Physical and scale-by-scale ana...
Dorschner, B. Frapolli, N. Chikatamarla, S. S. and Karlin, I. V. 2016. Grid refinement for entropic lattice Boltzmann models. Physical Review E, Vol. 94, Issue. 5,
Togni, Riccardo Cimarelli, Andrea Lozano-Durán, Adrián and Angelis, Elisabetta De 2016. Space and time behaviour of the temperature second-order structure function in Rayleigh-Bénard convection. Journal of Physics: Conference Series, Vol. 708, Issue. , p. 012007.
Togni, Riccardo Cimarelli, Andrea and De Angelis, Elisabetta 2017. Progress in Turbulence VII. Vol. 196, Issue. , p. 141.
Dabbagh, F. Trias, F. X. Gorobets, A. and Oliva, A. 2017. A prioristudy of subgrid-scale features in turbulent Rayleigh-Bénard convection. Physics of Fluids, Vol. 29, Issue. 10, p. 105103.
Crivellini, Andrea Franciolini, Matteo and Nigro, Alessandra 2017. Progress in Turbulence VII. Vol. 196, Issue. , p. 153.
Franciolini, Matteo Crivellini, Andrea and Nigro, Alessandra 2017. On the efficiency of a matrix-free linearly implicit time integration strategy for high-order Discontinuous Galerkin solutions of incompressible turbulent flows. Computers & Fluids, Vol. 159, Issue. , p. 276.
Frapolli, N. Chikatamarla, S.S. and Karlin, I.V. 2018. Entropic lattice Boltzmann simulation of thermal convective turbulence. Computers & Fluids, Vol. 175, Issue. , p. 2.
Yasuda, T. and Vassilicos, J. C. 2018. Spatio-temporal intermittency of the turbulent energy cascade. Journal of Fluid Mechanics, Vol. 853, Issue. , p. 235.
Gatti, Davide Remigi, Alberto Chiarini, Alessandro Cimarelli, Andrea and Quadrio, Maurizio 2019. An efficient numerical method for the generalised Kolmogorov equation. Journal of Turbulence, Vol. 20, Issue. 8, p. 457.
Fregni, A. Angeli, D. Cimarelli, A. and Stalio, E. 2019. Direct Numerical Simulation of a buoyant triple jet at low-Prandtl number. International Journal of Heat and Mass Transfer, Vol. 143, Issue. , p. 118466.
Togni, Riccardo Cimarelli, Andrea and De Angelis, Elisabetta 2019. Resolved and subgrid dynamics of Rayleigh–Bénard convection. Journal of Fluid Mechanics, Vol. 867, Issue. , p. 906.
Thiesset, F. Duret, B. Ménard, T. Dumouchel, C. Reveillon, J. and Demoulin, F. X. 2020. Liquid transport in scale space. Journal of Fluid Mechanics, Vol. 886, Issue. ,
Valori, Valentina Innocenti, Alessio Dubrulle, Bérengère and Chibbaro, Sergio 2020. Weak formulation and scaling properties of energy fluxes in three-dimensional numerical turbulent Rayleigh–Bénard convection. Journal of Fluid Mechanics, Vol. 885, Issue. ,
10 November 2015 , pp. 380-404
Physical and scale-by-scale analysis of Rayleigh–Bénard convection
Riccardo Togni (a1), Andrea Cimarelli (a1) (a2) and Elisabetta De Angelis (a1) (a3)
1 DIN, Università di Bologna, Via Fontanelle 40, 47121 Forlì, Italy
2 DISMI, Università degli Studi di Modena e Reggio Emilia, Via Giovanni Amendola 2, 42122 Reggio Emilia, Italy
3 School of Engineering, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, UK
DOI: https://doi.org/10.1017/jfm.2015.547
A novel approach for the study of turbulent Rayleigh–Bénard convection (RBC) in the compound physical/scale space domain is presented. All data come from direct numerical simulations of turbulent RBC in a laterally unbounded domain confined between two horizontal walls, for Prandtl number $0.7$ and Rayleigh numbers $1.7\times 10^{5}$ , $1.0\times 10^{6}$ and $1.0\times 10^{7}$ . A preliminary analysis of the flow topology focuses on the events of impingement and emission of thermal plumes, which are identified here in terms of the horizontal divergence of the instantaneous velocity field. The flow dynamics is then described in more detail in terms of turbulent kinetic energy and temperature variance budgets. Three distinct regions where turbulent fluctuations are produced, transferred and finally dissipated are identified: a bulk region, a transitional layer and a boundary layer. A description of turbulent RBC dynamics in both physical and scale space is finally presented, completing the classic single-point balances. Detailed scale-by-scale budgets for the second-order velocity and temperature structure functions are shown for different geometrical locations. An unexpected behaviour is observed in both the viscous and thermal transitional layers consisting of a diffusive reverse transfer from small to large scales of velocity and temperature fluctuations. Through the analysis of the instantaneous field in terms of the horizontal divergence, it is found that the enlargement of thermal plumes following the impingement represents the triggering mechanism which entails the reverse transfer. The coupling of this reverse transfer with the spatial transport towards the wall is an interesting mechanism found at the basis of some peculiar aspects of the flow. As an example, it is found that, during the impingement, the presence of the wall is felt by the plumes through the pressure field mainly at large scales. These and other peculiar aspects shed light on the role of thermal plumes in the self-sustained cycle of turbulence in RBC, and may have strong repercussions on both theoretical and modelling approaches to convective turbulence.
