Journal
JOURNAL OF FLUID MECHANICS
Volume 874, Issue -, Pages 263-284Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2019.405
Keywords
Benard convection; turbulent convection; turbulent mixing
Categories
Funding
- Hong Kong Research Grants Council [16306418, 16302718]
- National Natural Science Foundation of China [11772111]
- Shenzhen Startup Funds [CB11409001]
- Shenzhen Overseas Talent Project [CB24405026]
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We report a systematic study of spatial variations of the probability density function (PDF) $P(\unicode[STIX]{x1D6FF}T)$ for temperature fluctuations $\unicode[STIX]{x1D6FF}T$ in turbulent Rayleigh-Benard convection along the central axis of two different convection cells. One of the convection cells is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. By changing the distance $z$ away from the bottom conducting plate, we find the functional form of the measured $P(\unicode[STIX]{x1D6FF}T)$ in both cells evolves continuously with distinct changes in four different flow regions, namely, the thermal boundary layer, mixing zone, turbulent bulk region and cell centre. By assuming temperature fluctuations in different flow regions are all made from two independent sources, namely, a homogeneous (turbulent) background which obeys Gaussian statistics and non-uniform thermal plumes with an exponential distribution, we obtain the analytic expressions of $P(\unicode[STIX]{x1D6FF}T)$ in four different flow regions, which are found to be in good agreement with the experimental results. Our work thus provides a unique theoretical framework with a common set of parameters to quantitatively describe the effect of turbulent background, thermal plumes and their spatio-temporal intermittency on the temperature PDF $P(\unicode[STIX]{x1D6FF}T)$ .
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