DNS of Wave Packets in a Supersonic Boundary Layer: A Validation for a Popular Transition Prediction Method Based on Linear Stability Theory

For transition prediction of boundary layers using linear stability theory, one has to follow the evolution of individual Tollmien-Schlichting wave, or more specifically, to find the path of propagation and amplification factor of the wave, as well as to figure out the most critical one among all possible waves. However, its application in three-dimensional boundary layers is not straightforward. Among several different formulations of the method, the one proposed by Cebeci and Stewartson is mathematically most sensible, using least plausible argument. However, its physical implication is not so obvious, or even seems irrelevant to real problems. The aim of this study is to clarify these problems. It turned out to be that the evolution of the wave obtained by applying Cebeci-Stewartson's method is essentially the same as the evolution of the peak of a certain wave packet, and slow variation of the boundary layer, for example the non-parallelism of the boundary layer, does not cause problem, although in the original formulation of Cebeci and Stewartson, there was an implicit assumptison that the eigen-relation of the Tollmien-Schlichting waves should be kept unchanged during their evolutions.