Spatial stability of the compressible attachment-line boundary layer and generalized similarity properties

Abstract

We consider the linear stability of compressible attachment-line flow within the spatial framework. A fully two-dimensional approach is developed to compute the eigensolutions. The results show that compressibility has a stabilizing influence on the attachment-line boundary layer. The mode which satises the G¨ortler-H¨ammerlin assumption appears as the least stable mode. Furthermore, the results show that other two-dimensional modes which have approximately the same wave number and growth rate exist. These modes satisfy an extended similarity model and show algebraic growth in the chordwise coordinate for high Reynolds numbers. Thus, in the chordwise direction these two-dimensional modes are shown to grow faster than the mode satisfying the G¨ortler-H¨ammerlin assumption. Moreover, this algebraic growth in the chordwise direction increases for the more stable modes