Small-Scale Properties of Turbulent Rayleigh-B´ enard Convection Detlef Lohse 1 and Ke-Qing Xia 2 1 Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Center for Fluid Dynamics, and Impact-Institute, University of Twente, 7500 AE Enschede, The Netherlands; email: d.lohse@utwente.nl 2 Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China; email: kxia@phy.cuhk.edu.hk Annu. Rev. Fluid Mech. 2010. 42:335–64 First published online as a Review in Advance on September 2, 2009 The Annual Review of Fluid Mechanics is online at fluid.annualreviews.org This article’s doi: 10.1146/annurev.fluid.010908.165152 Copyright c  2010 by Annual Reviews. All rights reserved 0066-4189/10/0115-0335$20.00 Key Words thermal convection, turbulence, structure functions, Bolgiano scaling Abstract The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-B ´ enard convection are reviewed, from an experimental, theoretical, and numerical point of view. In particular, we address the ques- tion of whether, and if so where in the flow, the so-called Bolgiano-Obukhov scaling exists, i.e., S θ (r ) ∼ r 2/5 for the second-order temperature structure function and S u (r ) ∼ r 6/5 for the second-order velocity structure function. Apart from the anisotropy and inhomogeneity of the flow, insufficiently high Rayleigh numbers, and intermittency corrections (which all hinder the iden- tification of such a potential regime), there are also reasons, as a matter of principle, why such a scaling regime may be limited to at most a decade, namely the lack of clear scale separation between the Bolgiano length scale L B and the height of the cell. 335 Annu. Rev. Fluid Mech. 2010.42:335-364. Downloaded from arjournals.annualreviews.org by Prof. Ke-Qing Xia on 12/28/09. For personal use only.