Far downstream analysis for the Blasius boundary-layer stability problem

Abstract

In this paper, we examine the large Reynolds number (Re) asymptotic structure of the wave number in the Orr-Sommerfeld region for the Blasius boundary layer on a semi-infinite flat plate given by Goldstein (1983, J. Fluid Mech., 127, 59-81). 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 wave number. © The author 2007. Published by Oxford University Press; all rights reserved.