Maximum spatial growth of Görtler vortices

This study is concerned with the numerical calculation of the maximum spatial growth of Gortler vortices on a concave wall. The method is based on the direct computation of a discrete approximation to the spatial propagator that relates the downstream response to the inlet perturbation. The optimization problem is then solved directly by making use of the propagator matrix. The calculated inlet optimal perturbations and the outlet optimal response are similar to those found by Andersson Andersson et al. [2] and Luchini [14] in the case of the boundary layer on a flat plate. The only noticeable difference is that the perturbation keeps growing downstream when the wall is curved, whereas the growth is only transient when the wall is flat. The study of a simple "toy" model problem demonstrates that the streamwise evolution of perturbations is essentially determined by the non-normality of the spatial propagator.