Skip to main content Accessibility help
×
Home

Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection

  • Xin Chen (a1), Shi-Di Huang (a2), Ke-Qing Xia (a2) (a3) and Heng-Dong Xi (a1)

Abstract

We present an experimental study of the reversal of the large-scale circulation (LSC) in quasi-two-dimensional turbulent Rayleigh–Bénard convection. It is found that there exists a transition in the Rayleigh number ( $Ra$ ) dependence of the reversal rate $f$ with two distinct scalings: for $Ra$ less than a transitional value $Ra_{t}$ , the non-dimensionalized reversal rate $ft_{E}\sim Ra^{-1.09}$ ; however, for higher $Ra$ the scaling changes to $ft_{E}\sim Ra^{-3.06}$ , where $t_{E}$ is the turnover time of the LSC. Flow visualization shows that this regime transition originates from a change in flow topology from a single-roll state to a new, less stable, abnormal single-roll state with substructures inside the single roll. The emergence of the substructures inside the LSC lowers the energy barrier for the flow reversals to occur and leads to a slower decay of $f$ with $Ra$ . Detailed analysis reveals that, although it is the corner rolls that trigger the reversal event, the probability for the occurrence of reversals mainly depends on the stability of the LSC. This is supported by a model we proposed to predict the critical condition for the transition, which agrees well with the experimental results.

Copyright

Corresponding author

Email address for correspondence: hengdongxi@nwpu.edu.cn

References

Hide All
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503537.10.1103/RevModPhys.81.503
Araujo, F. F., Grossmann, S. & Lohse, D. 2005 Wind reversals in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95 (8), 084502.10.1103/PhysRevLett.95.084502
Assaf, M., Angheluta, L. & Goldenfeld, N. 2011 Rare fluctuations and large-scale circulation cessations in turbulent convection. Phys. Rev. Lett. 107 (4), 044502.10.1103/PhysRevLett.107.044502
Benzi, R. 2005 Flow reversal in a simple dynamical model of turbulence. Phys. Rev. Lett. 95 (2), 024502.10.1103/PhysRevLett.95.024502
Bershadskii, A. 2004 Clusterization of the solar flares peaks. Physica A 331 (1-2), 297299.10.1016/j.physa.2003.07.004
Biggin, A. J., Steinberger, B., Aubert, J., Suttie, N., Holme, R., Torsvik, T. H., van der Meer, D. G. & van Hinsbergen, D. J. J. 2012 Possible links between long-term geomagnetic variations and whole-mantle convection processes. Nature Geosci. 5, 526533.10.1038/ngeo1521
Brown, E. & Ahlers, G. 2007 Large-scale circulation model for turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98 (13), 134501.10.1103/PhysRevLett.98.134501
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech.: Theory Exp. 2007 (10), P10005.10.1088/1742-5468/2007/10/P10005
Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Reorientation of the large-scale circulation in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 95 (8), 084503.10.1103/PhysRevLett.95.084503
Chandra, M. & Verma, M. K. 2011 Dynamics and symmetries of flow reversals in turbulent convection. Phys. Rev. E 83, 067303.
Chandra, M. & Verma, M. K. 2013 Flow reversals in turbulent convection via vortex reconnections. Phys. Rev. Lett. 110 (11), 114503.10.1103/PhysRevLett.110.114503
Chilla, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.10.1140/epje/i2012-12058-1
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 (1), 013501.10.1103/PhysRevFluids.3.013501
van Doorn, E., Dhruva, B., Sreenivasan, K. R. & Cassella, V. 2000 Statistics of wind direction and its increments. Phys. Fluids 12 (6), 15291534.10.1063/1.870401
Funfschilling, D. & Ahlers, G. 2004 Plume motion and large-scale circulation in a cylindrical Rayleigh–Bénard cell. Phys. Rev. Lett. 92 (19), 194502.10.1103/PhysRevLett.92.194502
Gallet, B., Herault, J., Laroche, C., Pétrélis, F. & Fauve, S. 2012 Reversals of a large-scale field generated over a turbulent background. Geophys. Astrophys. Fluid Dyn. 106, 468492.10.1080/03091929.2011.648629
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 (6756), 885890.10.1038/44776
Horstmann, G. M., Schiepel, D. & Wagner, C. 2018 Experimental study of the global flow-state transformation in a rectangular Rayleigh–Bénard sample. Intl J. Heat Mass Tranfer 126, 13331346.10.1016/j.ijheatmasstransfer.2018.05.097
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 (15), 154502.10.1103/PhysRevLett.115.154502
Huang, S.-D. & Xia, K.-Q. 2016 Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection. J. Fluid Mech. 794, 639654.10.1017/jfm.2016.181
Liu, B. & Zhang, J. 2008 Self-induced cyclic reorganization of free bodies through thermal convection. Phys. Rev. Lett. 100 (24), 244501.10.1103/PhysRevLett.100.244501
Lohse, D. & Toschi, F. 2003 Ultimate state of thermal convection. Phys. Rev. Lett. 90 (3), 034502.10.1103/PhysRevLett.90.034502
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42 (1), 335364.10.1146/annurev.fluid.010908.165152
Miesch, M. S. & Toomre, J. 2009 Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41 (1), 317345.10.1146/annurev.fluid.010908.165215
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, R5.10.1017/jfm.2015.433
Pétrélis, F., Fauve, S., Dormy, E. & Valet, J. P. 2009 Simple mechanism for reversals of Earth’s magnetic field. Phys. Rev. Lett. 102, 144503.10.1103/PhysRevLett.102.144503
Podvin, B. & Sergent, A. 2015 A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell. J. Fluid Mech. 766, 172201.10.1017/jfm.2015.15
Sreenivasan, K. R., Bershadskii, A. & Niemela, J. J. 2002 Mean wind and its reversal in thermal convection. Phys. Rev. E 65, 056306.
Sugiyama, K., Ni, R., Stevens, R. J., 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 (3), 034503.10.1103/PhysRevLett.105.034503
Vasilev, A. Y. & Frick, P. G. 2011 Reversals of large-scale circulation in turbulent convection in rectangular cavities. JETP Lett. 93 (6), 330334.10.1134/S0021364011060117
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25 (8), 085110.10.1063/1.4819141
Wang, Q., Xia, S.-N., Wang, B.-F., Sun, D.-J., Zhou, Q. & Wan, Z.-H. 2018a Flow reversals in two-dimensional thermal convection in tilted cells. J. Fluid Mech. 849, 355372.10.1017/jfm.2018.451
Wang, Y., Lai, P.-Y., Song, H. & Tong, P. 2018b Mechanism of large-scale flow reversals in turbulent thermal convection. Sci. Adv. 4 (11), eaat7480.10.1126/sciadv.aat7480
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, 4756.10.1017/S0022112004008079
Xi, H.-D. & Xia, K.-Q. 2007 Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E 75 (6 Pt 2), 066307.
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, 3151.10.1017/jfm.2016.572
Xi, H.-D., Zhou, S.-Q., Zhou, Q., Chan, T.-S. & Xia, K.-Q. 2009 Origin of the temperature oscillation in turbulent thermal convection. Phys. Rev. Lett. 102 (4), 044503.10.1103/PhysRevLett.102.044503
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3 (5), 052001.10.1063/2.1305201
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.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed