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Effects of Prandtl number in quasi-two-dimensional Rayleigh–Bénard convection

Published online by Cambridge University Press:  16 March 2021

Xiao-Ming Li ,
Ji-Dong He ,
Ye Tian ,
Peng Hao  and
Shi-Di Huang Open the ORCID record for Shi-Di Huang [Opens in a new window]
Xiao-Ming Li
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
Ji-Dong He
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Ye Tian
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
Peng Hao
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Shi-Di Huang*
Affiliation:
Center for Complex Flows and Soft Matter Research, and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
*
†Email address for correspondence: huangsd@sustech.edu.cn
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Abstract

We report an experimental study of the Prandtl-number effects in quasi-two-dimensional (quasi-2-D) Rayleigh–Bénard convection. The experiments were conducted in four rectangular convection cells over the Prandtl-number range of $11.7 \leqslant Pr \leqslant 650.7$ and over the Rayleigh-number range of $6.0\times 10^8 \leqslant Ra \leqslant 3.0\times 10^{10}$. Flow visualization reveals that, as $Pr$ increases from 11.7 to 145.7, thermal plumes pass through the central region much less frequently and their self-organized large-scale motion is more confined along the periphery of the convection cell. The large-scale flow is found to break down for higher $Pr$, resulting in a regime transition in the Reynolds number $Re$. For the $Pr$ range with a large-scale flow of system size, the $Re$ number, Nusselt number $Nu$ and local temperature fluctuations were investigated systematically. It is found that $Re$ scales as $Re \sim Ra^{0.58}Pr^{-0.82}$ in the present geometry, which suggests that it is in line with the behaviour in the 2-D configuration. On the other hand, the measured $Nu(Ra, Pr)$ relation $Nu \sim Ra^{0.289}Pr^{-0.02}$ tends to be compatible with the finding in a three-dimensional (3-D) system. For the temperature fluctuations in the cell centre and near the sidewall, they exhibit distinct $Ra$-dependent scalings that could not be accounted for with existing theories, but their $Pr$ dependences for $Pr \lesssim 50$ are in agreement with the predictions by Grossmann & Lohse (Phys. Fluids, vol. 16, 2004, pp. 4462–4472). These results enrich our understanding of quasi-2-D thermal convection, and its similarities and differences compared to 2-D and 3-D systems.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A60
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Ahlers, G., Brown, E., Fontenele Araujo, F., Funfschilling, D., Grossmann, S. & Lohse, D. 2006 Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection. J. Fluid Mech. 569, 409–445.CrossRefGoogle Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
Ahlers, G. & Xu, X. 2001 Prandtl-number dependence of heat transport in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 86, 3320.CrossRefGoogle ScholarPubMed
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, 491–511.CrossRefGoogle Scholar
Bao, Y., Chen, J., Liu, B.-F., She, Z.-S., Zhang, J. & Zhou, Q. 2015 Enhanced heat transport in partitioned thermal convection. J. Fluid Mech. 784, R5.CrossRefGoogle Scholar
Belkadi, M., Guislain, L., Sergent, A., Podvin, B., Chillà, F. & Salort, J. 2020 Experimental and numerical shadowgraph in turbulent Rayleigh–Bénard convection with a rough boundary: investigation of plumes. J. Fluid Mech. 895, A7.CrossRefGoogle Scholar
Breuer, M, Wessling, S, Schmalzl, J & Hansen, U 2004 Effect of inertia in Rayleigh–Bénard convection. Phys. Rev. E 69, 026302.CrossRefGoogle ScholarPubMed
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. 2007, P10005.CrossRefGoogle Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204, 1–30.CrossRefGoogle Scholar
Chavanne, X., Chillà, F., Chabaud, B., Castaing, B. & Hébral, B. 2001 Turbulent Rayleigh–Bénard convection in gaseous and liquid He. Phys. Fluids 13, 1300–1320.CrossRefGoogle Scholar
