Experiments on critical Reynolds number and global instability in roughness-induced laminar–turbulent transition

Abstract

The effects of isolated, cylindrical roughness elements on laminar–turbulent transition in a flat-plate boundary layer are investigated in a laminar water channel. Our experiments aim at providing a comparison to global linear stability theory (LST) by means of hot-film anemometry and particle image velocimetry. Although the critical Reynolds number from theory does not match the transition Reynolds number observed in experiments, there are distinct experimental observations indicating a changeover from purely convective to absolute/global instability very close to the critical Reynolds number predicted by theory. Forcing with a vibrating wire reveals the evolution of the system dynamics from an amplifier to a wavemaker when the critical Reynolds number is exceeded. The mode symmetry is varicose for thick roughness elements and a changeover from varicose to sinuous modes is observed at the critical Reynolds number for thin roughness elements. Therefore, most predictions by global LST can be confirmed, but additional observations in the physical flow demonstrate that not all features can be captured adequately by global LST.