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Large aspect ratio Rayleigh–Bénard convection perturbed by a floating immersed body
Published online by Cambridge University Press: 05 November 2025
Abstract
Turbulent Rayleigh–Bénard convection in an extended layer of square cross-section with moderate aspect ratio 
$L/H=8.6$ (
$L$ is the length of the cell, 
$H$ is its height) is studied numerically for Rayleigh numbers in the range 
${\textit{Ra}}= 10^6{-}10^8$. We focus on the influence of different types of boundary conditions, including asymmetrical ones, on the characteristics of Rayleigh–Bénard convection with and without an immersed freely floating body. Convection without a floating body is characterised by the formation of stable thermal superstructures with preferred location. The crucial role of the symmetry of the boundary conditions is revealed. In the case of thermal boundary conditions of different types at the upper and lower boundaries, the flow pattern in Rayleigh–Bénard convection has a regular shape. The immersed body makes random wanderings and actively mixes the fluid, preventing the formation of superstructures. The mean flow structure with an immersed body is similar for all combinations of boundary conditions except for the case of a fixed heat flux at both boundaries. The floating disk does not change the tendency of turbulent convection to form a circulation of the maximal available scale under symmetric Neumann-type conditions. The type of boundary conditions has a weak influence on the Nusselt and Reynolds number values, significantly changing the ratio of the mean and fluctuating components of the heat flux. As the Rayleigh number increases, the motions of the body become more intensive and intermittent. The increase of 
$Ra$ also changes the structure of the mean flow without the body but the additional mixing provided by the floating body preserves the flow structure.
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References
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.10.1103/RevModPhys.81.503CrossRefGoogle Scholar
Akashi, M., Yanagisawa, T., Sakuraba, A., Schindler, F., Horn, S., Vogt, T. & Eckert, S. 2022 Jump rope vortex flow in liquid metal Rayleigh–Bénard convection in a cuboid container of aspect ratio. J. Fluid Mech. 932, A27.10.1017/jfm.2021.996CrossRefGoogle Scholar
Bulnes, F. 2022 Recent Advances in Wavelet Transforms and Their Applications. IntechOpen.10.5772/intechopen.97926CrossRefGoogle Scholar
Celik, I.B., Ghia, U., Roache, P.J. & Freitas, C.J. 2008 Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Engng 130 (7), 078001.Google Scholar
Chapman, C.J. & Proctor, M.R. 1980 Nonlinear Rayleigh–Bénard convection between poorly conducting boundaries. J. Fluid Mech. 101 (4), 759–782.10.1017/S0022112080001917CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E
35, 1–25.10.1140/epje/i2012-12058-1CrossRefGoogle ScholarPubMed
Elder, J. 1967 Convective self-propulsion of continents. Nature 214 (5089), 657–660.10.1038/214657a0CrossRefGoogle Scholar
Filimonov, S., Gavrilov, A., Frick, P., Sukhanovskii, A. & Vasiliev, A. 2025 2D and 3D numerical simulations of a convective flow with a free-floating immersed body. Heat Transfer Res. 56 (7), 13–26.10.1615/HeatTransRes.2024054471CrossRefGoogle Scholar
Filimonov, S.A., Gavrilov, A.A., Dekterev, A.A. & Litvintsev, K.Y. 2023 Mathematical modeling of the interaction of a thermal convective flow and a moving body. Comput. Contin. Mech. 16 (1), 89–100.10.7242/1999-6691/2023.16.1.7CrossRefGoogle Scholar
Frick, P., Filimonov, S., Gavrilov, A., Popova, E., Sukhanovskii, A. & Vasiliev, A. 2024 Rayleigh–Bénard convection with immersed floating body. J. Fluid Mech. 979, A23.10.1017/jfm.2023.1064CrossRefGoogle Scholar
Frick, P., Popova, E., Sukhanovskii, A. & Vasiliev, A. 2023 A random 2D walk of a submerged free-floating disc in a convective layer. Phys. D Nonlinear Phenom. 455, 133882.10.1016/j.physd.2023.133882CrossRefGoogle Scholar
Frick, P.G., Sokoloff, D.D. & Stepanov, R.A. 2022 Wavelets for the space-time structure analysis of physical fields. Phys. Uspekhi 65 (1), 62–89.10.3367/UFNe.2020.10.038859CrossRefGoogle Scholar