Chen, J., Bao, Y., Yin, Z.X. & She, Z.-S. 2017 Theoretical and numerical study of enhanced heat transfer in partitioned thermal convection. Intl J. Heat Mass Transfer 115, 556–569.CrossRefGoogle Scholar
Chen, X., Huang, S.-D., Xia, K.-Q. & Xi, H.-D. 2019 Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection. J. Fluid Mech. 877, R1.CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 58.CrossRefGoogle ScholarPubMed
Chong, K.L., Huang, S.-D., Kaczorowski, M. & Xia, K.-Q. 2015 Condensation of coherent structures in turbulent flows. Phys. Rev. Lett. 115, 264503.CrossRefGoogle ScholarPubMed
Chong, K.L., Wagner, S., Kaczorowski, M., Shishkina, O. & Xia, K.-Q. 2018 Effect of Prandtl number on heat transport enhancement in Rayleigh–Bénard convection under geometrical confinement. Phys. Rev. Fluids 3, 013501.CrossRefGoogle Scholar
Chong, K.L. & Xia, K.-Q. 2016 Exploring the severely confined regime in Rayleigh–Bénard convection. J. Fluid Mech. 805, R4.CrossRefGoogle Scholar
Daya, Z.A. & Ecke, R.E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87, 184501.CrossRefGoogle Scholar
Daya, Z.A. & Ecke, R.E. 2002 Prandtl-number dependence of interior temperature and velocity fluctuations in turbulent convection. Phys. Rev. E 66, 045301.CrossRefGoogle ScholarPubMed
Emran, M.S. & Shishkina, O. 2020 Natural convection in cylindrical containers with isothermal ring-shaped obstacles. J. Fluid Mech. 882, A3.CrossRefGoogle Scholar
Foroozani, N., Niemela, J.J., Armenio, V. & Sreenivasan, K.R. 2019 Turbulent convection and large scale circulation in a cube with rough horizontal surfaces. Phys. Rev. E 99, 033116.CrossRefGoogle Scholar
Globe, S. & Dropkin, D. 1959 Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. Trans. ASME: J. Heat Transfer 81, 24–28.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86, 3316.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66, 016305.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16, 4462–4472.CrossRefGoogle Scholar
Guo, S.-X., Zhou, S.-Q., Cen, X.-R., Qu, L., Lu, Y.-Z., Sun, L. & Shang, X.-D. 2015 The effect of cell tilting on turbulent thermal convection in a rectangular cell. J. Fluid Mech. 762, 273–287.CrossRefGoogle Scholar
He, G.-W. & Zhang, J.-B. 2006 Elliptic model for space-time correlations in turbulent shear flows. Phys. Rev. E 73, 055303.CrossRefGoogle ScholarPubMed
He, J.-C., Fang, M.-W., Gao, Z.-Y., Huang, S.-D. & Bao, Y. 2021 Effects of Prandtl number in two-dimentional turbulent convection. Chin. Phys. B (submitted).Google Scholar
He, X., He, G.-W. & Tong, P. 2010 Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis. Phys. Rev. E 81, 065303.CrossRefGoogle ScholarPubMed
Huang, S.-D., Kaczorowski, M., Ni, R. & Xia, K.-Q. 2013 Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett. 111, 104501.CrossRefGoogle ScholarPubMed
Huang, S.-D., Wang, F., Xi, H.-D. & Xia, K.-Q. 2015 Comparative experimental study of fixed temperature and fixed heat flux boundary conditions in turbulent thermal convection. Phys. Rev. Lett. 115, 154502.CrossRefGoogle ScholarPubMed
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639–654.CrossRefGoogle Scholar
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.CrossRefGoogle Scholar
Jiang, L., Sun, C. & Calzavarini, E. 2019 Robustness of heat transfer in confined inclined convection at high Prandtl number. Phys. Rev. E 99, 013108.CrossRefGoogle ScholarPubMed
Kerr, R.M. & Herring, J.R. 2000 Prandtl number dependence of Nusselt number in direct numerical simulations. J. Fluid Mech. 419, 325–344.CrossRefGoogle Scholar
Kraichnan, R.H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 1374–1389.CrossRefGoogle Scholar
Lakkaraju, R., Stevens, R.J.A.M., Verzicco, R., Grossmann, S., Prosperetti, A., Sun, C. & Lohse, D. 2012 Spatial distribution of heat flux and fluctuations in turbulent Rayleigh-Bénard convection. Phys. Rev. E 86, 056315.CrossRefGoogle ScholarPubMed
Lam, S., Shang, X.-D., Zhou, S.-Q. & Xia, K.-Q. 2002 Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh–Bénard convection. Phys. Rev. E 65, 066306.CrossRefGoogle ScholarPubMed
