Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T06:19:48.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Regime crossover in Rayleigh–Bénard convection with mixed boundary conditions

Published online by Cambridge University Press:  30 September 2020

Rodolfo Ostilla-Mónico Open the ORCID record for Rodolfo Ostilla-Mónico [Opens in a new window]  and
Amit Amritkar Open the ORCID record for Amit Amritkar [Opens in a new window]
Rodolfo Ostilla-Mónico*
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA
Amit Amritkar
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA HPE Data Science Institute, University of Houston, Houston, TX77204, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We numerically simulate three-dimensional Rayleigh–Bénard convection, the flow in a fluid layer heated from below and cooled from above, with inhomogeneous temperature boundary conditions, to explore two distinct regimes described in recent literature. We fix the non-dimensional temperature difference, i.e. the Rayleigh number, to $Ra=10^8$, and vary the Prandtl number between $1$ and $100$. By introducing stripes of adiabatic boundary conditions on the top plate, and making the surface of the top plate only $50\,\%$ conducting, we modify the heat transfer, the average temperature profiles and the underlying flow properties. We find two regimes: when the pattern wavelength is small, the flow is barely affected by the stripes. The heat transfer is reduced, but remains a large fraction of that of the unmodified case, and the underlying flow is only slightly modified. When the pattern wavelength is large, the heat transfer saturates to approximately two-thirds of the value of the unmodified problem, the temperature in the bulk increases substantially, and velocity fluctuations in the directions normal to the stripes are enhanced. The transition between the two regimes happens at pattern wavelength around the distance between the two plates, with different quantities transitioning at slightly different wavelength values. This transition is approximately Prandtl-number-independent, even if the statistics in the long-wavelength regime slightly vary.

JFM classification

Geophysical and Geological Flows: Mantle convection Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A39
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503.CrossRefGoogle Scholar
Bakhuis, D., Ostilla-Mónico, R., Van Der Poel, E. P., Verzicco, R. & Lohse, D. 2018 Mixed insulating and conducting thermal boundary conditions in Rayleigh–Bénard convection. J. Fluid Mech. 835, 491–511.CrossRefGoogle Scholar
Brown, E., Funfschilling, D., Nikolaenko, A. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection: effect of finite top- and bottom conductivity. Phys. Fluids 17, 075108.CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.CrossRefGoogle ScholarPubMed
Cooper, C. M., Moresi, L.-N. & Lenardic, A. 2013 Effects of continental configuration on mantle heat loss. Geophys. Res. Lett. 40 (11), 2647–2651.CrossRefGoogle Scholar
Kunnen, R. P. J., Ostilla-Mónico, R, van der Poel, E. P., Verzicco, R. & Lohse, D. 2016 Transition to geostrophic convection: the role of the boundary conditions. J. Fluid Mech. 799, 413–432.CrossRefGoogle Scholar
Lenardic, A & Moresi, L 2003 Thermal convection below a conducting lid of variable extent: heat flow scalings and two-dimensional, infinite Prandtl number numerical simulations. Phys. Fluids 15 (2), 455–466.CrossRefGoogle Scholar
Lenardic, A., Moresi, L.-N., Jellinek, A. M. & Manga, M. 2005 Continental insulation, mantle cooling, and the surface area of oceans and continents. Earth Planet. Sci. Lett. 234 (3–4), 317–333.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Ann. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Ostilla-Mónico, R. 2017 Mixed thermal conditions in convection: how do continents affect the mantle's circulation? J. Fluid Mech. 822, 1–4.CrossRefGoogle Scholar
Pekeris, C. L. 1935 Thermal convection in the interior of the earth. Geophys. J. Intl 3, 343–367.CrossRefGoogle Scholar
van der Poel, E. P., Ostilla-Monico, R., Donners, J. & Verzicco, R. 2015 A pencil distributed finite difference code for strongly turbulent wall-bounded flows. Comput. Fluids 116, 10–16.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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, 636–663.CrossRefGoogle Scholar
Rusaouën, E., Liot, O., Castaing, B., Salort, J. & Chillà, F. 2018 Thermal transfer in Rayleigh–Bénard cell with smooth or rough boundaries. J. Fluid Mech. 837, 443–460.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 1990 Heat transport in high-Rayleigh number convection. Phys. Rev. A 42, 3650–3653.CrossRefGoogle ScholarPubMed
Solomatov, V. S. & Moresi, L.-N. 2000 Scaling of time-dependent stagnant lid convection: application to small-scale convection on earth and other terrestrial planets. J. Geophys. Res. 105 (B9), 21795–21817.CrossRefGoogle Scholar
Stevens, R. J. A. M., Blass, A., Zhu, X., Verzicco, R. & Lohse, D. 2018 Turbulent thermal superstructures in Rayleigh–Bénard convection. Phys. Rev. Fluids 3 (4), 041501.CrossRefGoogle Scholar
Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507.CrossRefGoogle Scholar
Tisserand, J. C., Creyssels, M., Gasteuil, Y., Pabiou, H., Gibert, M., Castating, B. & Chilla, F. 2011 Comparison between rough and smooth plates within the same Rayleigh–Bénard cell. Phys. Fluids 23, 015105.CrossRefGoogle Scholar
Verzicco, R. 2004 Effect of non-perfect thermal sources in turbulent thermal convection. Phys. Fluids 16, 1965–1979.CrossRefGoogle Scholar
Wang, F., Huang, S.-D. & Xia, K.-Q. 2017 Thermal convection with mixed thermal boundary conditions: effects of insulating lids at the top. J. Fluid Mech. 817, R1.CrossRefGoogle Scholar
Xia, K.-Q. & Lui, S.-L. 1997 Turbulent thermal convection with an obstructed sidewall. Phys. Rev. Lett. 79, 5006–5009.CrossRefGoogle Scholar