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Flow reversals in two-dimensional thermal convection in tilted cells

Published online by Cambridge University Press:  18 June 2018

Qi Wang Open the ORCID record for Qi Wang [Opens in a new window] ,
Shu-Ning Xia ,
Bo-Fu Wang ,
De-Jun Sun ,
Quan Zhou Open the ORCID record for Quan Zhou [Opens in a new window]  and
Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window]
Qi Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
Shu-Ning Xia
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Bo-Fu Wang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
De-Jun Sun
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
Quan Zhou
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Zhen-Hua Wan*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
*
†Email address for correspondence: [email protected]
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Abstract

The influence of tilt on flow reversals in two-dimensional thermal convection in rectangular cells with two typical aspect ratios, $\unicode[STIX]{x1D6E4}=\text{width/height}=1$ and 2, are investigated by means of direct numerical simulations. For $\unicode[STIX]{x1D6E4}=1$, tilt tends to suppress flow reversals. However, it is found that flow reversals characterized by two main rolls are promoted by tilt for $\unicode[STIX]{x1D6E4}=2$, which are even observed for some cases of small Prandtl numbers ($Pr$) and large tilt angles ($\unicode[STIX]{x1D6FD}$). Different from level cases where the four corner rolls all have opportunities to grow and trigger a flow reversal, the reversals in an anticlockwise tilted cell with $\unicode[STIX]{x1D6E4}=2$ are always led by the growth of the bottom-right or the top-left corner roll. Tilt is favourable for the growth of the bottom-right or the top-left corner roll and thus for breaking the balance between the two main rolls and triggering a flow reversal. The mode decomposition analysis shows that the appearance of the intermediate single-roll mode is crucial for reversals, and flow reversals in a tilted cell with $\unicode[STIX]{x1D6E4}=2$ can be viewed as a mode competition process between single-roll mode and horizontally adjacent double-roll mode. They can only occur in a limited range of $\unicode[STIX]{x1D6FD}$ where the two modes have comparable strength. Furthermore, the Nusselt numbers at the hot plate $Nu_{h}$ and at the cold plate $Nu_{c}$ behave differently during a flow reversal for $\unicode[STIX]{x1D6E4}=2$ due to the preference of single corner roll growth.

JFM classification

Convection: Convection Convection: Convection in cavities
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 355 - 372
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© 2018 Cambridge University Press 

