Viscous modes within the compressible boundary-layer flow due to a broad rotating cone

P. D. Towers, Z. Hussain, Paul Griffiths, Stephen Garrett

Research output: Contribution to journalArticlepeer-review


We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the 3D boundary layer over rotating cones with half-angle greater than 40∘ . The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui 1990 , A nonlinear investigation of the stability models of instability of the trhee-dimensional Compresible boundary layer due to a rotating disc Q. J. Mech. Appl. Math. , 43, pt. 4. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.
Original languageEnglish
Pages (from-to)940–960
Number of pages20
JournalIMA Journal of Applied Mathematics
Issue number5
Early online date29 Aug 2016
Publication statusPublished - 1 Oct 2016

Bibliographical note

© The author 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record is available online at:

Funding Information:
Engineering and Physical Sciences Research Council (grant EP/G061637/1 to S.J.G. and P.D.T.); Royal Academy of Engineering and the Leverhulme Trust (LSRF1415/11/29 to S.J.G and P.T.G.).


  • Rotating cone
  • Type II
  • Compressible boundary-layer flow


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