Liu, S., Jiang, L., Chong, K.L., Zhu, X., Wan, Z.-H., Verzicco, R., Stevens, R.J.A.M., Lohse, D. & Sun, C. 2020 From Rayleigh–Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure. J. Fluid Mech. 895, A18.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Musilová, V., Králik, T., La Mantia, M., Macek, M., Urban, P. & Skrbek, L. 2017 Reynolds number scaling in cryogenic turbulent Rayleigh–Bénard convection in a cylindrical aspect ratio one cell. J. Fluid Mech. 832, 721–744.CrossRefGoogle Scholar
Ni, R., Huang, S.-D. & Xia, K.-Q. 2011 a Local energy dissipation rate balances local heat flux in the center of turbulent thermal convection. Phys. Rev. Lett. 107, 174503.CrossRefGoogle Scholar
Ni, R., Zhou, S.-Q. & Xia, K.-Q. 2011 b An experimental investigation of turbulent thermal convection in water-based alumina nanofluid. Phys. Fluids 23, 022005.Google Scholar
Niemela, J.J. & Sreenivasan, K.R. 2003 Rayleigh-number evolution of large-scale coherent motion in turbulent convection. Europhys. Lett. 62, 829–833.CrossRefGoogle Scholar
Pandey, A., Verma, M.K., Chatterjee, A.G. & Dutta, B. 2016 Similarities between 2D and 3D convection for large Prandtl number. Pramana-J. Phys. 87, 13.CrossRefGoogle Scholar
van der Poel, E.P., Stevens, R.J.A.M. & Lohse, D. 2013 Comparison between two- and three-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 736, 177–194.CrossRefGoogle Scholar
van der Poel, E.P., Stevens, R.J.A.M., Sugiyama, K. & Lohse, D. 2012 Flow states in two-dimensional Rayleigh–Bénard convection as a function of aspect-ratio and Rayleigh number. Phys. Fluids 24, 085104.CrossRefGoogle Scholar
Ripesi, P., Biferale, L., Sbragaglia, M. & Wirth, A. 2014 Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes. J. Fluid Mech. 742, 636–663.CrossRefGoogle Scholar
Roche, P.-E., Castaing, B., Chabaud, B. & Hébral, B. 2002 Prandtl and Rayleigh numbers dependences in Rayleigh–Bénard convection. Europhys. Lett. 58, 693.CrossRefGoogle Scholar
Rusaouën, E., Liot, O., Castaing, B., Salort, J. & Chillà, F. 2018 Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries. J. Fluid Mech. 837, 443–460.CrossRefGoogle Scholar
Schmalzl, J., Breuer, M. & Hansen, U. 2004 On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 67, 390.CrossRefGoogle Scholar
Shang, X.-D., Tong, P. & Xia, K.-Q. 2008 Scaling of the local convective heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 100, 244503.CrossRefGoogle ScholarPubMed
Shishkina, O., Emran, M.S., Grossmann, S. & Lohse, D. 2017 Scaling relations in large-Prandtl-number natural thermal convection. Phys. Rev. Fluids 2, 103502.CrossRefGoogle Scholar
Shishkina, O. & Horn, S. 2016 Thermal convection in inclined cylindrical containers. J. Fluid Mech. 790, R3.CrossRefGoogle Scholar
Shraiman, B.I. & Siggia, E.D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42, 3650–3653.CrossRefGoogle ScholarPubMed
Silano, G., Sreenivasan, K.R. & Verzicco, R. 2010 Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between $10^{-1}$ and $10^4$ and Rayleigh numbers between $10^5$ and $10^9$. J. Fluid Mech. 662, 409–446.CrossRefGoogle Scholar
Stevens, R.J.A.M., Lohse, D. & Verzicco, R. 2011 Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection. J. Fluid Mech. 688, 31–43.CrossRefGoogle Scholar
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, 295–308.CrossRefGoogle Scholar
Sugiyama, K., Calzavarini, E., Grossmann, S. & Lohse, D. 2009 Flow organization in two-dimensional non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. J. Fluid Mech. 637, 105–135.CrossRefGoogle Scholar
Sugiyama, K., Ni, R., Stevens, R.J.A.M., Chan, T.S., Zhou, S.-Q., Xi, H.-D., Sun, C., Grossmann, S., Xia, K.-Q. & Lohse, D. 2010 Flow reversals in thermally driven turbulence. Phys. Rev. Lett. 105, 034503.CrossRefGoogle ScholarPubMed
Toppaladoddi, S., Succi, S. & Wettlaufer, J.S. 2017 Roughness as a route to the ultimate regime of thermal convection. Phys. Rev. Lett. 118, 074503.CrossRefGoogle ScholarPubMed
Verzicco, R. & Camussi, R. 1999 Prandtl number effects in convective turbulence. J. Fluid Mech. 383, 55–73.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25, 085110.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2015 Heat flux enhancement by regular surface roughness in turbulent thermal convection. J. Fluid Mech. 763, 109–135.CrossRefGoogle Scholar