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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, 503–537.Google Scholar
Araujo, F. F., Grossmann, S. & Lohse, D. 2005 Wind reversals in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084502.Google 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.Google 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.Google Scholar
Benzi, R. 2005 Flow reversal in a simple dynamical model of turbulence. Phys. Rev. Lett. 95, 024502.Google Scholar
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.Google Scholar
Brown, E. & Ahlers, G. 2007 Large-scale circulation model for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 134501.Google Scholar
Brown, E. & Ahlers, G. 2008 Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Fluids 20, 105105.Google Scholar
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95, 084503.Google Scholar
Castillo-Castellanos, A., Sergent, A. & Rossi, M. 2016 Reversal cycle in square Rayleigh–Bénard cells in turbulent regime. J. Fluid Mech. 808, 614–640.Google Scholar
Chandra, M. & Verma, M. K. 2011 Dynamics and symmetries of flow reversals in turbulent convection. Phys. Rev. E 83, 067303.Google Scholar
Chandra, M. & Verma, M. K. 2013 Flow reversals in turbulent convection via vortex reconnections. Phys. Rev. Lett. 110, 114503.Google Scholar
Chong, K.-L., Huang, S.-D., Kaczorowski, M. & Xia, K.-Q. 2015 Condensation of coherent structures in turbulent flows. Phys. Rev. Lett. 115, 264503.Google Scholar
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. Fluid 3 (1), 013501.Google Scholar
van Doorn, E., Dhruva, B., Sreenivasan, K. R. & Cassella, V. 2000 Statistics of wind direction and its increments. Phys. Fluids 12, 1529–1534.Google Scholar
Foroozani, N., Niemela, J. J., Armenio, V. & Sreenivasan, K. R. 2017 Reorientations of the large-scale flow in turbulent convection in a cube. Phys. Rev. E 95, 033107.Google 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.Google Scholar
Glatzmaier, G. A. & Roberts, P. H. 1995 A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203–209.Google Scholar
Gubbins, D., Sreenivasan, B., Mound, J. & Rost, S. 2011 Melting of the Earth’s inner core. Nature 473, 361–363.Google 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.Google Scholar
Guo, S.-X., Zhou, S.-Q., Qu, L., Lu, Y.-Z., Sun, L. & Shang, X.-D. 2017 Evolution and statistics of thermal plumes in tilted turbulent convection. Intl J. Heat Mass Transfer 111, 933–942.Google Scholar
Howard, R. & LaBonte, B.-J. 1980 The Sun is observed to be a torsional oscillator with a period of 11 years. Astrophys. J. 239, L33–L36.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.Google Scholar
Mannattil, M., Pandey, A., Verma, M. K. & Chakraborty, S. 2017 On the applicability of low-dimensional models for convective flow reversals at extreme Prandtl numbers. Eur. Phys. J. B 90, 259.Google Scholar
Mishra, P. K., De, A. K., Verma, M. K. & Eswaran, V. 2011 Dynamics of reorientations and reversals of large-scale flow in Rayleigh–Bénard convection. J. Fluid Mech. 668, 480–499.Google Scholar
Ni, R., Huang, S.-D. & Xia, K.-Q. 2015 Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection. J. Fluid Mech. 778, R5.Google Scholar
Petschel, K., Wilczek, M., Breuer, M., Friedrich, R. & Hansen, U. 2011 Statistical analysis of global wind dynamics in vigorous Rayleigh–Bénard convection. Phys. Rev. E 84, 026309.Google Scholar
Podvin, B. & Sergent, A. 2015 A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell. J. Fluid Mech. 766, 172–201.Google Scholar
Podvin, B. & Sergent, A. 2017 Precursor for wind reversal in a square Rayleigh–Bénard cell. Phys. Rev. E 95, 013112.Google Scholar
van der Poel, E. P., Ostilla-Mónico, R., Verzicco, R., Grossmann, S. & Lohse, D. 2015 Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 115, 154501.Google Scholar
van der Poel, E. P., Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2014 Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh–Bénard convection. Phys. Rev. E 90, 013017.Google 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.Google 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.Google Scholar
Scheel, J. D. & Schumacher, J. 2016 Global and local statistics in turbulent convection at low Prandtl numbers. J. Fluid Mech. 802, 147–173.Google Scholar
Schumacher, J., Götzfried, P. & Scheel, J. D. 2015 Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids. Proc. Natl Acad. Sci. USA 112, 9530–9535.Google Scholar
Shishkina, O. & Horn, S. 2016 Thermal convection in inclined cylindrical containers. J. Fluid Mech. 790, R3.Google Scholar
Shishkina, O. & Wagner, C. 2011 Modelling the influence of wall roughness on heat transfer in thermal convection. J. Fluid Mech. 686, 568–582.Google 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.Google 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.Google Scholar
Sun, C., Xi, H.-D. & Xia, K.-Q. 2005 Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5. Phys. Rev. Lett. 95, 074502.Google Scholar
Toppaladoddi, S., Succi, S. & Wettlaufer, J. S. 2017 Roughness as a route to the ultimate regime of thermal convection. Phys. Rev. Lett. 118, 074503.Google Scholar
Valet, J. P., Fournier, A., Courtillot, V. & Herrero-Bervera, E. 2012 Dynamical similarity of geomagnetic field reversals. Nature 490, 89–93.Google Scholar
Verma, M. K., Ambhire, S. C. & Pandey, A. 2015 Flow reversals in turbulent convection with free-slip walls. Phys. Fluids 27, 047102.Google Scholar
Verma, M. K., Kumar, A. & Pandey, A. 2017 Phenomenology of buoyancy-driven turbulence: recent results. New J. Phys. 19, 025012.Google Scholar
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25, 085110.Google Scholar
Wang, Q., Xu, B.-L., Xia, S.-N., Wan, Z.-H. & Sun, D.-J. 2017 Thermal convection in a tilted rectangular cell with aspect ratio 0.5. Chin. Phys. Lett. 34, 104401.Google Scholar
Weiss, S. & Ahlers, G. 2011 Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio 𝛤 = 0. 50 and Prandtl number Pr = 4. 38. J. Fluid Mech. 676, 5–40.Google 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.Google Scholar
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75, 066307.Google Scholar
Xi, H.-D. & Xia, K.-Q. 2008a 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.Google Scholar
Xi, H.-D. & Xia, K.-Q. 2008b Flow mode transitions in turbulent thermal convection. Phys. Fluids 20, 055104.Google Scholar
Xi, H.-D., Zhang, Y.-B., Hao, J.-T. & Xia, K.-Q. 2016 Higher-order flow modes in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 805, 31–51.Google Scholar
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73, 056312.Google Scholar
Xia, K.-Q. 2011 How heat transfer efficiencies in turbulent thermal convection depend on internal flow modes. J. Fluid Mech. 676, 1–4.Google Scholar
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3.Google Scholar
Xia, S.-N., Wan, Z.-H., Liu, S., Wang, Q. & Sun, D.-J. 2016 Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects. J. Fluid Mech. 798, 628–642.Google 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.Google Scholar
Xu, B.-L., Wang, Q., Wan, Z.-H., Yan, R. & Sun, D.-J. 2018 Heat transport enhancement and scaling law transition in two-dimensional Rayleigh–Bénard convection with rectangular-type roughness. Intl J. Heat Mass Transfer. 121, 872–883.Google Scholar
Zhang, Y., Huang, Y.-X., Jiang, N., Liu, Y.-L., Lu, Z.-M., Qiu, X. & Zhou, Q. 2017a Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh–Bénard convection. Phys. Rev. E 96, 023105.Google 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.Google Scholar
Zhang, Y., Zhou, Q. & Sun, C. 2017b Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 814, 165–184.Google Scholar
Zhou, Q., Stevens, R. J. A. M., Sugiyama, K., Grossmann, S., Lohse, D. & Xia, K.-Q. 2010 Prandtl–Blasius temperature and velocity boundary-layer profiles in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 664, 297–312.Google Scholar
Zhou, Q., Sugiyama, K., Stevens, R. J. A. M., Grossmann, S., Lohse, D. & Xia, K.-Q. 2011 Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh–Bénard convection. Phys. Fluids 23, 125104.Google Scholar
Zhu, X.-J., Mathai, V., Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2018 Transition to the ultimate regime in two-dimensional Rayleigh–Bénard convection. Phys. Rev. Lett. 120, 144502.Google Scholar
Zhu, X.-J., 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.Google Scholar