Gurnis, M. 1988 Large-scale mantle convection and the aggregation and dispersal of supercontinents. Nature 332 (6166), 695–699.10.1038/332695a0CrossRefGoogle Scholar
Hartlep, T., Tilgner, A. & Busse, F.H. 2003 Large scale structures in Rayleigh–Bénard convection at high Rayleigh numbers. Phys. Rev. Lett. 91 (6), 064501.10.1103/PhysRevLett.91.064501CrossRefGoogle ScholarPubMed
Hartlep, T., Tilgner, A. & Busse, F.H. 2005 Transition to turbulent convection in a fluid layer heated from below at moderate aspect ratio. J. Fluid Mech. 544, 309–322.10.1017/S0022112005006671CrossRefGoogle Scholar
Krug, D., Lohse, D. & Stevens, R.J.A.M. 2020 Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow. J. Fluid Mech. 887, A2.10.1017/jfm.2019.1054CrossRefGoogle Scholar
Mac Huang, J., Zhong, J.Q., Zhang, J. & Mertz, L. 2018 Stochastic dynamics of fluid–structure interaction in turbulent thermal convection. J. Fluid Mech. 854, R5.10.1017/jfm.2018.683CrossRefGoogle Scholar
Mao, Y. 2021 An insulating plate drifting over a thermally convecting fluid: the effect of plate size on plate motion, coupling modes and flow structure. J. Fluid Mech. 916, A18.10.1017/jfm.2021.192CrossRefGoogle Scholar
Mao, Y., Zhong, J.Q. & Zhang, J. 2019 The dynamics of an insulating plate over a thermally convecting fluid and its implication for continent movement over convective mantle. J. Fluid Mech. 868, 286–315.10.1017/jfm.2019.189CrossRefGoogle Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.10.1146/annurev.fluid.37.061903.175743CrossRefGoogle Scholar
Moller, S., Käufer, T., Pandey, A., Schumacher, J. & Cierpka, C. 2022 Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection. J. Fluid Mech. 945, A22.10.1017/jfm.2022.538CrossRefGoogle Scholar
Nordlund, M., Stanic, M., Kuczaj, A.K., Frederix, E.M.A. & Geurts, B.J. 2016 Improved PISO algorithms for modeling density varying flow in conjugate fluid–porous domains. J. Comput. Phys. 306, 199–215.10.1016/j.jcp.2015.11.035CrossRefGoogle Scholar
Pandey, A., Scheel, J.D. & Schumacher, J. 2018 Turbulent superstructures in Rayleigh–Bénard convection. Nat. Commun. 9 (1), 2118.10.1038/s41467-018-04478-0CrossRefGoogle ScholarPubMed
Parodi, A., von Hardenberg, J., Passoni, G., Provenzale, A. & Spiegel, E.A. 2004 Clustering of plumes in turbulent convection. Phys. Rev. Lett. 92 (19), 194503.10.1103/PhysRevLett.92.194503CrossRefGoogle ScholarPubMed
Pope, S.B. 2001 Turbulent flows. Meas. Sci. Technol. 12 (11), 2020–2021.10.1088/0957-0233/12/11/705CrossRefGoogle Scholar
Popova, E.N. & Frik, P.G. 2003 Large-scale flows in a turbulent convective layer with an immersed moving thermal insulator. Fluid Dyn. 38 (6), 862–867.10.1023/B:FLUI.0000015226.47864.b8CrossRefGoogle Scholar
Popova, E.N., Vasiliev, A.Yu, Sukhanovskii, A.N. & Frick, P.G. 2022 Dynamics of a convective system with a floating extended thermal insulator. Bulletin of Perm University. Physics 3, 38–47.10.17072/1994-3598-2022-3-38-47CrossRefGoogle Scholar
Schubert, G., Turcotte, D.L. & Olson, P. 2001 Mantle Convection in the Earth and Planets. Cambridge University Press.10.1017/CBO9780511612879CrossRefGoogle Scholar
Specklin, M. & Delauré, Y. 2018 A sharp immersed boundary method based on penalization and its application to moving boundaries and turbulent rotating flows. Eur. J. Mech. B/Fluids 70, 130–147.10.1016/j.euromechflu.2018.03.003CrossRefGoogle Scholar
Stevens, R.J., Blass, A., Zhu, X., Verzicco, R. & Lohse, D. 2018 Turbulent thermal superstructures in Rayleigh–Bénard convection. Phys. Rev. Fluids 3 (4), 041501.10.1103/PhysRevFluids.3.041501CrossRefGoogle Scholar
Stevens, R.J.A.M., Hartmann, R., Verzicco, R. & Lohse, D. 2024 How wide must Rayleigh–Bénard cells be to prevent finite aspect ratio effects in turbulent flow? J. Fluid Mech. 1000, A58.10.1017/jfm.2024.996CrossRefGoogle Scholar
Sukhanovskii, A., Vasiliev, A. & Popova, E. 2024 Experimental study of convective heat transfer with a multi-scale roughness. Phys. Fluids 36 (11), 115128.10.1063/5.0237073CrossRefGoogle Scholar
Teimurazov, A., Singh, S., Su, S., Eckert, S., Shishkina, O. & Vogt, T. 2023 Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit. J. Fluid Mech. 977, A16.10.1017/jfm.2023.936CrossRefGoogle Scholar
