Free-stream receptivity of a hypersonic blunt cone using input–output analysis and a shock-kinematic boundary condition

David A Cook, Joseph W. Nichols

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Traditional stability tools have done much in the last few decades to demonstrate the significance of modal instabilities as a pathway for laminar to turbulent transition in hypersonic flows, but are less effective at predicting transition in flows with significant streamwise variation and strong shock waves. Because of this, most stability analyses over blunt cones tend to focus on the growth of instabilities in regions of the flow away from the blunt tip and downstream of any strong shock waves. We develop a new shock-kinematic boundary condition which is compatible with both the finite-volume method and input–output analysis. This boundary condition enables analysis of the receptivity of blunt cones to disturbances in the free stream by careful treatment of linear interactions of small disturbances with the shock. In particular, a Mach 5.8 flow over a 7 half-angle cone with a 0.15" nose radius is analyzed, showing significant amplification of disturbances along the cone frustum in a 5–15 kHz bandwidth due to the destabilization of a slow acoustic boundary layer mode, and significant amplification of entropy layer instabilities between 100 and 180 kHz due to rotation/deceleration of entropy/vorticity waves. These mechanisms are receptive to free-stream disturbances in very localized positions upstream of the bow shock.

Original languageEnglish (US)
Pages (from-to)155-180
Number of pages26
JournalTheoretical and Computational Fluid Dynamics
Issue number1
StatePublished - Feb 2022

Bibliographical note

Funding Information:
Support from ONR grant number N00014-19-1-2037 is gratefully acknowledged. The authors thank Prof. Graham Candler for helpful comments on an early version of this manuscript. We are also grateful to an anonymous reviewer for extensive, thoughtful comments that helped significantly improve this manuscript.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Input–output analysis
  • Non-modal growth
  • Receptivity
  • Shock-perturbation interaction


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