Transition prediction and linear stability theory

Abstract

Linear stability theory is used in computing the amplitude ratio for other than two-dimensional instability waves. The wave motion is obtained from the ray equations of kinematic wave theory, and the amplitude ratio by simply integrating the spatial amplification rate of the parallel flow theory along a ray. Both the temporal and spatial theories are examined for two- and three-dimensional incompressible and two-dimensional compressible boundary layers. The dispersion relation is most directly obtained with the temporal theory, but the magnitude and direction of the group velocity have to be computed to give the spatial amplification rate, and then only approximately. The spatial theory gives the spatial amplification rate directly, but only after the direction of the group velocity is known. Transition prediction methods, divided into amplitude-density and amplitude methods, are discussed.