Temperature Fluctuation Profiles in Turbulent Thermal Convection: A Logarithmic Dependence versus a Power-Law Dependence

We report an experimental measurement of the rms temperature (σₓ) profiles in two regions inside a large aspect ratio (Γ=4. 2) rectangular convection cell. It is found that, in the region where the boundary layer is sheared by a large-scale wind, σₓ has a power-law dependence on the vertical distance (z) from the plate, whereas in the region where plumes are abundant, σₓ has a logarithmic dependence on z. The power-law profile may be understood by balancing the inertia force and the viscous force in the equations of motion, and the logarithmic profile may be understood in terms of the balance between the buoyancy and the inertia forces. When normalized by a convective temperature scale, θ*, the profiles of σₓ collapse onto a single curve for different values of the Rayleigh number. This shows that the convective temperature first proposed by Deardorff is the suitable temperature scale outside the thermal boundary layer for both logarithmic and power-law profiles. Our finding suggests a strong connection between plumes and the logarithmic rms temperature profile. The present Letter reveals that multiple force balance mechanisms can coexist in the bulk of highly turbulent flows.