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Rayleigh-Bénard convection. --- Rayleigh-Bénard, Convection de --- 532.517.4 --- Turbulent flow --- 532.517.4 Turbulent flow --- Rayleigh-Bénard convection. --- Rayleigh-Bénard, Convection de --- Rayleigh-Bénard convection --- Heat --- Bénard cells --- Convection --- Convection de Rayleigh-Bénard. --- Convection de Rayleigh-Bénard.

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This Brief addresses two issues of interest of turbulent Rayleigh-Bénard  convection. The first issue is the characterization and understanding of the statistics of the velocity and temperature fluctuations 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.

Rayleigh-Bénard convection. --- Bénard cells. --- Bénard convection --- Bénard convection cells --- Engineering. --- Fluids. --- Thermodynamics. --- Heat engineering. --- Heat transfer. --- Mass transfer. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Engineering Thermodynamics, Heat and Mass Transfer. --- Fluid- and Aerodynamics. --- Heat --- Rayleigh-Bénard convection --- Bénard cells --- Convection --- Hydraulic engineering. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat-engines --- Quantum theory --- Construction --- Industrial arts --- Technology --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Hydrostatics --- Permeability --- Mass transport (Physics) --- Thermodynamics --- Transport theory --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Mechanical engineering --- Hydromechanics --- Continuum mechanics --- Rayleigh-Benard convection. --- Benard cells.

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The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

Bénard cells. --- Heat --- Kinetic theory of gases. --- Marangoni effect. --- Nonlinear theories. --- Chaotic behavior in systems. --- Convection. --- Bénard, Henri, --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Nonlinear problems --- Nonlinearity (Mathematics) --- Convection, Marangoni --- Flow, Marangoni --- Marangoni convection --- Marangoni flow --- Gases, Kinetic theory of --- Convection of heat --- Bénard convection --- Bénard convection cells --- Bénard, H. --- Bénard, Henri Claude, --- Statistical Physics, Dynamical Systems and Complexity. --- Classical Continuum Physics. --- Bâenard cells --- Kinetic theory of gases --- Marangoni effect --- Convection --- Physics. --- Continuum physics. --- Statistical physics. --- Dynamical systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Classical field theory --- Continuum physics --- Continuum mechanics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical methods --- Differentiable dynamical systems --- Nonlinear theories --- System theory --- Calculus --- Mathematical analysis --- Mathematical physics --- Liquid-liquid interfaces --- Gases --- Molecular theory --- Statistical mechanics --- Rayleigh-Bénard convection --- Complex Systems. --- Classical and Continuum Physics. --- Statistical Physics and Dynamical Systems.