Stability of mean flows over an infinite flat plate

The present investigation is mainly concerned with a stability analysis for the linearized Navier-Stokes equations for parallel and nonparallel mean flows over an infinite flat plate. The system of equations for parallel flows is presented. The system is viewed as a generalized Orr-Sommerfeld equation. Attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues. The proof given in the investigation is applicable to both the generalized Orr-Somerfeld equations and the modified equations for nonparallel flow. The fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations.