Kinetic thermal structure in turbulent Rayleigh-B\'{e}nard convection

Plumes are believed to be the most important heat carrier in turbulent Rayleigh--B\'{e}nard convection (RBC). However, a physically sound and clear definition of plume is still absent. We report here the investigation of a definition of plume called kinetic thermal structure (KTS), based on the analysis of vertical velocity gradient ($\Lambda = \partial w/\partial z$), using direct numerical simulation (DNS) data of the three-dimensional RBC in a rectangular cell for $Pr=0.7$ and $Ra=1\times10^8\sim5\times10^9$. It is shown that the conditional average of temperature on $\Lambda$ exhibits such a behavior that when $\Lambda$ is larger than a threshold, the volume carries a constant temperature of fluid, hence defines an unambiguous thermal structure, KTS. The DNS show that the KTS behaves in a sheet-like shape near the conducting plate, and becomes slender and smaller with increasing $Ra$. The heat flux carried by KTS displays a scaling law, with an exponent larger than the global-$Nu$--$Ra$ scaling, indicating stronger heat transport than the turbulent background. An advantage of the KTS is its connection to the balance equation allowing, for the first time, a prediction of the $Ra$-dependence of its vertical velocity and the characteristic $\Lambda$ threshold, validated by DNS.