Direct numerical simulations of turbulent flows over permeable substrates

We conduct direct numerical simulations to fully resolve turbulent flows over and inside isotropic permeable substrates in a channel. The substrates are made up of periodically staggered solid cubes, and the immersed boundary method is employed to impose no-slip conditions on all solid surfaces. Simulation results of mean velocity profiles and turbulent statistics and spectra are presented under a variety of substrate properties, including depth, porosity, and inclusion size. The effects of surface transpiration and surface roughness on the overlying turbulence are analyzed and compared with simulations that include separately either effect.