Optimal disturbances in suction boundary layers

A well-known optimization procedure is used to find the optimal disturbances in two different suction boundary layers within the spatial framework. The maximum algebraic growth in the asymptotic suction boundary layer is presented and compared to previous temporal results. Furthermore, the spatial approach allows a study of a developing boundary layer in which a region at the leading edge is left free from suction. This new flow, which emulates the base flow of a recent wind-tunnel experiment, is herein denoted a semi-suction boundary layer. It is found that the optimal disturbances for these two suction boundary layers consist of streamwise vortices that develop into streamwise streaks, as previously found for a number of shear flows. It is shown that the maximum energy growth in the semi-suction boundary layer is obtained over the upstream region where no suction is applied. The result indicates that the spanwise scale of the streaks is set in this region, which is in agreement with previous experimental findings.