Skip Navigation


The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 4, 2006
The Quarterly Journal of Mechanics and Applied Mathematics 2006 59(2):253-276; doi:10.1093/qjmam/hbl001
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
59/2/253    most recent
hbl001v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Walker, J. D. A.
Right arrow Articles by Ruban, A. I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Q. Jl Mech. Appl. Math, Vol. 59. No. 2 © The author 2006. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Instabilities of a flexible surface in supersonic flow

J. D. A. Walker{dagger} and A. Fletcher

( Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA )

A. I. Ruban

( Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL )

{dagger} Published posthumously.

The stability of a supersonic boundary layer above a flexible surface is considered in the limit of large Reynolds number and for Mach numbers O(1). Asymptotic theory of viscous–inviscid interaction has been used for this purpose. We found that for a simple elastic surface, for which deflections are proportional to local pressure differences, the boundary-layer flow remains stable as it is for a rigid wall. However, when either damping or surface inertia is included the flow becomes unstable. Moreover, in a certain range of wave numbers the boundary layer develops more then one unstable mode. It is interesting that these modes are connected to one another via saddle points in the complex-frequency plane. A more complex Kramer-type surface is also analysed and in some parameter ranges is found to permit the evolution of unstable Tollmien–Schlichting waves. The neutral curves are found for a variety of situations related to the parameters associated with the flexible surface.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.