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 $<\Delta T_r^p>$, where $\Delta T_r$ is the absolute value of the temperature increment over a distance $r$, can be well represented in an intermediate range of scales by $r^{{\zeta }_p}\varphi (r{)}^p$, where the ${\zeta }_p$ are the scaling exponents appropriate to the passive scalar problem in hydrodynamic turbulence and the function $\varphi (r)=1-a(\ln r/r_h{)}^2$. Measurements are made in the midplane of the apparatus near the sidewall, but outside the boundary layer.