July 22, 2002Open Access
Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection
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Abstract
The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001) are presented and compared with various recent experimental findings. This dependence Re(Ra,Pr) is more complicated than a simple global power law. For Pr=5.5 and 10(8)<Ra<10(10) the effective or local power law exponent of Re as a function of Ra is definitely less than 0.50, namely, Re approximately Ra(0.45), in agreement with Qiu and Tong's experimental findings Phys. Rev. E 64, 036304 (2001). We also calculated the kinetic boundary layer width. Both in magnitude and in Ra scaling it is consistent with the data.