Three-dimensional extraction and analysis of thermal plumes in turbulent Rayleigh-B\'enard convection

We report a new method for extracting the thermal plumes (TPs) in turbulent Rayleigh-B\'enard convection (RBC) which allows us to analyze the properties of the TPs and the background fluid. The investigation is based on direct numerical simulations of RBC in a cube ($8\times10^6 \le Ra \le 5\times10^9$) filled with fluid of Prandtl number $Pr = 4.38$. The basis of our extraction method is the idea that plumes convectively transport heat through the fluid, so that a heat flux threshold can be employed to extract the TPs. It is shown that this method yields reliable results over a wide range of $Ra$ and at any vertical wall distance $z$. Characteristic quantities of the flow are investigated on the boundaries of the TPs and the mean properties of the TPs and the background fluid are investigated as a function of the vertical coordinate. The $Ra$-scaling of a characteristic length scale of the TPs is examined and compared to taht of the thermal boundary layer thickness.