Wang, B.-F., Zhou, Q. & Sun, C. 2020 a Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement. Sci. Adv. 6, eaaz8239.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Wang, F., Huang, S.-D., Zhou, S.-Q. & Xia, K.-Q. 2016 Laboratory simulation of the geothermal heating effects on ocean overturning circulation. J. Geophys. Res.: Oceans 121, 7589–7598.CrossRefGoogle Scholar
Wang, Q., Chong, K.L., Stevens, R.J.A.M., Verzicco, R. & Lohse, D. 2020 b From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates. J. Fluid Mech. 905, A21.CrossRefGoogle Scholar
Wang, Q., Xia, S.-N., Wang, B.-F., Sun, D.-J., Zhou, Q. & Wan, Z.-H. 2018 Flow reversals in two-dimensional thermal convection in tilted cells. J. Fluid Mech. 849, 355–372.CrossRefGoogle Scholar
Wei, P., Ni, R. & Xia, K.-Q. 2012 Enhanced and reduced heat transport in turbulent thermal convection with polymer additives. Phys. Rev. E 86, 016325.CrossRefGoogle ScholarPubMed
Wen, B., Goluskin, D., LeDuc, M., Chini, G.P. & Doering, C.R. 2020 Steady Rayleigh–Bénard convection between stress-free boundaries. J. Fluid Mech. 905, R4.CrossRefGoogle Scholar
Wu, X.-Z. & Libchaber, A. 1991 Non-Boussinesq effects in free thermal convection. Phys. Rev. A 43, 2833–2839.CrossRefGoogle ScholarPubMed
Wunsch, S. & Kerstein, A.R 2005 A stochastic model for high-Rayleigh-number convection. J. Fluid Mech. 528, 173–205.CrossRefGoogle Scholar
Xi, H.-D., Lam, S. & Xia, K.-Q. 2004 From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech. 503, 47–56.CrossRefGoogle Scholar
Xi, H.-D. & Xia, K.-Q. 2008 Azimuthal motion, reorientation, cessation, and reversal of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio one and one-half geometries. Phys. Rev. E 78, 036326.CrossRefGoogle ScholarPubMed
Xia, K.-Q., Lam, S. & Zhou, S.-Q. 2002 Heat-flux measurement in high-Prandtl-number turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 88, 064501.CrossRefGoogle ScholarPubMed
Xia, K.-Q., Sun, C. & Zhou, S.-Q. 2003 Particle image velocimetry measurement of the velocity field in turbulent thermal convection. Phys. Rev. E 68, 066303.CrossRefGoogle ScholarPubMed
Xie, Y.-C., Cheng, B.-Y.-C., Hu, Y.-B. & Xia, K.-Q. 2019 Universal fluctuations in the bulk of Rayleigh–Bénard turbulence. J. Fluid Mech. 878, R1.CrossRefGoogle Scholar
Xie, Y.-C. & Xia, K.-Q. 2017 Turbulent thermal convection over rough plates with varying roughness geometries. J. Fluid Mech. 825, 573–599.CrossRefGoogle Scholar
Yang, R., Chong, K.L., Wang, Q., Verzicco, R., Shishkina, O. & Lohse, D. 2020 a Periodically modulated thermal convection. Phys. Rev. Lett. 125, 154502.CrossRefGoogle ScholarPubMed
Yang, Y.-H., Zhu, X., Wang, B.-F., Liu, Y.-L. & Zhou, Q. 2020 b Experimental investigation of turbulent Rayleigh–Bénard convection of water in a cylindrical cell: the Prandtl number effects for $Pr >1$. Phys. Fluids 32, 015101.CrossRefGoogle Scholar
Zhang, J., Childress, S. & Libchaber, A. 1997 Non-Boussinesq effect: thermal convection with broken symmetry. Phys. Fluids 9, 1034–1042.CrossRefGoogle Scholar
Zhang, Y., Zhou, Q. & Sun, C. 2017 Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 814, 165–184.CrossRefGoogle Scholar
Zhang, Y.-Z., Sun, C., Bao, Y. & Zhou, Q. 2018 How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 836, R2.CrossRefGoogle Scholar
Zhou, Q., Liu, B.-F., Li, C.-M. & Zhong, B.-C. 2012 Aspect ratio dependence of heat transport by turbulent Rayleigh–Bénard convection in rectangular cells. J. Fluid Mech. 710, 260–276.CrossRefGoogle Scholar
Zhu, X., Stevens, R.J.A.M., Shishkina, O., Verzicco, R. & Lohse, D. 2019 $Nu \sim Ra^{1/2}$ scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4.CrossRefGoogle Scholar
Zwirner, L., Khalilov, R., Kolesnichenko, I., Mamykin, A., Mandrykin, S., Pavlinov, A., Shestakov, A., Teimurazov, A., Frick, P. & Shishkina, O. 2020 The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection. J. Fluid Mech. 884, A18.CrossRefGoogle Scholar

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