Fully developed turbulent channel flow with rough bottom wall and smooth top wall is investigated using direct numerical simulation. The roughness is composed of periodically arranged two-dimensional spanwise rods whose cross-section is square and separated in the streamwise direction by λ= 8k, where k is roughness height. The roughness height is 0.06h where h is the half channel width.
The Reynolds number based on the friction velocity and channel half width is $Re_τ =314$. Friction velocity is calculated by wall shear stress equal to the sum of the skin frictional drag and form drag. A fully-implicit decoupling method is employed to simulate the flow. This method is validated by testing a direct numerical simulation of turbulent channel flow with smooth wall. The roughness is treated by the immersed boundary method without the need of computation intensive body-fitted grids. Effects of roughness on the turbulent flow field have been studied. Compared to the smooth wall, the mean velocity profile shifted down in the log region by $ΔU^{+}=6.6$. The large deviation of turbulent intensities was observed in outer region. The present numerical results show that the roughness effects are not confined to the wall region.
