The mixing evolution and geometric properties of a passive scalar field in turbulent Rayleigh–Bénard convection

Abstract

We report on measurements of a two-dimensional (2D) dye concentration field in turbulent Rayleigh–Bénard (RB) convection using the planar laser-induced fluorescence technique. The measurements were made in a vertical plane near the sidewall of a rectangular convection cell filled with water and with the Rayleigh number Ra varying from 109 to 1010, all at a fixed Prandtl number Pr=5.3 and Schmidt number Sc=2100. The mixing evolution and geometric properties of the measured passive scalar field are studied. It is shown that the mixing evolution of the passive scalar field in buoyancy-driven turbulence possesses certain features that are similar to those found in other types of turbulent flows, such as turbulent jets and grid-generated turbulence. These features include a power-law decrease in the mean concentration and exponential tails of single-point probability density function along the evolution path. Our results also show that the log-Poisson distribution is universal for the geometric measures of the passive scalar iso-contours, such as the perimeter, area, shape complexity and absolute value of local curvature; and the log-Poisson statistics may be used to model them. Regarding the influence of buoyancy on the turbulent scalar mixing, it is found that the buoyant scale, i.e. the Bolgiano scale ℓB, cannot be identified from the measured geometric properties.