Narrow Results

The fundamental problem of turbulent transition in wall-bounded hydrodynamic flow is still not well understood. Previous studies of channel and pipe flows do not include the role of wall roughness and only consider linear treatment with fluctuations to unsuccessfully destabilize the flow. We investigate if small amplitude distributed wall roughness with and without fluctuations could initiate the transition to turbulence by direct numerical simulation using a lattice-Boltzmann method that is equivalent to solving the nonlinear Navier-Stokes equation. The results show how a single roughness feature with microscopic amplitude on an otherwise smooth wall can generate the transition to turbulence in plane Poiseuille flow. The effect of fluctuations with smooth walls or the combined effect of fluctuations and wall perturbances predicts the onset of turbulence at about the same critical Reynolds number which is about twice the experimental one.