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A direct numerical simulation of a turbulent channel flow, with regularly spaced two-dimensional roughness elements mounted at the wall and perpendicular to the flow direction, was performed at a very low Reynolds number of Re  940 based on the centerline velocity and the full channel height. Using the lattice Boltzmann numerical algorithm, all essential scales were resolved with about 19·106 grid points (1155 x 129 x 128 in the x1, x2 and x3 directions). The computed results confirm the existence of turbulence at such a low Reynolds number. Turbulence persisted over the entire computation time, which was sufficiently long to prove its self-maintenance. By examination of statistical features of the flow across the anisotropy-in variant map, it was found that these coincide with conclusions emerging from the analysis of transition and breakdown to turbulence in a laminar boundary layer exposed to small, statistically stationary, neutrally stable axisymmetric disturbances with the stream wise intensity component ( u'1) lower than the intensities in the normal ( u'1) and span wise directions u'1< u'2 = u'3. To further support the concept and the results of theoretical considerations of the laminar to turbulent transition process in wall-bounded flows using statistical techniques and to demonstrate its great potential for engineering, an additional simulation was performed of a plane channel flow with regularly spaced riblet elements mounted at the wall and aligned parallel with the flow direction. The supplementary simulation was done at a Reynolds number of Re = 6584 using about 250·106 grid points (4096 x 257 x 240). Analysis of the simulation results carried out across the flow region located in the mid plane between the riblet elements confirms the central result which lies in the root of the statistical dynamics of the velocity fluctuations in wall-bounded flows: when the velocity fluctuations close to the wall tend towards the one-component state, so that the stream wise intensity component is much larger than the intensities in the normal and span wise directions, u'1< u'2 = u'3, the turbulent dissipation rate vanishes at the wall, leading to a significant reduction of the wall shear stress. For the simulated flow case the local value of wall shear stress reduction was found to exceed the wall shear stress reduction SR  92% which corresponds to a fully developed laminar channel flow with smooth walls at the same Reynolds number.
PAPER REVISED: 2006-05-23
PAPER ACCEPTED: 2006-06-15
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