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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on July 11, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(3):255-274; doi:10.1093/qjmam/hbm011
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Q. Jl Mech. Appl. Math, Vol. 60. No. 3 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Far downstream analysis for the Blasius boundary-layer stability problem

MR Turner{dagger}

( School of Mathematics, University of East Anglia, Norwich NR4 7TJ )

{dagger} Current address: School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter EX4 4QF, UK. < m.r.turner{at}exeter.ac.uk>

Received 20 February 2006. Revise 23 April 2007.
  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.


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