Görtler vortices in boundary layers with streamwise pressure gradient: Linear theory

Abstract

Linear theory is used to analyze the stability of two-dimensional boundary layer flows to stationary Görtler vortices. The basic flow profiles in the boundary layer are described by the Falkner–Skan similarity solutions. We approach the problem both with local linear theory (with the streamwise position held fixed) and with a streamwise marching technique (to represent the evolution of the inlet disturbance). Comparisons of solutions obtained by the two methods are presented: The results are consistent in showing that adverse pressure gradients are destabilizing, as in the case of Tollmien–Schlichting waves. This is at odds with recent findings by Otto and Denier and underscores the sensitivity of the results to initial conditions.