rough plates with varying roughness geometries. J. Fluid Mech. 825, 573599.
Yang, Y., van der Poel, E. P., Ostilla-Mónico, R., Sun, C., Verzicco, R., Grossmann, S. & Lohse, D. 2015 Salinity transfer in bounded double diffusive convection. J. Fluid Mech. 768, 476491.
Yang, Y., Verzicco, R. & Lohse, D. 2016 Scaling laws and flow structures of double diffusive convection in the finger regime. J. Fluid Mech. 802, 667689.
Zhu, X., Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2017 Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection. Phys. Rev. Lett. 119, 154501.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
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