Non-modal secondary growth in a boundary layer modulated by primary crossflow vortices

The problem of linear non-modal secondary growth in a compressible three-dimensional boundary layer on a swept-wedge model is considered. Self-similar solutions and stationary primary crossflow modes with nonlinearly saturated amplitudes constitute the base flows that are respectively obtained by numerically solving Falkner–Skan–Cooke self-similar equations and nonlinear parabolized stability equations. A temporal bi-global optimal analysis is formulated on the basis of a two-dimensional stability theory and singular-value decomposition. The effects of primary crossflow vortices (PCVs) on energy gains and the localization areas of optimal perturbations are investigated. Results show initial rapid non-modal augmentation or transient peaks in the energy gains as well as the existence of the Orr mechanism distorted by the PCVs. Structural disparities amongst short-term transient perturbations and long-term asymptotic perturbations are also presented.