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 10 7 to 10 10 . 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 δ θ ∼ Ra −0.30 approximately, but the local values vary a lot for different Pr , which become more uniform with Pr increasing.