Theory of instability and transition

The strongly nonlinear area of theory is discussed, as well as linear and weakly nonlinear (i.e., perturbation) theories, and it is noted that the weaknesses of the weakly nonlinear theory are essentially the inappropriate formulation in earlier works and the lack of guidance for the choice of the lowest-order basis. Attention is focused on the areas of theoretical/numerical development contributing to understanding the transition mechanism and new means for analyzing and predicting transition quantitatively. The nonlinear stability of nonparallel flows, linear secondary instability, and nonlinear wave interaction are analyzed. The incompressible flow over a flat plate with zero-pressure gradient is chosen as an example, while applications range to other shear flows including three-dimensional and compressible boundary layers.