Vasiliev, A. & Sukhanovskii, A. 2021 Turbulent convection in a cube with mixed thermal boundary conditions: low Rayleigh number regime. Intl J. Heat Mass Transfer 174, 121290.10.1016/j.ijheatmasstransfer.2021.121290CrossRefGoogle Scholar
Vasiliev, A., Sukhanovskii, A. & Frick, P. 2022 Influence of horizontal heat-insulating plates on the structure of convective flows and heat transfer in a closed cavity. Comput. Contin. Mech. 15 (1), 83–97.10.7242/1999-6691/2022.15.1.7CrossRefGoogle Scholar
Verma, M.K. 2018 Physics of Buoyant Flows: From Instabilities to Turbulence. World Scientific.10.1142/10928CrossRefGoogle Scholar
Vieweg, P.P., Käufer, T., Cierpka, C. & Schumacher, J. 2025 Digital twin of a large-aspect-ratio Rayleigh–Bénard experiment: role of thermal boundary conditions, measurement errors and uncertainties. Flow 5, E4.10.1017/flo.2024.35CrossRefGoogle Scholar
Vieweg, P.P., Scheel, J.D. & Schumacher, J. 2021 Supergranule aggregation for constant heat flux-driven turbulent convection. Phys. Rev. Res. 3 (1), 013231.10.1103/PhysRevResearch.3.013231CrossRefGoogle Scholar
Vieweg, P.P., Scheel, J.D., Stepanov, R. & Schumacher, J. 2022 Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection. Phys. Rev. Res. 4 (4), 043098.10.1103/PhysRevResearch.4.043098CrossRefGoogle Scholar
von Hardenberg, J., Parodi, A., Passoni, G., Provenzale, A. & Spiegel, E.A. 2008 Large-Scale patterns in Rayleigh–Bénard convection. Phys. Lett. A 372 (13), 2223–2229.10.1016/j.physleta.2007.10.099CrossRefGoogle Scholar
Whitehead, J.A. & Behn, M.D. 2015 The continental drift convection cell. Geophys. Res. Lett. 42 (11), 4301–4308.10.1002/2015GL064480CrossRefGoogle Scholar
Xia, K.Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3 (5), 052001.10.1063/2.1305201CrossRefGoogle Scholar
Zhang, J. & Libchaber, A. 2000 Periodic boundary motion in thermal turbulence. Phys. Rev. Lett. 84 (19), 4361–4364.10.1103/PhysRevLett.84.4361CrossRefGoogle ScholarPubMed
Zhong, J.Q. & Zhang, J. 2005 Thermal convection with a freely moving top boundary. Phys. Fluids 17 (11), 115105.10.1063/1.2131924CrossRefGoogle Scholar
Zhong, J.Q. & Zhang, J. 2007 Dynamical states of a mobile heat blanket on a thermally convecting fluid. Phys. Rev. E
75 (5), 055301.10.1103/PhysRevE.75.055301CrossRefGoogle ScholarPubMed
Zhong, S. & Gurnis, M. 1993 Dynamic feedback between a continentlike raft and thermal convection. J. Geophys. Res.: Solid Earth 98 (B7), 12219–12232.10.1029/93JB00193CrossRefGoogle Scholar
Filimonov et al. supplementary movie 1
The movie shows the evolution of the temperature field in the mid-height cross section for the reference case without an immersed disk. The thermal boundary conditions are of the first type, with a fixed temperature at the upper and lower boundaries. The color range is limited and was chosen to better represent the flow pattern.
File
10 MB
Filimonov et al. supplementary movie 2
The movie shows the evolution of the temperature field in the mid-height cross section for the case with an immersed disk. The thermal boundary conditions are of the first type, with a fixed temperature at the upper and lower boundaries. The color range is limited and was chosen to better represent the flow pattern.
File
35.4 MB
Filimonov et al. supplementary movie 3
The movie shows the evolution of the temperature field in the mid-height cross section for the reference case without an immersed disk for the highest value o the Rayleigh number (10^8). The thermal boundary conditions are of the first type (bottom) and second type (top), with a fixed temperature at the upper and lower boundaries. The color range is limited and was chosen to better represent the flow pattern.
File
9.5 MB
Filimonov et al. supplementary movie 4
The movie shows the evolution of the temperature field in the mid-height cross section for the case with an immersed disk for the highest value o the Rayleigh number (10^8). The thermal boundary conditions are of the first type (bottom) and second type (top), with a fixed temperature at the upper and lower boundaries. The color range is limited and was chosen to better represent the flow pattern.
File
51.3 MB