Numerical calculation of the stability of parallel flows

A numerical approach to solving the two-dimensional, incompressible Navier-Stokes equations is presented and is used to study the stability and evolution of disturbance in a boundary layer. Previous numerical approaches have used streamfunction-vorticity formulations that take advantage of the special properties of two-dimensional flow. The present method solves a finite-difference form of the momentum equations and may therefore be extended to three-dimensions more readily. Computations using this technique are compared with the result of linear stability theory for small amplitude disturbances and are found to give satisfactory agreement, while calculations at large amplitude support the conjecture that non-linear effects can be destabilizing. (Author)