Transient growth of Görtler vortices in two-dimensional compressible boundary layers. Application to surface waviness

Abstract

This work is related to the numerical calculation of the maximum spatial growth of Görtler vortices using a set of linear partial differential equations derived to take curvature effects into account. The method is based on the calculation of the most amplified perturbation using a direct/adjoint iterative procedure. A new method for computing the optimal perturbation which attain largest growth at the shortest streamwise location is presented. The resulting neutral curve is shown to restore the concept of neutral curve for the Görtler problem, defining an envelope for the unstable domain. The present paper also highlights the potential for transient growth in the development of Görtler vortices. Compressible boundary layers over curved surfaces are considered in the framework of studying the effects of surface imperfections on laminar–turbulent transition. Non-negligible values of N-factor are shown to arise over the first streamwise locations due to interactions between non-normal modes. This result emphasizes the need to take transient growth into account when predicting transition location over wavy walls.