Boundary-layer Flows Past an Hemispherical Roughness Element: DNS, Global Stability and Sensitivity Analysis

We investigate the full three-dimensional instability mechanism arising in the wake of an hemispherical roughness element immersed in a laminar Blasius boundary layer. The inherent three-dimensional flow pattern beyond the critical Reynolds number is characterized by coherent vortical structures called hairpin vortices. Direct numerical simulation is used to analyze the formation and the shedding of hairpin packets inside the shear layer. The first bifurcation characteristics are investigated by global stability tools. We show the spatial structure of the linear direct and adjoint global eigenmodes of the linearized Navier-Stokes operator and use structural sensitivity analysis to locate the region where the instability mechanism acts. Results show that the “wavemaker” driving the self-sustained instability is located in the region immediately past the roughness element, in the shear layer separating the outer flow from the wake region.