Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-17T12:43:29.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Realizing the ultimate scaling in convection turbulence by spatially decoupling the thermal and viscous boundary layers

Published online by Cambridge University Press:  25 May 2021

Shufan Zou Open the ORCID record for Shufan Zou [Opens in a new window]  and
Yantao Yang Open the ORCID record for Yantao Yang [Opens in a new window]
Shufan Zou
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing100871, PR China
Yantao Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
*
†Email address for correspondence: yantao.yang@pku.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulent convection plays a crucial role in many natural environments and engineering applications. One of the most fundamental questions is how the heat flux depends on the thermal driving and fluid property. It has been proposed that when the fluid layer experiences extremely strong thermal driving, the boundary layers will become fully turbulent and the so-called ultimate regime will emerge. In this work we proposed a numerical experiment in which the thermal boundary layer can be spatially decoupled with the viscous one. We demonstrate that, once the thermal boundary layer is fully decoupled from the viscous boundary layer and locates entirely inside the turbulent bulk, the scaling laws corresponding to the ultimate regime can be obtained, namely $Nu \sim Ra^{1/2}Pr^{1/2}$ and $Re \sim Ra^{1/2} Pr^{-1/2}$ with $Nu$ being the Nusselt number, $Re$ the Reynolds number, $Ra$ the Rayleigh number and $Pr$ the Prandtl number, respectively. Therefore, our results support the physical conjecture of the ultimate regime for the turbulent convection.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , R3
Check for updates
Copyright
© The Author(s), 2021. 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 (2), 503–537.CrossRefGoogle Scholar
Bouillaut, V., Lepot, S., Aumaître, S. & Gallet, B. 2019 Transition to the ultimate regime in a radiatively driven convection experiment. J. Fluid Mech. 861, R5.CrossRefGoogle Scholar
Calzavarini, E., Doering, C.R., Gibbon, J.D., Lohse, D., Tanabe, A. & Toschi, F. 2006 Exponentially growing solutions in homogeneous Rayleigh–Bénard convection. Phys. Rev. E 73 (3), 035301.CrossRefGoogle ScholarPubMed
Calzavarini, E., Lohse, D., Toschi, F. & Tripiccione, R. 2005 Rayleigh and Prandtl number scaling in the bulk of Rayleigh–Bénard turbulence. Phys. Fluids 17 (5), 055107.CrossRefGoogle Scholar
Chavanne, X., Chillà, F., Castaing, B., Hebral, B., Chabaud, B. & Chaussy, J. 1997 Observation of the ultimate regime in Rayleigh–Bénard convection. Phys. Rev. Lett. 79 (19), 3648–3651.CrossRefGoogle Scholar
Childs, H., et al. 2012 VisIt: an end-user tool for visualizing and analyzing very large data. In High Performance Visualization-Enabling Extreme-Scale Scientific Insight (eds E.W. Bethel, H. Childs & C. Hansen), pp. 357–372. Chapman & Hall, CRC Computational Science.Google Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 1–25.CrossRefGoogle ScholarPubMed
Fadlun, E.A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161 (1), 35–60.CrossRefGoogle Scholar
Gibert, J., Culver, D., Dole-Olivier, M., Malard, F., Christman, M.C. & Deharveng, L. 2009 Assessing and conserving groundwater biodiversity: synthesis and perspectives. Freshwat. Biol. 54 (4), 930–941.CrossRefGoogle Scholar
Gibert, M., Pabiou, H., Chillà, F. & Castaing, B. 2006 High-Rayleigh-number convection in a vertical channel. Phys. Rev. Lett. 96 (8), 084501.CrossRefGoogle Scholar
Glazier, J.A., Segawa, T., Naert, A. & Sano, M. 1999 Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers. Nature 398 (6725), 307–310.CrossRefGoogle Scholar
Goluskin, D. 2016 Internally Heated Convection and Rayleigh–Bénard Convection. Springer.CrossRefGoogle Scholar