© 2015 Cambridge University Press
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
†Email address for correspondence: DeAngelisE@cardiff.ac.uk
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.
Brown, E. & Ahlers, G. 2006 Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 568, 351–386.
Calzavarini, E., Toschi, F. & Tripiccione, R. 2002 Evidences of Bolgiano–Obhukhov scaling in three-dimensional Rayleigh–Bénard convection. Phys. Rev. E 66, 016304.
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35, 1–25.
Ching, E. S., Guo, H., Shang, X.-D., Tong, P. & Xia, K.-Q. 2004 Extraction of plumes in turbulent thermal convection. Phys. Rev. Lett. 93, 124501.
Ching, E. S., Tsang, Y.-K., Fok, T. N., He, X. & Tong, P. 2013 Scaling behavior in turbulent Rayleigh–Bénard convection revealed by conditional structure functions. Phys. Rev. E 87, 013005.
Cimarelli, A., De Angelis, E. & Casciola, C. M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436–451.
Deardorff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675–704.
Domaradzki, J. A., Liu, W., Härtel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6, 1583–1599.
Gauding, M., Wick, A., Pitsch, H. & Peters, N. 2014 Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers. J. Turbul. 15 (12), 857–882.
Gayen, B., Hughes, G. O. & Griffiths, R. W. 2013 Completing the mechanical energy pathways in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 111, 124301.
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16, 4462–4472.
Hill, R. J. 2002 Exact second-order structure–function relationships. J. Fluid Mech. 468, 317–326.
Kaczorowski, M. & Xia, K.-Q. 2013 Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell. J. Fluid Mech. 722, 596–617.
Kadanoff, L. P. 2001 Turbulent heat flow: structures and scaling. Phys. Today 54, 34–39.
Kolmogorov, A. N. 1941 Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.
Kunnen, R. P. J., Clercx, H. J. H., Geurts, B. J., Van Bokhoven, L. J. A., Akkermans, R. A. D. & Verzicco, R. 2008 Numerical and experimental investigation of structure–function scaling in turbulent Rayleigh–Bénard convection. Phys. Rev. E 77, 016302.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.
Lundbladh, A., Henningson, D. S. & Johansson, A. V.1992 An efficient spectral integration method for the solution of the Navier–Stokes equations. NASA STI/Recon Technical Report No. 93-29009.
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191–215.
Shang, X.-D., Qiu, X.-L., Tong, P. & Xia, K.-Q. 2003 Measured local heat transport in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 90, 074501.
Shang, X.-D., Qiu, X.-L., Tong, P. & Xia, K.-Q. 2004 Measurements of the local convective heat flux in turbulent Rayleigh–Bénard convection. Phys. Rev. E 70, 026308.
Shishkina, O. & Wagner, C. 2008 Analysis of sheet-like thermal plumes in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 599, 383–404.
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26 (1), 137–168.
Stevens, R. J., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507.
Van Reeuwijk, M., Jonker, H. J. J. & Hanjalić, K. 2005 Identification of the wind in Rayleigh–Bénard convection. Phys. Fluids 17 (5), 051704.
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.
Wörner, M. & Grötzbach, G. 1998 Pressure transport in direct numerical simulations of turbulent natural convection in horizontal fluid layers. Intl J. Heat Fluid Flow 19, 150–158.
Xi, H.-D., Zhou, Q. & Xia, K.-Q. 2006 Azimuthal motion of the mean wind in turbulent thermal convection. Phys. Rev. E 73 (5), 056312.
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3, 052001.
Yaglom, A. M. 1949 On the local structure of a temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR 69, 743–746.
Zhou, Q., Sun, C. & Xia, K.-Q. 2007 Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 074501.
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JFM classification
Convection: Bénard convection
Convection: Convection
Convection: Plumes/thermals