Skip to main content Accessibility help

Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top

  • Fei Wang (a1), Shi-Di Huang (a1) and Ke-Qing Xia (a1)


The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times 10^{9}\leqslant Ra_{F}\leqslant 1.8\times 10^{11}$ and cylindrical cells in the range $1.4\times 10^{10}\leqslant Ra_{F}\leqslant 1.2\times 10^{12}$ with the Prandtl number $Pr$ fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading-order level, the magnitude of temperature fluctuations in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function in the bulk is essentially invariant with respect to both the insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_{F}$ , the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas an asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical velocity.


Corresponding author

Email address for correspondence:


Hide All
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.
Andreas, E. L. & Murphy, B. 1986 Bulk transfer coefficients for heat and momentum over leads and polynyas. J. Phys. Oceanogr. 16, 18751883.
Bott, M. H. P. 1964 Convection in the Earth’s mantle and the mechanism of continental drift. Nature 259, 583584.
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 125.
Cooper, C. M., Lenardic, A. & Moresi, L. 2004 The thermal structure of stable continental lithosphere within a dynamic mantle. Earth Planet. Sci. Lett. 222 (34), 807817.
Cooper, C. M., Moresi, L.-N. & Lenardic, A. 2013 Effects of continental configuration on mantle heat loss. Geophys. Res. Lett. 40 (11), 26472651.
Guillou, L., Mareschal, J. C., Jaupart, C., Garipy, C., Bienfait, G. & Lapointe, R. 1994 Heat flow, gravity and structure of the Abitibi Belt, Superior Province, Canada: implications for mantle heat flow. Earth Planet. Sci. Lett. 122 (1), 103123.
Gurnis, M. 1988 Large-scale mantle convection and the aggregation and dispersal of supercontinents. Nature 332 (6166), 695699.
King, S. D., Lowman, J. P. & Gable, C. W. 2002 Episodic tectonic plate reorganizations driven by mantle convection. Earth Planet. Sci. Lett. 203 (1), 8391.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42 (1), 335364.
Lowman, J. P. & Jarvis, G. T. 1993 Mantle convection flow reversals due to continental collisions. Geophys. Res. Lett. 20 (19), 20872090.
Lowman, J. P. & Jarvis, G. T. 1995 Mantle convection models of continental collision and breakup incorporating finite thickness plates. Phys. Earth Planet. Inter. 88 (1), 5368.
Maykut, G. A. 1982 Large-scale heat exchange and ice production in the central Arctic. J. Geophys. Res. 87 (C10), 79717984.
Maykut, G. A. 1986 The Surface Heat and Mass Balance, pp. 395463. Springer.
Pinet, C., Jaupart, C., Mareschal, J. C., Gariepy, C., Bienfait, G. & Lapointe, R. 1991 Heat flow and structure of the lithosphere in the eastern Canadian Shield. J. Geophys. Res. 96 (B12), 1994119963.
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, 636663.
Trubitsyn, V., Kaban, M. K. & Rothacher, M. 2008 Mechanical and thermal effects of floating continents on the global mantle convection. Phys. Earth Planet. Inter. 171 (14), 313322.
Wilson, J. T. 1966 Did the Atlantic close and then re-open? Nature 211 (5050), 676681.
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3, 052001.
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.
Zhang, J. & Libchaber, A. 2000 Periodic boundary motion in thermal turbulence. Phys. Rev. Lett. 84, 43614364.
Zhong, J.-Q. & Zhang, J. 2005 Thermal convection with a freely moving top boundary. Phys. Fluids 17, 115105.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top

  • Fei Wang (a1), Shi-Di Huang (a1) and Ke-Qing Xia (a1)


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