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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on April 6, 2006
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbl003
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© The author 2006. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received December 12, 2003
Revised March 1, 2006

Article

NONLINEAR INSTABILITY OF HYPERSONIC FLOW OVER A CONE

Sharon O. Stephen 1 *

( 1 School of Mathematics, University of Birmingham, Birmingham B15 2TT
)

* To whom correspondence should be addressed.
Sharon O. Stephen, E-mail: s.o.stephen{at}bham.ac.uk


  Abstract

This study investigates the nonlinear stability of hypersonic viscous flow over a sharp slender cone. The attached shock and the effects of curvature are taken into account. Asymptotic methods are used for large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. A weakly nonlinear analysis is carried out allowing an equation for the amplitude of disturbances to be derived. The coefficients of the terms in the amplitude equation are evaluated for axisymmetric and non-axisymmetric disturbances. Thus, the effects of the shock and curvature on the nonlinear stability of the flow may be deduced.


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