Optimal spatial disturbances along the swept attachment line

Optimal spatial perturbations are described in the context of swept Hiemenz flow. The two parameters are the Reynolds number $Re$ based on the flow stretching rate and spanwise sweep velocity, and the width $L$ of the chordwise energy weight that defines the region of interest around the attachment line. At Reynolds numbers $Re\sim 500$ typically found in commercial aircrafts optimal spatial disturbances take the shape of counter-rotating spanwise vortices. Energy is amplified by the so-called lift-up mechanism in the spanwise direction. Amplification is stronger at higher Reynolds numbers but is mostly unchanged as $L$ increases, although more counter-rotating spanwise vortices are observed. A physical interpretation is suggested that accounts for the shape of the perturbations and energy amplification scalings with $L$ and the Reynolds number $Re$.