Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms

The linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of height h and diameter d = 3 h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one in- vestigated experimentally by Fransson et al. 10. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.