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

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 `B, cannot be identified from the measured geometric properties. 3 Author to whom any correspondence should be addressed. New Journal of Physics 12 (2010) 083029 1367-2630/10/083029+28$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft