Scaling of the local convective heat flux in turbulent Rayleigh-B{\'e}nard convection

Local convective heat flux $J(r)$ in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in a cylindrical cell filled with water. The measured $J(r)$ at different locations in the convection cell is found to scale with the Rayleigh number Ra as $J( r) \sim Ra^{\beta}$. The scaling exponent $\beta$ at the cell center far away from the cell boundaries is found to be $\beta\simeq 0.5$, in agreement with the Kraichnan scaling for the ultimate state of thermal convection. Near the sidewall and lower conducting plate, we find $\beta\simeq 0.24$. The experiment thus provides new insights into the mechanism of heat transport in turbulent convection. \newline \newline *Work supported by the Research Grants Council of Hong Kong SAR.