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

We report a systematic study of the collective effect of thermal plumes on the probability density function (p.d.f.) P(delta T) of temperature fluctuations delta T(t) in turbulent Rayleigh-Benard convection. By decomposing delta T(t) into four basic fluctuation modes associated with single and multiple warm and cold plumes and a turbulent background, we derive an analytic form of P(delta T) based on the convolutions of the five independent modes. To test the derived form of P(delta T) in the multiple-plume regions, where the thermal plumes are heavily populated, we conduct time series measurements of temperature fluctuations 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 cell, all of the measured p.d.f.s P(delta T) for different Rayleigh numbers fall onto a single master curve, once delta T is normalized by its root-mean-square (r.m.s.) value sigma(T). It is found that the measured P(delta T/sigma(T)) at different locations along the symmetric horizontal and vertical axes of the convection cells can all be well described by the derived form of P(delta T/sigma(T)). The fitted values of the parameters associated with the number of plumes in multiple plume clusters and their relative strengths and degrees of intermittency are closely linked to the spatial distribution of thermal plumes and local dynamics of the large-scale circulation in a closed convection cell. Our work thus provides a unified theoretical approach for understanding scalar p.d.f.s 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.

Automated summary

This study systematically investigates the collective impact of thermal plumes on temperature fluctuations in turbulent Rayleigh-Benard convection. By analyzing temperature fluctuations in different convection cells, the study reveals that the probability density functions fall onto a single master curve when normalized. The fitted parameters associated with the number of plumes and their strengths provide insights into the spatial distribution of thermal plumes and local dynamics in closed convection cells.