Influence of the computational domain on DNS of turbulent heat transfer up to Reτ=2000 for Pr=0.71

We present a new set of direct numerical simulation data of a passive thermal flow in a turbulent plane Poiseuille flow with constant Prandtl number Pr=0.71, and mixed boundary conditions. Simulations were performed at Reτ=500,1000, and 2000 for several computational domains in the range of lx=2πhto8πh and lz=πhto3πh. As a first key result we found that a length of lx=2πh and a width of lz=π is enough to accurately obtain the one-point statistics and the budgets of the thermal kinetic energy, its dissipation and the thermal fluxes. None of them collapse exactly in wall units. On the other hand, the value of the thermal Kármán constant grows very slightly with the Reynolds number with a value of κth=0.44 for Reτ=2000. The statistics of all simulations can be downloaded from the web page of our http://personales.upv.es/serhocal/group.