Computations of channel flow with rough walls comprising staggered arrays of cubes having various plan area densities are presented and discussed. The cube height h is<br/>12.5% of the channel half-depth and Reynolds numbers (u? h/?) are typically around 700 – well into the fully rough regime. A direct numerical simulation technique, using<br/>an immersed boundary method for the obstacles, was employed with typically 35 million cells. <br/><br/>It is shown that the surface drag is predominantly form drag, which is greatest at an area coverage around 15%. The height variation of the axial pressure force across the obstacles weakens significantly as the area coverage decreases, but is always largest near the top of the obstacles. <br/><br/>Mean flow velocity and pressure data allow precise determination of the zero-plane displacement (defined as the height at which the axial surface drag force acts) and this leads to noticeably better fits to the log-law region than can be obtained by using the zero-plane displacement<br/>merely as a fitting parameter. <br/><br/>There are consequent implications for the value of<br/>von K´arm´ an’s constant. As the effective roughness of the surface increases, it is also shown that there are significant changes to the structure of the turbulence<br/>field around the bottom boundary of the inertial sublayer. <br/><br/>In distinct contrast to twodimensional roughness (longitudinal or transverse bars), increasing the area density of this three-dimensional roughness leads to a monotonic decrease in normalized vertical stress around the top of the roughness elements. <br/><br/>Normalized turbulence stresses in the outer part of the flows are nonetheless very similar to those in smooth-wall<br/>flows
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