Temperature fluctuations in turbulent Rayleigh-B{\'e}nard convection

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-B{\'e}nard convection (RBC) is an example of such a NESS, in which the measured PDF $P(\delta T)$ of temperature fluctuations $\delta T$ in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate $\epsilon$. The conditional PDF $G(\delta T \vert \epsilon)$ of $\delta T$ under a constant $\epsilon$ is found to be of Gaussian form and its variance $\sigma^2_T$ for different values of $\epsilon$ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF $P(\delta T)$. This work thus provides a physical mechanism of the observed exponential distribution of $\delta T$ in RBC and also sheds new light on the origin of non-Gaussian fluctuations in other NESSs.