Equilibrium boundary layers over very rough surfaces

Commonly used wall shear stress correlations appropriate for rough walls imply a degree of equilibrium between the boundary layer and the wall. For two roughness geometries examined experimentally in zero pressure gradient, equilibrium in the mean velocity appears to exist beyond 350 times the roughness height from the origin of roughness. For moderately close spacing of simple three dimensional roughness elements, a correlation due to Dvorak appears accurate; for less dense spacing (but still fully rough conditions) the correlation underestimates the wall stress significantly. The equilibrium boundary layer studied experimentally showed unexpectedly large turbulent intensities, constant integral length scales, no region of constant stress and a semi-logarithmic region best described with a von Karman constant of 0.36 + or - .02.