Goluskin, D. & van der Poel, E.P. 2016 Penetrative internally heated convection in two and three dimensions. J. Fluid Mech. 791, R6.CrossRefGoogle Scholar
Goluskin, D. & Spiegel, E.A. 2012 Convection driven by internal heating. Phys. Lett. A 377 (1–2), 83–92.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86 (15), 3316–3319.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66 (1), 016305.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16 (12), 4462–4472.CrossRefGoogle Scholar
He, X., Funfschilling, D., Nobach, H., Bodenschatz, E. & Ahlers, G. 2012 Transition to the ultimate state of turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 108 (2), 024502.CrossRefGoogle ScholarPubMed
Iyer, K.P., Scheel, J.D., Schumacher, J. & Sreenivasan, K.R. 2020 Classical $1/3$ scaling of convection holds up to $Ra= 10^{15}$. Proc. Natl Acad. Sci. USA 117 (14), 7594–7598.CrossRefGoogle Scholar
Kraichnan, R.H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5 (11), 1374–1389.CrossRefGoogle Scholar
Lepot, S., Aumaître, S. & Gallet, B. 2018 Radiative heating achieves the ultimate regime of thermal convection. Proc. Natl Acad. Sci. USA 115 (36), 8937–8941.CrossRefGoogle ScholarPubMed
Lohse, D. & Toschi, F. 2003 Ultimate state of thermal convection. Phys. Rev. Lett. 90 (3), 034502.CrossRefGoogle ScholarPubMed
Malkus, W.V.R. 1954 The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225 (1161), 196–212.Google Scholar
Niemela, J.J., Skrbek, L., Sreenivasan, K.R. & Donnelly, R.J. 2000 Turbulent convection at very high Rayleigh numbers. Nature 404 (6780), 837–840.CrossRefGoogle ScholarPubMed
Ostilla-Mónico, R., Yang, Y., van der Poel, E.P., Lohse, D. & Verzicco, R. 2015 A multiple-resolution strategy for direct numerical simulation of scalar turbulence. J. Comput. Phys. 301, 308–321.CrossRefGoogle Scholar
Pawar, S.S. & Arakeri, J.H. 2016 Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube. Phys. Rev. Fluids 1, 042401(R).CrossRefGoogle Scholar
Plumley, M. & Julien, K. 2019 Scaling laws in Rayleigh–Bénard convection. Earth Space Sci. 6 (9), 1580–1592.CrossRefGoogle Scholar
Priestley, C.H. 1954 Convection from a large horizontal surface. Aust. J. Phys. 7, 176–201.CrossRefGoogle Scholar
Salort, J., Liot, O., Rusaouen, E., Seychelles, F., Tisserand, J.-C., Creyssels, M., Castaing, B. & Chillà, F. 2014 Thermal boundary layer near roughnesses in turbulent Rayleigh–Bénard convection: flow structure and multistability. Phys. Fluids 26 (1), 015112.CrossRefGoogle Scholar
Spiegel, E.A. 1971 Convection in stars I. Basic Boussinesq convection. Annu. Rev. Astro. Astrophys. 9 (1), 323–352.CrossRefGoogle Scholar
Stevens, R.J.A., Lohse, D. & Verzicco, R. 2011 Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection. J. Fluid Mech. 688, 31–43.CrossRefGoogle Scholar
Stevens, R., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507.CrossRefGoogle Scholar
Wang, B.-F., Zhou, Q. & Sun, C. 2020 Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement. Sci. Adv. 6 (21), eaaz8239.CrossRefGoogle ScholarPubMed
Wang, Q., Lohse, D. & Shishkina, O. 2021 Scaling in internally heated convection: a unifying theory. Geophys. Res. Lett. 48 (4), e2020GL091198.Google Scholar
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. 3 (5), 052001.CrossRefGoogle Scholar
Xie, Y.-C. & Xia, K.-Q. 2017 Turbulent thermal convection over rough plates with varying roughness geometries. J. Fluid Mech. 825, 573–599.CrossRefGoogle Scholar
Zhu, X., Mathai, V., Stevens, R., Verzicco, R. & Lohse, D. 2018 Transition to the ultimate regime in two-dimensional Rayleigh–Bénard convection. Phys. Rev. Lett. 120 (14), 144502.CrossRefGoogle ScholarPubMed
Zhu, X., Stevens, R., Shishkina, O., Verzicco, R. & Lohse, D. 2019 $Nu \sim Ra^{1/2}$ scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4.CrossRefGoogle Scholar
Zhu, X., Stevens, R., 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 (15), 154501.CrossRefGoogle Scholar