Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh-Bénard convection.

Abstract

We report results from high Prandtl number turbulent thermal convection experiments. The viscous boundary layer and the Reynolds number are measured in four different fluids over wide ranges of the Prandtl number Pr and the Rayleigh number Ra, all in a single convection cell of unity aspect ratio. We find that the normalized viscous layer thickness may be represented as delta(v)/L=0.65Pr(0.24)Ra(-0.16). The Reynolds number based on the oscillation frequency of the large-scale flow is found as Re(o)(Ra,Pr)=1.1Ra(0.43)Pr(-0.76) and that based on the rms velocity Re(rms)(Ra,Pr)=0.84Ra(0.40)Pr-0.86. Both the Ra and the Pr exponents of Re(V(m))(Ra,Pr) based on the maximum velocity of the circulating wind appear to vary across the range of Pr covered, changing from 0.5 to 0.68 and -0.88 to -0.95, respectively, as Pr is increased from 6 to 1027.