Logarithmically modified scaling of temperature structure functions in thermal convection

Abstract

Using experimental data on thermal convection, obtained at a Rayleigh number of 1.5 $\times 10^{11}$, it is shown that the temperature structure functions $<ΔT_{r}^p>$, where $ΔT_r$ is the absolute value of the temperature increment over a distance $r$, can be well represented in an intermediate range of scales by $r^{ζ_p} ϕ(r)^{p}$, where the $ζ_p$ are the scaling exponents appropriate to the passive scalar problem in hydrodynamic turbulence and the function $ϕ(r) = 1-a(\ln r/r_h)^2$. Measurements are made in the midplane of the apparatus near the sidewall, but outside the boundary layer.