Statistics and Scaling in Turbulent Rayleigh-Bénard Convection

This Brief addresses two issues of interest of turbulent Rayleigh-Bénard convection. The rst issue is the characterization and understanding of the statistics of the velocity and temperature uctuations in the system. The second issue is the revelation and understanding of the nature of the scaling behavior of the velocity temperature structure functions. The problem under the Oberbeck-Boussinesq approximation is formulated. The statistical tools, including probability density functions (PDF) and conditional statistics, for studying fluctuations are introduced, and implicit PDF formulae for fluctuations obeying certain statistical symmetries are derived. Applications of these PDF formulae to study the fluctuations in turbulent Rayleigh-Bénard convection are then discussed. The phenomenology of the different types of scaling behavior: the Bolgiano-Obhukov scaling behavior when buoyancy effects are significant and the Kolmogorov-Obukhov-Corrsin scaling behavior when they are not, is introduced. A crossover between the two types of scaling behavior is expected to occur at the Bolgiano length scale above which buoyancy is important. The experimental observations are reviewed. In the central region of the convective cell, the Kolmogorov-Obukhov-Corrsin scaling behavior has been observed. On the other hand, the Bolgiano-Obukhov scaling remains elusive only until recently. By studying the dependence of the conditional temperature structure functions on the locally averaged thermal dissipation rate, evidence for the Bolgiano-Obukhov scaling has recently been found near the bottom plate. The different behaviors observed in the two regions could be attributed to the different size of the Bolgiano scale. What physics determines the relative size of the Bolgiano scale remains to be understood. The Brief is concluded by a discussion of these outstanding issues.

Autorentext

Dr. Emily S.C. Ching is a theoretical physicist, and is currently a Professor in the Department of Physics at the Chinese University of Hong Kong. Her general research interests lie in non-equilibrium systems, and particularly on the longstanding problem of fluid turbulence. She received her Ph.D. in Physics from the University of Chicago. Later, she was a postdoctoral fellow at the Institute for Theoretical Physics at the University of California, Santa Barbara before returning to Hong Kong. She joined the Department of Physics at the Chinese University of Hong Kong in 1995. She was awarded the Achievement in Asia Award from the Overseas Chinese Physics Association in 1999 "for contributions to the understanding of the complex fluctuations in fluid turbulence". She was elected the Fellow of the UK Institute of Physics and the American Physical Society in 2004 and 2005 respectively. The citation for her American Physical Society Fellowship reads "For leadership in the analysis of turbulent and chaotic dynamics, and particularly for elucidating the structure of turbulent correlations in turbulent systems". She also serves in the Editorial board of various journals including the Journal of Turbulence.

Zusammenfassung

This Brief addresses two issues of interest of turbulent Rayleigh-Bénard convection. The rst issue is the characterization and understanding of the statistics of the velocity and temperature uctuations in the system. The second issue is the revelation and understanding of the nature of the scaling behavior of the velocity temperature structure functions. The problem under the Oberbeck-Boussinesq approximation is formulated. The statistical tools, including probability density functions (PDF) and conditional statistics, for studying fluctuations are introduced, and implicit PDF formulae for fluctuations obeying certain statistical symmetries are derived. Applications of these PDF formulae to study the fluctuations in turbulent Rayleigh-Bénard convection are then discussed. The phenomenology of the different types of scaling behavior: the Bolgiano-Obhukov scaling behavior when buoyancy effects are significant and the Kolmogorov-Obukhov-Corrsin scaling behavior when they are not, is introduced. A crossover between the two types of scaling behavior is expected to occur at the Bolgiano length scale above which buoyancy is important. The experimental observations are reviewed. In the central region of the convective cell, the Kolmogorov-Obukhov-Corrsin scaling behavior has been observed. On the other hand, the Bolgiano-Obukhov scaling remains elusive only until recently. By studying the dependence of the conditional temperature structure functions on the locally averaged thermal dissipation rate, evidence for the Bolgiano-Obukhov scaling has recently been found near the bottom plate. The different behaviors observed in the two regions could be attributed to the different size of the Bolgiano scale. What physics determines the relative size of the Bolgiano scale remains to be understood. The Brief is concluded by a discussion of these outstanding issues.

Inhalt

The Rayleigh-Bénard Convection System.- Statistical Analysis of Turbulent Fluctuations.- Phenomenology and Scaling Theories.- Observed Scaling Behavior.- Summary and Outlook.