Effects of Prandtl number in two-dimensional turbulent convection*

Abstract

We report a numerical study of the Prandtl-number (Pr) effects in two-dimensional turbulent Rayleigh–Bénard convection. The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number (Ra) range from 107 to 1010. We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr, and the flow pattern becomes plume-dominated at high Pr. The evolution in flow pattern is quantified by the Reynolds number (Re), with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and –0.87 to –0.93, respectively. It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr, but their difference becomes marginal as Ra increases. For the thermal boundary layer, the spatially averaged thicknesses for all the Pr numbers can be described by δθ ∼ Ra −0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.