Physical implication of two problems in transition prediction of boundary layers based on linear stability theory

Up to now, the most widely used method for transition prediction is the one based on linear stability theory. When it is applied to three-dimensional boundary layers, one has to choose the direction, or path, along which the growth rate of the disturbance is to be integrated. The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable. However, unlike the saddle point method applied to water waves, here its physical meaning is not so obvious, as the frequency and wave number may be complex. And on some occasions, in advancing the integration of the growth rate of the disturbance, up to a certain location, one may not be able to continue the integration, because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number. In this paper, these two problems are discussed, and suggestions for how to do transition prediction under the latter condition are provided.