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Statistics and Scaling in Turbulent Rayleigh-Benard Convection (Paperback, 2014 ed.)
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Statistics and Scaling in Turbulent Rayleigh-Benard Convection (Paperback, 2014 ed.)
Series: SpringerBriefs in Applied Sciences and Technology
Expected to ship within 10 - 15 working days
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This Brief addresses two issues of interest of turbulent
Rayleigh-Benard 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-Benard
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.
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