Abstract
The statistical properties of the thermal dissipation rate in turbulent Rayleigh-Bénard convection in a cylindrical cell are studied by means of three-dimensional direct numerical simulations for a fixed Prandtl number Pr = 0.7 and aspect ratio Γ = 1. The Rayleigh numbers Ra are between 107 and 3 × 1010. We apply a criterion that decomposes the cell volume into two disjoint subsets: the plume-dominated part and the turbulent background part. The plume-dominated set extends over the whole cell volume and is not confined to the boundary layers. It forms a complex spatial skeleton on which the heat is transported in the convection cell and its volume fraction decreases with increasing Rayleigh number. The latter finding holds also when the threshold, which separates both subvolumes, is varied. The Rayleigh number dependence of the mean moments and probability density functions of the thermal dissipation are analyzed on the subvolumes and related to other possible divisions of the convection volume, such as into boundary layer and bulk. The largest thermal dissipation events are always found in the plume-dominated subset.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Chillà, J. Schumacher, Eur. Phys. J. E 35, 58 (2012).
S. Grossmann, D. Lohse, J. Fluid Mech. 407, 27 (2000).
S. Grossmann, D. Lohse, Phys. Fluids 16, 4462 (2004).
X. He, P. Tong, K.-Q. Xia, Phys. Rev. Lett. 98, 144501 (2007).
X. He, P. Tong, Phys. Rev. E 79, 026306 (2009).
A.N. Kolmogorov, J. Fluid Mech. 13, 82 (1962).
X. He, P. Tong, E.S.C. Ching, J. Turb. 11, 35 (2010).
X. He, E.S.C. Ching, P. Tong, Phys. Fluids 23, 025106 (2011).
O. Shishkina, C. Wagner, J. Fluid Mech. 546, 51 (2006).
O. Shishkina, C. Wagner, J. Fluid Mech. 599, 383 (2008).
M.S. Emran, J. Schumacher, J. Fluid Mech. 611, 13 (2008).
M. Kaczorowski, C. Wagner, J. Fluid Mech. 618, 89 (2009).
R. Verzicco, R. Camussi, J. Fluid Mech. 477, 19 (2003).
R. Verzicco, Eur. Phys. J. B 35, 133 (2003).
E.S.C. Ching, H. Guo, X.-D. Shang, P. Tong, K.-Q. Xia, Phys. Rev. Lett. 93, 124501 (2004).
Y. Gasteuil, W.L. Shew, M. Gibert, F. Chillà, B. Castaing, J.-F. Pinton, Phys. Rev. Lett. 99, 234302 (2007).
M.S. Emran, J. Schumacher, Phys. Rev. E 82, 016303 (2010).
X.-D. Shang, X.-L. Qiu, P. Tong, K.-Q. Xia, Phys. Rev. Lett. 90, 074501 (2003).
X.-D. Shang, P. Tong, K.-Q. Xia, Phys. Rev. Lett. 100, 244503 (2008).
R. Lakkaraju, R.J.A.M. Stevens, R. Verzicco, S. Grossmann, A. Prosperetti, C. Sun, D. Lohse to be published in Phys. Rev. E (2012).
R. Verzicco, P. Orlandi, J. Comput. Phys. 123, 402 (1996).
G. Grötzbach, J. Comput. Phys. 49, 241 (1983).
J. Bailon-Cuba, M.S. Emran, J. Schumacher, J. Fluid Mech. 655, 152 (2010).
R.J.A.M. Stevens, R. Verzicco, D. Lohse, J. Fluid Mech. 643, 495 (2010).
T. Watanabe, T. Gotoh, New J. Phys. 6, 40 (2004).
J. Schumacher, K.R. Sreenivasan, Phys. Fluids 17, 125107 (2005).
J. Schumacher, Phys. Rev. E 79, 056301 (2009).
J. Schumacher, Phys. Rev. Lett. 100, 134502 (2008).
J.J. Niemela, K.R. Sreenivasan, Phys. Rev. Lett. 100, 184502 (2008).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Emran, M.S., Schumacher, J. Conditional statistics of thermal dissipation rate in turbulent Rayleigh-Bénard convection. Eur. Phys. J. E 35, 108 (2012). https://doi.org/10.1140/epje/i2012-12108-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2012-12108-8