Temperature statistics in turbulent Rayleigh–Bénard convection with a Prandtl number of Pr = 12.3

Abstract

The transport of plumes in turbulent convective systems must be understood to study the mantle and various industrial applications. We measured the probability density function P(T) of the temperature at various radial and vertical positions in the bulk of a convection cell. The asymmetric-shaped distribution was decomposed into a turbulent background and plumes. The temperature of the turbulent background was fitted by a Gaussian function according to the peak of P(T). We proposed a simple quantity A ≡ (⟨T⟩ − Tbg) to describe the effective strength of the plume, where ⟨T⟩ is the time-averaged value of the local temperature. The hot plume diminishes as it rises in the cell. The plume strength varies logarithmically with the vertical position. For larger Ra, the plume along the centerline has a longer travel distance in terms of the thermal boundary layer. For a given Ra, the strength and travel distance of the plume increase as the measurements move closer to the sidewall. At the cell center, the temperature fluctuations can be decomposed into fluctuations due to the turbulent background σbg and fluctuations due to the plume. The value of σbg is so small that the relation between σbg and the vertical position can be fitted by a logarithmic function or a power law. The Ra dependence on these two fluctuations was also investigated. The measurements were collected in a cylindrical cell with a unity aspect ratio of 1, and FC72 was used as the working fluid.