No CrossRef data available.
Article contents
Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement
Published online by Cambridge University Press: 23 February 2024
Abstract
Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number 
$Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The 
$Ra_c$ and the transition to fully developed turbulence Rayleigh number 
$Ra_f$ depend on the aspect ratio 
$\varGamma$ with 
$Ra_c\sim \varGamma ^{-4.05}$ and 
$Ra_f\sim \varGamma ^{-3.01}$, implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number 
$Ra/Ra_{c}$ (
$Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at 
$Ra\approx 200Ra_c$ in a 
$\varGamma =1$ cell, the same transition in a 
$\varGamma =1/20$ cell only requires 
$Ra\approx 3Ra_c$. Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with 
$\varGamma <1$, the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.
JFM classification
- Type
- JFM Rapids
- Information
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press
References
Ahlers, G., et al. 2022 Aspect ratio dependence of heat transfer in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 128, 084501.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
Bailon-Cuba, J., Emran, M.S. & Schumacher, J. 2010 Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection. J. Fluid Mech. 655, 152–173.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Chen, X.-Y., Xie, Y.-C., Yang, J.-C. & Ni, M.-J. 2023 Strong coupling of flow structure and heat transport in liquid metal thermal convection. J. Fluid Mech. 975, A21.CrossRefGoogle Scholar
Chillá, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 58.CrossRefGoogle ScholarPubMed
Chong, K.L., Ding, G. & Xia, K.-Q. 2018 Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence. J. Comput. Phys. 375, 1045–1058.CrossRefGoogle Scholar
Chong, K.L., Yang, Y., Huang, S.-D., Zhong, J.-Q., Stevens, R.J.A.M., Verzicco, R., Lohse, D. & Xia, K.-Q. 2017 Confined Rayleigh–Bénard, rotating Rayleigh–Bénard, and double diffusive convection: a unifying view on turbulent transport enhancement through coherent structure manipulation. Phys. Rev. Lett. 119, 064501.CrossRefGoogle ScholarPubMed
Funfschilling, D., Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger. J. Fluid Mech. 536, 145–154.CrossRefGoogle Scholar
Glatzmaier, G.A., Coe, R.S., Hongre, L. & Roberts, P.H. 1999 The role of the Earth's mantle in controlling the frequency of geomagnetic reversals. Nature 401, 885–890.CrossRefGoogle Scholar
He, X., Bodenschatz, E. & Ahlers, G. 2022 Universal scaling of temperature variance in Rayleigh–Bénard convection near the transition to the ultimate state. J. Fluid Mech. 931, A7.CrossRefGoogle Scholar
Hébert, F., Hufschmid, R., Scheel, J. & Ahlers, G. 2010 Onset of Rayleigh–Bénard convection in cylindrical containers. Phys. Rev. E 81, 046318.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
Kraichnan, R.H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 1374–1389.CrossRefGoogle Scholar
Lim, Z.L., Chong, K.L., Ding, G.-Y. & Xia, K.-Q. 2019 Quasistatic magnetoconvection: heat transport enhancement and boundary layer crossing. J. Fluid Mech. 870, 519–542.CrossRefGoogle Scholar
Lohse, D. & Shishkina, O. 2023 Ultimate turbulent thermal convection. Phys. Today 76, 26–32.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
Malkus, W.V.R. & Veronis, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.CrossRefGoogle Scholar
Müller, G., Neumann, G. & Weber, W. 1984 Natural convection in vertical Bridgman configurations. J. Cryst. Growth 70, 78–93.CrossRefGoogle Scholar
Pandey, A., Krasnov, D., Schumacher, J., Samtaney, R. & Sreenivasan, K.R. 2022 Similarities between characteristics of convective turbulence in confined and extended domains. Physica D 442, 133537.CrossRefGoogle Scholar
Ren, L., Tao, X., Zhang, L., Ni, M.-J., Xia, K.-Q. & Xie, Y.-C. 2022 Flow states and heat transport in liquid metal convection. J. Fluid Mech. 951, R1.CrossRefGoogle Scholar
Roche, P.-E., Gauthier, F., Kaiser, R. & Salort, J. 2010 On the triggering of the ultimate regime of convection. New J. Phys. 12, 085014.CrossRefGoogle Scholar
Schindler, F., Eckert, S., Zürner, T., Schumacher, J. & Vogt, T. 2022 Collapse of coherent large scale flow in strongly turbulent liquid metal convection. Phys. Rev. Lett. 128, 164501.CrossRefGoogle ScholarPubMed
Shishkina, O. 2021 Rayleigh–Bénard convection: the container shape matters. Phys. Rev. Fluids 6, 090502.CrossRefGoogle Scholar
Van Der Poel, E.P., Stevens, R.J.A.M. & Lohse, D. 2011 Connecting flow structures and heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. E 84, 045303.CrossRefGoogle ScholarPubMed
Verzicco, R. & Camussi, R. 1997 Transitional regimes of low-Prandtl thermal convection in a cylindrical cell. Phys. Fluids 9, 1287–1295.CrossRefGoogle Scholar
Wang, Q., Verzicco, R., Lohse, D. & Shishkina, O. 2020 Multiple states in turbulent large-aspect-ratio thermal convection: what determines the number of convection rolls? Phys. Rev. Lett. 125, 074501.CrossRefGoogle ScholarPubMed
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3, 052001.CrossRefGoogle Scholar
Xia, K.-Q., Huang, S.-D., Xie, Y.-C. & Zhang, L. 2023 Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence. Nat. Sci. Rev. 10, nwad012.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., Wei, P. & Xia, K.-Q. 2013 Dynamics of the large-scale circulation in high-Prandtl-number turbulent thermal convection. J. Fluid Mech. 717, 322–346.CrossRefGoogle Scholar
Zhang, L. & Xia, K.-Q. 2023 Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell. J. Fluid Mech. 973, R5.CrossRefGoogle Scholar
Zhong, J.-Q., Stevens, R.J.A.M., Clercx, H.J.H., Verzicco, R., Lohse, D. & Ahlers, G. 2009 Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh–Bénard convection. Phys. Rev. Lett. 102, 044502.CrossRefGoogle ScholarPubMed
Zürner, T., Schindler, F., Vogt, T., Eckert, S. & Schumacher, J. 2019 Combined measurement of velocity and temperature in liquid metal convection. J. Fluid Mech. 876, 1108–1128.CrossRefGoogle Scholar
Zwirner, L., Tilgner, A. & Shishkina, O. 2020 Elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 125, 054502.CrossRefGoogle ScholarPubMed
Ren et al. supplementary movie 1
Temporal evolution of the large-scale flow structure in a Γ = 1 cell shown in figure 4.
File
2 MB
Ren et al. supplementary movie 2
Temporal evolution of the large-scale flow structure in a Γ = 1/2 cell shown in figure 4.
File
6.4 MB
Ren et al. supplementary movie 3
Temporal evolution of the large-scale flow structure in a Γ = 1/3 cell shown in figure 4.
File
6.2 MB
Ren et al. supplementary movie 4
Temporal evolution of the large-scale flow structure in a Γ = 1/5 cell shown in figure 4.
File
5.3 MB
Ren et al. supplementary movie 5
Temporal evolution of the large-scale flow structure in a Γ = 1/10 cell shown in figure 4.
File
8.2 MB
Ren et al. supplementary movie 6
Temporal evolution of the large-scale flow structure in a Γ = 1/20 cell shown in figure 4.
File
6.8 MB