DNS of turbulent boundary layer over a flat plate at Re$_\theta=5200$

We performed direct numerical simulations (DNS) of a spatially developing turbulent boundary layer over a flat plate at Re$_\theta=5200$. At this Reynolds number, our DNS results show that the overlap region of inner and outer layers extends for about $150$ wall units. The turbulent inflow conditions were generated using the method of Ferrante \& Elghobashi [J.~Comput.~Phys.~198 (2004)]. The computational domain of the main simulation is a parallelepiped with $2048\times1024\times512$ grid points in the streamwise, spanwise and wall-normal direction, respectively. The closest grid point to the wall is at $z^+=0.4$. The turbulence statistics were collected over a period of about 80 large-eddy turnover times. These simulations were made possible thanks to our development of an optimized and scalable 3D Poisson solver, which reduced the time to integrate the incompressible Navier-Stokes equations by 40\%. Our DNS results are in excellent agreement with the experimental data of DeGraaff and Eaton [J.~Fluid Mech.~422 (2000)] at the same Re$_\theta$.