Collective effect of thermal plumes on temperature fluctuations in a closed Rayleigh-Bénard convection cell

We report a systematic study of the collective effect of thermal plumes on the probability density function (PDF) P(δT) of temperature fluctuations δT in turbulent Rayleigh-Bénard convection. By decomposing δT into five basic fluctuation modes associated with single and multiple plumes and a turbulent background, we derive an analytic form of P(δT) based on convolutions of the five modes. To test our theory, we conduct temperature measurements in two convection cells: one is a vertical thin disk and the other is an upright cylinder of aspect ratio unity. For a given normalized position in most regions of the convection cells, all the measured P(δT) for different Rayleigh number fall onto a single curve, once δT is normalized by its rms value σ_T. The P(δT) measured along the symmetric horizontal and vertical axes of the convection cells agrees excellently with our theoretical predictions. The fitting parameters are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a convection cell. Our work thus provides a unified theoretical approach for understanding scalar PDFs in a turbulent field, which is very useful not only for the present study but also for the study of many turbulent mixing problems of practical interest.