POD analysis of the instability mode of a low-speed streak in a laminar boundary layer

Abstract

The instability of one single low-speed streak in a zero-pressure-gradient laminar boundary layer is investigated experimentally via both hydrogen bubble visualization and planar particle image velocimetry (PIV) measurement. A single low-speed streak is generated and destabilized by the wake of an interference wire positioned normal to the wall and in the upstream. The downstream development of the streak includes secondary instability and self-reproduction process, which leads to the generation of two additional streaks appearing on either side of the primary one. A proper orthogonal decomposition (POD) analysis of PIV measured velocity field is used to identify the components of the streak instability in the POD mode space: for a sinuous/varicose type of POD mode, its basis functions present anti-symmetric/symmetric distributions about the streak centerline in the streamwise component, and the symmetry condition reverses in the spanwise component. It is further shown that sinuous mode dominates the turbulent kinematic energy (TKE) through the whole streak evolution process, the TKE content first increases along the streamwise direction to a saturation value and then decays slowly. In contrast, varicose mode exhibits a sustained growth of the TKE content, suggesting an increasing competition of varicose instability against sinuous instability.