Far downstream analysis for the Blasius boundary-layer stability problem

In this paper we examine the large Reynolds number, Re, asymptotic structure of the wavenumber in the Orr-Sommerfeld region, for the Blasius boundary-layer on a semi-infinite flat plate given by Goldstein (1). We show that the inclusion of the term which contains the leading order non-parallel effects, at O(Re^{−1/2}), leads to a non-uniform expansion. By considering the far downstream form of each term in the asymptotic expansion, we derive a length scale at which the non-uniformity appears, and compare this position with the position seen in plots of the wavenumber.