  Direct numerical simulation is used to study turbulent flow over irregular
rough surfaces in the periodic minimal channel configuration. The generation of
irregular rough surface is based on a random algorithm, in which the power
spectrum of the roughness height function along with its probability density
function can be directly prescribed. The hydrodynamic properties of the
roughness are investigated and compared to those obtained from full-size DNS
for 12 roughness topographies with systematically varied PDF and PS at four
roughness height. The comparison confirms the viability of the minimal channel
approach for characterization of rough surfaces providing excellent agreement
in roughness function and zero-plane displacement across various types of
roughness and different regimes. Results also indicates that different
realizations of roughness, with a fixed PS and PDF, translate to similar values
of roughness function with a small scatter. In addition to the global flow
properties, the distribution of time-averaged surface force exerted by the
roughness onto the fluid is examined and compared to the roughness height
distribution for different cases. It is shown that the surface force
distribution has an anisotropic structure with spanwise-elongated coherent
regions. The anisotropy translates into a very small streamwise integral length
scale, which weakly depends on the considered roughness topography, while the
larger spanwise integral length scale shows a stronger dependence on roughness
characteristics. It is also shown that the sheltering model describes well the
spatial distribution of the surface force. Finally, existing roughness
correlations are assessed using the present dataset. It was shown that the most
correlations can reproduce the values of equivalent sand-grain roughness from
DNS within+-30% error while none of the correlations shows a superior
predictive accuracy.
